![1. Introduction
Multi-agent systems (MAS) are a promising theoretical concept to approach practical challenges
related to the exibility, adaptivity, and distribution of computer systems. The agent metaphor
combines an object-oriented encapsulation of program state and control ow with ideas on the
mechanics of [...] decision making (Davis et al., 1989) rooted in articial intelligence, sociology,
and economics.
1 One common example of MAS are teams of real or simulated robots competing
in the robot soccer league Robo Cup
2 (see e.g. Nair et al., 2004).
Accordingly, agent-based abstractions are used in several subelds of computer science; e.g. soft-
ware engineering, distributed systems, and robotics. (Page and Kreutzer, 2005, pp. 339). Inde-
pendent from the application context, a major problem is posed by the need to analyze and
understand the behavior of agent-based systems, and in particular to assess their validity. This
term, which will be dened precisely later, means in short that a system fullls its intended
functions in an appropriate way.
An agent-based simulation model should, for instance, represent the microscopic agent-level as
well as the macroscopic system-level of the corresponding original system in detail to allow for
reliable conclusions about reality. The increasing application of agent technology in domains
with high safety or real-time requirements (e.g. manufacturing control) calls for particularly
powerful validation techniques. The call for appropriate methods and tools to support the
analysis and validation of agent-based systems has been uttered in early publications on agent-
based software engineering already (e.g. Gasser and Huhns, 1989) and apparently not been
answered suciently (see e.g. Guessoum et al., 2004, pp. 440). Therefore, the aim of this thesis
is to shed light on innovative techniques to validate agent-based models.
1.1. Motivation
For a number of reasons, the analysis and validation of MAS poses severe problems that are
inherent to the approach. The distributed system state and high sensitivity of ABS [agent-based
simulations] often results in an unmanageable and unpredictable global behaviour. (Knaak, 2007,
p. 29, see also Klügl, 2008, Sec. 2.2). Minor deviations in the system's initial conditions might
give rise to strong deviations in behavioral trajectories (Rand et al., 2003, p. 2)
3. Due to
the microscopic modelling perspective, global [system] properties are not inuenced directly (Knaak,
2007, pp. 29-30), but only by specifying the behavior of individual agents. Since relations be-
tween microscopic causes and macroscopic eects are generally hard to determine in distributed
1
A paragraph with similar content also forms the introduction to our pre-publication (Cabac et al., 2006c).
2
http://robocup.org, last visit 2012-11-17
3
page numbers relate to the version of the article downloadable at http://masi.cscs.lsa.umich.edu/
sluce/publications/sluce-abs.pdf (last visit 2012-10-06)
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![1. Introduction
systems, this situation often complicates tasks like calibration and optimization (Klügl, 2000,
p. 205).
Certain uses of the agent metaphor even prohibit an a-priori specication of the system's
behavior as in traditional software engineering: Innovative elds such as social simulation,
swarm intelligence (Kennedy, 2001) or the engineering of self-organizing systems (Potgieter,
2004) explicitly strive to investigate or benet from self-organizing or emergent eects observed
in certain MAS (David et al., 2002, p. 91). For the analysis and validation of MAS several
approaches reaching from formal to simulation-based techniques have been proposed.
Formal verication is based on representations using formalisms such as Petri nets or modal
logic. Due to their conciseness, formal methods are increasingly applied in agent-oriented
software-engineering. However, as noted in (Cabac et al., 2006b, Sec. 1) only simple and often
practically irrelevant classes of MAS (Edmonds and Bryson, 2004) can be analyzed with formal
methods alone.
The simulation-based approach relies on the empirical observation of operational MAS and
an a-posteriori analysis of the observed behavior. The empirical analysis of MAS and agent
behavior is an important means for validation, often outperforming the application of formal
methods (see e.g. Cohen, 1995 and Guessoum et al., 2004). According to Uhrmacher (2000,
p. 39) the development of software agents is [...] mainly an experimental process
4. However,
as cited in (Cabac et al., 2006b, Sec. 1) the observation of even simple multi-agent systems might
produce large and complex amounts of data (Sanchez and Lucas, 2002), the interpretation of which
requires complex, computer-supported analysis techniques.
The literature provides complementary approaches for analyzing and validating MAS based
on empirical observations: While conrmatory techniques such as statistical hypothesis tests
or model-based trace-analysis (e.g. Howard et al., 2003) allow for the falsication of a-priori
specications or hypotheses, exploratory techniques serve to investigate and better understand
previously unknown aspects of MAS behavior (e.g. Botía et al., 2004).
Due to the experimental character of MAS development (Uhrmacher, 2000, p. 39), exploratory
analysis techniques seem well-suited to foster analysis and validation tasks. Several MAS
development tools support exploratory analysis by means of powerful visualization techniques
(e.g. Ndumu and Nwana, 1999). To overcome inherent drawbacks of visualization (e.g. in
handling large amounts of high-dimensional data) the additional use of data mining (DM) in
MAS analysis and validation has increasingly been proposed in the last years (e.g. Remondino
and Correndo, 2005).
5
The notion of data mining will be introduced later in detail. For the moment it is used as an
umbrella term for computer supported methods from machine learning and exploratory statis-
tics that automatically generate models from large amounts of data. In MAS analysis, data
mining is in particular suited to nd implicit interaction patterns and relations between pro-
cesses at multiple levels of a system. Such patterns can serve as meaningful high-level system
descriptions supporting data-intensive analysis tasks such as validation (see also Remondino
and Correndo, 2005). This has some tradition in simulation analysis where simulation out-
put is aggregated to more abstract meta models used in result interpretation, validation, and
optimization (e.g. Barton and Szczerbicka, 2000).
4
All literal citations from German sources were translated by the author of this thesis.
5
see also Cabac et al. (2006b, Sec. 1)
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![1.2. Objectives and Contributions of the Thesis
Since processes are an important aspect and event logs an important data source in ABS, a
class of highly appropriate techniques is found in a DM subeld called process mining (PM)
(Aalst and Weijters, 2004). These techniques are typically applied in workow management
and serve to reconstruct process models from workow execution logs.
Similar to ABS, PM research considers multiple system views with a focus on concurrent
control ow and organisational models. Despite these similarities, relations between both
elds have not been considered in the literature often. There are only few explicit entries
(e.g. Hiel, 2005) and [...] recent [...] case example[s] ([e.g.] Dongen et al., 2006b). (Knaak,
2007, p. 30)
However, process mining has been applied in 'MAS-like' domains, such as inter-organizatio-
nal workows (e.g. Aalst, 2004), computer-supported cooperative work (Aalst, 2005a), or web
services (e.g. Gombotz et al., 2005). Related techniques such as grammar inference have been
applied to the analysis of MAS as well (e.g. Mounier et al., 2003).
Summarizing as will be substantiated later the 'research landscape' in this eld has evolved
rapidly within the last years on the one hand (see also Dongen et al., 2006b). On the other
hand, the approaches appear heterogeneous and sometimes far from being applicable to real
world scenarios in MAS and simulations.
1.2. Objectives and Contributions of the Thesis
Though the spectrum of topics and applications discussed in this thesis is quite broad, the
presented work is positioned in the eld of multi-agent-based simulation (MABS). More specic,
the main objective is to evaluate and methodologically enhance the applicability of process mining
and related techniques to the analysis and validation of MABS.
This restriction seems sensible for several reasons: Firstly, the motivation for this work origi-
nates from the lack of appropriate validation techniques in agent-based simulation that became
apparent to the author during a research project on courier service logistics (Bachmann et al.,
2004; Deecke et al., 2004; Knaak et al., 2003). Secondly, analyzing and validating simulation
output is a restricted problem characterized by good data quality and a need for semi- (instead
of fully) automated techniques. Considering the current state of process mining techniques, this
problem seems manageable, and developments from this context can be extended in the future
towards more complex tasks such as autonomous learning. Thirdly, the presented approach can
straightforwardly be transfered to the more general but closely related eld of agent-oriented
software engineering (AOSE).
1.2.1. Research Questions
To rene the general objective stated above, the following research questions will be discussed
in the thesis:
1. Q1 - State-of-the-art: In which way have process mining and related techniques already
been applied to MABS and similar domains? What aspects of the systems have been
analyzed and which analysis tasks (such as validation or calibration) have been supported?
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![1.2. Objectives and Contributions of the Thesis
A novel aspect [of the framework] is the use of the Petri net-based Mulan model (MULti Agent Nets,
Rölke, 2004) as a formal foundation (Knaak, 2007, p. 30) for integrating process mining into
MA(B)S. Mulan is a Petri net-based MAS architecture that builds upon the Reference net
formalism by Kummer (2002). Petri nets are a common means for result representation in
process mining. Mulan provides further structure by distinguishing multiple Petri net-based
views of a MAS. Thereby, it might help to formalize the framework's analysis perspectives in
order to perform more MAS-specic analyses. Reference nets can also be used to formalize the
use cases in the style of scientic workows.
1.2.3. Techniques, Tools, and Case Studies
After dening the conceptual frame, the scope of the discussion is narrowed down to the appli-
cation and extension of specic process mining techniques and tools for MABS analysis (and
thereby refer to research questions 3, 4, and 5). From the various perspectives discussed be-
fore, the focus is put on agent behavior and interactions. Two complementary modeling and
simulation approaches developed at the University of Hamburg will be chosen as case examples
for an integration of process mining. These will be explained in the following.
1.2.3.1. Process Mining in the PAOSE Approach
The rst is the model-driven Petri net-based AOSE (Paose, see e.g. Cabac, 2010) approach
developed at the University of Hamburg's theoretical foundations group (TGI). In Paose,
simulation is mainly used to validate the developed applications. Since process mining appears
as a promising support technique due to its strong relation to the Petri net formalism, an
integration is attempted in cooperation with members of this group (mainly Dr. Lawrence
Cabac and Dr. Daniel Moldt).
At the conceptual level, it will be shown that the Mulan model (Rölke, 2004) with its related
development process and tools (Cabac, 2010) is an appropriate basis for realizing the analysis
and validation tasks described in the framework. This is mainly due to the fact, that a com-
mon executable formalism is available to represent the conceptual and computer model, the
meta-models extracted from observed data, and the experimentation and analysis processes
themselves.
At the technical level, an approach towards the reconstruction of agent interaction protocols
from message logs observed during simulation is presented. Agent interaction mining is a
complex task that requires to combine and extend several existing process mining techniques.
While the interaction mining approach is closely related to parallel work from the web service
context (e.g. Gaaloul, 2005; Gombotz et al., 2005), it contains some novel aspects indicated in
the following.
A processing chain will be presented as an extension of work by Schütt (2003) that allows to
reconstruct models of basic interactions between pairs of agents. One central part is a simple
algorithm to mine process models with non-unique activity labels from event-based message
logs. Schütt (2003) proposes a hybrid algorithm consisting of a subsequent grammar inference
and concurrency detection stage. The grammar inference is, however, restricted to cycle-free
models and the concurrency detection is only described conceptually.
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![2. Modeling and Simulation
On the one hand, it is applied in an intuitive way to describe self-organized systems that have
many components and many characteristic aspects, exhibit many structures in various scales, undergo
many processes in various rates, and have the capability to change abruptly and adapt to external
environments (Auyang, 1998, p. 13). In the same manner, Page and Kreutzer (2005, p. 5) state
that system complexity depends on the number of state variables (properties) and the density of their
connections.
On the other hand, formal approaches from computer science dene the term more concisely.
A well-known measure is the computational complexity of a problem, i.e. the number of steps
(computation time complexity) and the amount of memory (computation space complexity)
needed to algorithmically solve the problem in relation to the size of its encoding (see e.g.
Auyang, 1998, p. 13 or Gruska, 1997, Ch. 5).
Another formal measure is the information content complexity
1 of a character sequence dened
as the length in bits of the smallest program capable of specifying it completely to a computer
(Auyang, 1998, p. 13). This measure assigns the lowest complexity to very regular sequences,
and the highest complexity to purely random sequences without any patterns (Auyang, 1998,
p. 13). While the former seems plausible, the latter might appear counter-intuitive, since
complexity is not commonly understood as a complete lack of structure.
Formal denitions of complexity seem less useful in the context of this thesis due to their limited
scope: Computational complexity is a dierent concept than complexity in system theory.
Information content complexity might be interpreted to that eect that a more complex system
(program) is able to generate more variable patterns of behavior (character sequences). A purely
random sequence contains so many variations that it cannot be described more compactly than
by stating the sequence itself (Auyang, 1998, p. 13). In system theory, we are often interested in
phenomena with a medium information content complexity, i.e. systems that exhibit behavioral
variety, but still allow for the recognition of patterns.
2 The possibility to aggregate system
behavior to a more compact description is of great importance for the applicability of data
mining techniques described below.
A related quality of complex systems is emergence. This concept is based on the observation
that systems include multiple levels with at least a macroscopic level of the system as a whole
and a microscopic level of the basic components. According to Jones (2003, p. 418), the term is
applied to the appearance of novel, coherent objects [at the macroscopic level] that are not predictable
from the system's [microscopic] parts.
The notion of emergence is used quite ambiguously, since for some authors, it denotes an
invocation of something mystical (Jones, 2003, p. 418), while others use it as a shorthand ex-
planation for multi-level phenomena within a reductionist world view (Jones, 2003, p. 421).
Cariani (1991, p. 771)
3, for instance, subsumes the fact that complex global forms can arise from
local computations under the notion of computational emergence. This includes deterministic
phenomena like swarm formation in articial life simulations or the appearance of identiable
shapes in cellular automata.
In this thesis, we use the term complexity in the intuitive way for systems that
1
which is also called Kolmogorov complexity, see e.g. Gruska (1997, p. 398)
2
See also the discussion on pattern-formation by Gribbin (2005, p. 135), who uses the term edge of chaos.
3
cited in Jones (2003, p. 418)
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![2.2. Computer Simulation
• consist of a large number of components, where each component itself exhibits a certain
behavioral variability and exibility (i.e. complex micro-level processes),
• contain a large number of relations and interactions between the components (includ-
ing feedback) and possibly a variable structure (i.e. complex macro-level structures and
processes),
• can be viewed at multiple levels, where relations between the levels are often obscured due
to distributed and sensitive cause-eect dependencies (i.e. complex inter-level relations).
We will avoid using the term emergence due to its non-scientic connotations. However, we will
regard multi-agent systems that exhibit computational emergence where macroscopic patterns
emerge from microscopic interactions through deterministic computations. Data mining will
be applied to expose such patterns and the rules that generated them from observed data.
2.1.2. Models
The term model describes a simplied image of a system. As a main benet, a model allows to
conduct controlled experiments that might be inconvenient or impossible with the real system
(see Niemeyer, 1977, p. 57 cited in Page and Kreutzer, 2005, p. 5).
The complexity of the system under analysis is reduced by considering only the most relevant
parts in the model and by putting them in a simplied form (see e.g. Heinrich, 2002, p. 1046).
This abstraction and idealization (Page and Kreutzer, 2005, p. 6) needs to preserve structural
similarity between the model and the real system (Heinrich, 2002, p. 1046) with regard to a
certain purpose or set of questions [... the model] can answer (Page and Kreutzer, 2005, p. 5).
Given this similarity, the model is considered as valid and its analysis allows to draw conclusions
on the real system.
The notion of models is also central to statistics and data mining. In this context, Hand et al.
(2001, p. 9) dene a model (structure) as a global summary of a data set. According to Han and
Kamber (2000, p. 24), one main purpose of data mining is nding models [...] that describe and
distinguish data classes or concepts [...] The derived model is based on the analysis of a set of training
data [...].
Large data sets are thus algorithmically aggregated to abstract models that describe the data
more compactly. This is somehow similar to modeling in simulation with the exception that
the abstraction is performed automatically. One important property of models in statistics and
machine learning is generalization. To be useful for prediction and classication tasks (see Han
and Kamber, 2000, p. 24), a model should not only describe the specic training data set that
it has been derived from, but a possibly large range of data that the underlying system might
be able to generate. We will continue this discussion in Section 4.1.2.
2.2. Computer Simulation
To understand complex systems we analyze abstract models and draw conclusions on the origi-
nal. The analysis of formal models can be performed either with analytical methods that allow
to compute a closed-form solution 'in one go', or by using simulation, where the model state is
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![2. Modeling and Simulation
advanced step by step in order to emulate the temporal development of the real system (Page
and Kreutzer, 2005, p. 10).
Simulation can thus be dened as the process of describing a real system and using this model
for experimentation with the goal of understanding the system's behaviour or to explore alternative
strategies for its operation (Shannon, 1975, cited in Page and Kreutzer, 2005, p. 9). This general
denition ts many activities in computer science such as the stepwise execution of a computer
program for the purpose of debugging or the token-game in Petri nets (see Section 2.3.2.1).
Though this general meaning is sometimes referred to here, we mostly draw to the more specic
denition of Page and Kreutzer (2005, p. 9), who use the term to denote the eld of computer
simulation as well as the execution of a computer simulation study. In this context, the model
building process is explicitly mentioned, and simulation is characterized as the modelling of dynamic
processes in real systems, based on real data and seeking predictions for a real system's behaviour
[. . . where] models are represented by (simulation) programs, and simulation experiments (runs) are
performed by a models's execution for a specic data set. (Page and Kreutzer, 2005, p. 9)
This denition emphasizes the embedding of the actual 'simulations' into a scientic or indus-
trial research study, where activities like data acquisition, model validation, experimentation,
result analysis, and presentation are of equal importance than the modeling and simulation
itself.
2.2.1. Classication of Simulation Models
Typical dimensions for the classication of models in simulation, which may also apply to other
elds, are shown in Figure 2.1 (e.g. form of analysis, purpose, etc.). From these dimensions,
Page and Kreutzer (2005, pp. 6) emphasize the purpose, the representation medium, and the
type of state changes occurring in the model.
4
2.2.1.1. Purpose of Models
Models are used to better explain and understand the represented system, to predict its fu-
ture behavior, to support the design of a planned system or to optimize the operation of an
existing one (Page and Kreutzer, 2005, p. 7): The purpose of a model strongly inuences its
properties. Explanatory models should represent the system's structure and behavior in an
appropriate and interpretable way to allow for an understanding of the observed phenomena.
For predictive models it might be sucient to mimic the system's behavior closely enough for
successful predictions, even if the model's behavior is generated by unrealistic or not explicitly
understandable structures. We will take up this point in Section 4.1.2.
2.2.1.2. Representation Forms
Models are represented in dierent forms ranging from physical and verbal models to graphical
and mathematical models (Page and Kreutzer, 2005, p. 6). One might additionally consider the
explicitness and conciseness of model representation (Page and Kreutzer, 2005, p. 6): Mental
4
Brade (2003, Sec. 1.2) focuses on the latter two dimensions as well.
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![2. Modeling and Simulation
2.3.1. UML 2
As noted in (Knaak and Page, 2006, p. 33), UML is quite commonly used as a simulation
modeling language today. Several applications (see e.g. De Wet and Kritzinger, 2004) and
extensions (see e.g. Oechslein et al., 2001) are reported in the literature (Knaak and Page,
2006, p. 33). Page and Kreutzer (2005, Ch. 4) as well as Knaak and Page (2006) present our
way of applying and extending UML 2 for discrete event simulation that is briey reviewed
below.
2.3.1.1. The Unied Modeling Language
In (Page and Kreutzer, 2005, p. 60)
7 we have introduced the Unied Modeling Language by
determining
what UML is and of equal importance what it is not. According to the UML reference
manual, it is a general-purpose visual modeling language that is used to specify, visualise,
construct, and document the artifacts of a software system. As Jeckle et al. (2002, p. 10)
point out, UML is not complete, not a programming language, not a formal language, not
specialized to an application area and [...] rst of all not a method or software process.
Further following the shorter presentation in (Knaak and Page, 2006, pp. 34-35):
UML 2.0 contains a total of 13 diagram types to visualise dierent aspects of object-
oriented modelling (Jeckle et al., 2002, p. 15). According to Jeckle et al. (2002, p. 16) these
diagrams can be broadly divided into three classes [mirroring the dualism of structure and
behavior mentioned in Section 2.1]:
• Structural diagrams model the static structure of a system. Among them are class
diagrams, object diagrams, package diagrams, component diagrams, composition struc-
ture diagrams and deployment diagrams.
• Behaviour diagrams serve to display the [...] behaviour of objects or components
at dierent levels of detail. This [...] includes use case diagrams, activity diagrams,
statechart diagrams and several interaction diagram types.
• Interaction diagrams are special behaviour diagrams that focus on the interactions
going on between [...] objects in a system. [... They] can be divided into sequence
diagrams and timing diagrams that emphasise the temporal order of interaction events
on the one hand and communication diagrams that highlight the general structure of
the cooperation between partners in an interaction on the other hand (Jeckle et al.,
2002, p. 391). [...] interaction overview [...] diagrams represent a mixture between
activity diagrams and interaction diagrams showing the causal and temporal interplay
among dierent interaction scenarios (Jeckle et al., 2002, p. 419).
[...] the concepts and notations of the UML are [...] dened in [a so-called meta] model that
is [itself] expressed in terms of the UML (Born et al., 2004, p. 12). This object-oriented
language denition makes extensions of the UML quite easy. [...] Such extensions are either
stated as extensions of the metamodel itself, or by using a lightweight extension mechanism
called stereotyping (Born et al., 2004, p. 245). According to Jeckle et al. (2002, p. 95) a
7
and similarly in (Knaak and Page, 2006)
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![2.3. Modeling Techniques
stereotype is a a class in the metamodel that is able to further specify other classes [...]
by extension.
[... As an example, we might] represent entity types in DES models [by extending] the
meta class Class [...] with a stereotype entity. [...] Now entity types in class diagrams
are marked by attaching the term entity in angle brackets to the respective model
elements.
2.3.1.2. UML in Simulation
A main feature that makes UML suitable for the DES domain [... is] the event-based communication
model underlying all behaviour diagrams (see Jeckle et al., 2002, pp. 172) (Knaak and Page, 2006,
p. 36). Similar to DES, an event in UML is a relevant occurrence such as sending a message
or invoking an operation (Jeckle et al., 2002, p. 173). Dierent from DES, a UML event has
a lifecycle consisting of creation, distribution and consumption, and its occurrence in a real
system might consume time (Jeckle et al., 2002, p. 173). We can, however, abstract from these
aspects and regard UML events in DES models as instantaneous.
Simulation practitioners benet from UML diagrams as a common and simulation-software inde-
pendent basis for documenting, visualizing and understanding the model structure (Richter and März,
2000, p. 2). The dierent UML diagrams provide multiple views focusing on [... complementary] aspects
of the model. (Knaak and Page, 2006, p. 36)
In an industrial or non-computer-science context, the diagrams might be understood more
easily than more abstract formal languages like Petri nets (see Section 2.3.2.1). Nevertheless,
the quite concise semi-formal semantics of UML 2 behaviour diagrams [...] provide support for the task
of model validation and verication as well as code generation (Knaak and Page, 2006, p. 36).
Current approaches towards model driven software development apply transformation rules that
map UML models to executable code.
8
In the following, we briey introduce UML activity and interaction diagrams for modeling
the dynamics of discrete simulations. The presentation is based on Page and Kreutzer (2005,
Ch. 4) and Knaak and Page (2006). Basic concepts of object orientation (such as inheritance)
and their representation in class, object and package diagrams are taken for granted (for an
overview see e.g. Jeckle et al., 2002, Chs. 3, 4, 5).
2.3.1.3. Activity Diagrams
In (Page and Kreutzer, 2005, pp. 77), we introduced activity diagrams with a focus on DES:
According to Jeckle et al. (2002, p. 199) activity diagrams are [an appropriate] notation [...]
for modelling [...] operations, use cases, and business processes. [... Consequently, they]
are particularly well suited for modelling lifecycles of simulation processes in [... DES].
Since they provide features such as concurrency, object ow[,] and message passing they
are convenient for showing the synchronization of two or more processes. [...] In UML 2.0,
the statechart-like event-handling semantics of [UML 1.x ...] has been replaced by a Petri
net-like token semantics [see also Section 2.3.2.1].
8
On the application of model driven software development in the simulation context see Sandu (2007).
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![2. Modeling and Simulation
In (Knaak and Page, 2005, p. 404) we observed that the synchronization operations of the
process-oriented world view (see Section 2.2.2)
map quite obviously to send- and receive-signal actions [...] (Jeckle et al., 2002, p. 214). [...]
Generally any time consumption is modelled using receive-signal actions, whereas normal
action nodes correspond to active process phases without passing of simulation time.
Figure 2.3 shows [an example of] two process classes [...] that synchronize via sending and
reception of activation signals.
Figure 2.3.: Synchronisation of [... simulation processes in an imaginary] Gravel Pit model via
sending and reception of signals. Figure and caption adopted from Knaak and Page
(2006, p. 38).
The separation by activity regions (Jeckle et al., 2002, pp. 245) makes it possible to display
multiple interacting processes in a single diagram. As carried out in (Knaak and Page, 2006,
p. 38) we denote process activations
by a send-signal action (Jeckle et al., 2002, p. 214) with the stereotype activate. [...]
The passive state is indicated by a receive-signal action (Jeckle et al., 2002, p. 214) with
the stereotype passive. [...]
[In compliance with ...] Jeckle et al. (2002, p. 215) [... the hold operation is] modelled using
a time signal reception node depicted by an hour glass symbol [...] with the additional
stereotype hold [... that] delays incoming tokens for a specied duration.
Further following Knaak and Page (2006, p. 39), data ow is displayed with the aid of
object nodes depicted by rectangles (Jeckle et al., 2002, pp. 218). When the outgoing
edge of an action node is connected to an object node, execution of the action produces
a so called data token that contains the result object of the execution. The data token is
stored in the object node and might serve as input to another action [... Object nodes can
36](https://image.slidesharecdn.com/17180-250225211355-04c51378/85/Process-Oriented-Analysis-and-Validation-of-Multi-Agent-Based-Simulations-1st-Edition-Nicolas-Denz-45-320.jpg)
![2.3. Modeling Techniques
be] used as synchronisation constructs in [... process- and transaction-oriented] models [see
Figure 2.3]. We use the stereotype queue to indicate that an object node has a queue
semantic.
A mapping of UML activity diagrams to further DES-specic constructs (e.g. interrupts) and
modeling styles (e.g. transaction orientation) is presented by Knaak and Page (2006) and Page
and Kreutzer (2005, Ch. 4 and 5).
2.3.1.4. Interaction Diagrams
Figure 2.4.: An example of using basic sequence diagrams in DES (adopted from Page and
Kreutzer, 2005, p. 89)
In (Page and Kreutzer, 2005, pp. 87-91) we described UML interaction diagrams as follows:
[While] the main purpose of [... activity] diagrams is the description of individual [...]
behaviour [...] interaction diagrams are often better suited to model the interplay between
multiple entities.
[...] basic [...] sequence diagrams display timely ordered message sequences describing an
interaction scenario [...] Figure 2.4 shows an [...] example [...that] can be regarded as a
possible [rened] execution sequence of the activity diagrams shown in Figure 2.3.
37](https://image.slidesharecdn.com/17180-250225211355-04c51378/85/Process-Oriented-Analysis-and-Validation-of-Multi-Agent-Based-Simulations-1st-Edition-Nicolas-Denz-46-320.jpg)
![2. Modeling and Simulation
[...] the dierent [...] roles [...] taking part in an interaction are plotted along the horizontal
axis, while the vertical axis represents time (Jeckle et al., 2002, p. 327). The main diagram
elements are the lifelines of the interaction partners and what messages pass between them.
[...] UML distinguishes several communication modes, each of which is symbolized by a
dierent arrow-head (Jeckle et al., 2002, p. 346). A lled black arrowhead indicates a
synchronous message, where the sender waits [...] until the message has been processed by
the receiver. The receiver answers by sending a response message, represented by a dashed
arrow with lled arrowhead. [...]
Asynchronous messages are symbolized by an open arrowhead. [... Here] the sender con-
tinues its lifecycle without waiting for the message to be processed by the receiver. [We
model method calls as synchronous messages and process interactions including passivation
as asynchronous messages.]
[...] Conditions ensuring the correctness of a scenario [...] can be expressed by [...] state
invariants (Jeckle et al., 2002, p. 356) [...] symbolized by using rounded rectangles [...]
[...] Time constraints can be inserted at any place in the diagram where they are meaningful
(Jeckle et al., 2002, p. 352).
[...] in UML 2 it is also possible to represent alternative, optional, parallel, and repeated
sequences of interaction [using block-structured interaction fragments]. Furthermore, dia-
grams might contain references to other sequence diagrams that contain a rened descrip-
tion of particular interaction steps. Due to their derivation from [...] High Level Message
Sequence Charts (Jeckle et al., 2002, p. 332), we will refer to this notation as high level
sequence diagrams.
Like activity diagrams [...], high level sequence diagrams do not display a single scenario
but rather a class of possible interaction sequences. A drawback of the extended notation
is that such diagrams can become [...] dicult to understand. (Page and Kreutzer, 2005,
pp. 87-91)
:Dispatcher :AGV
3[idle]:Accept(transport order)
3[not idle]: Reject(transport order)
:Truck
2:Request(transport order)
1:Arrival
Truck Arrival
sd
Figure 2.5.: A communication diagram displaying an interaction at an imaginary container
terminal.
A more detailed description of UML 2 sequence diagrams including a comparison with the
similar AgentUML interaction diagrams is provided in Section 3.3.2.1. An alternative view
upon communicating entities is provided by communication diagrams as shown in Figure 2.5
(see also Jeckle et al., 2002, pp. 391). The example shows a possible interaction taking place
38](https://image.slidesharecdn.com/17180-250225211355-04c51378/85/Process-Oriented-Analysis-and-Validation-of-Multi-Agent-Based-Simulations-1st-Edition-Nicolas-Denz-47-320.jpg)
![2.3. Modeling Techniques
at a container terminal.
9 On the arrival of a truck, the order dispatcher generates a transport
order to fetch a certain container and dispatches it to an automatic guided vehicle (AGV) that
might accept or reject the order depending on its state.
Note that communication diagrams do not focus on control ow (Jeckle et al., 2002, p. 392) but
display relations between communication partners similar to a social network Aalst and Song
(see e.g. 2004b). Nevertheless it is possible to indicate the order of messages by consecutive
numbering. While alternatives are expressed using the UML guard notation, other interaction
fragments (e.g. loops) are not supported (Jeckle et al., 2002, pp. 400).
2.3.2. Petri Nets
Despite several attempts to formalize and execute UML models, the UML remains a semi-
formal language without an explicit operational semantic. In contrast, Petri nets (PN) are
formal models to represent concurrent processes. In the following, we will focus on the reference
net formalism by Kummer (2002) and its relations to simulation and UML.
2.3.2.1. Petri Nets
Rölke (2004, p. 251) informally introduces a PN as a directed graph with two dierent node types:
places and transitions. A place [drawn as a circle] is a passive element corresponding to a storage [. . . ]
while a transition [drawn as a rectangle] represents an action or processing step. Arcs can only connect
a place with a transition or vice versa.
The PN formalism was proposed by Petri (1962) to model distributed system states and con-
currency (Rölke, 2004, p. 253). A set of events or actions are concurrent if they are not
causally interrelated and might therefore be executed in an arbitrary order or even simultane-
ously (Rölke, 2004, p. 253). The state of a PN is indicated by a marking of its places with
tokens (Rölke, 2004, p. 251), where each place can contain a number of tokens up to a certain
(possibly unlimited) capacity.
The behavior of a PN is realized by the ring of transitions. A transition's ability to re depends
on its local environment, i.e. the input places connected via incoming arcs and the output places
connected via outgoing arcs (Rölke, 2004, pp. 251). The transition is activated if all input
places contain enough tokens (with respect to the incoming arcs' weights) and the ring of
the transition does not exceed any output place's capacity (with respect to the outgoing arcs'
weights) (Jessen and Valk, 1987, p. 39). The ring removes tokens from the input places and
puts tokens into the output places (Rölke, 2004, p. 252).
Figure 2.6 exemplies a PN representing a 'gravel pit' model with two loading docks.
10 Since
places and arcs do not contain numerical inscriptions, each place capacity is unlimited and each
arc weight is 1 by default.
In the following, we review further aspects of PNs that will be relevant later in this thesis.
As usual (see e.g. Baumgarten, 1996 or Bause and Kritzinger, 1996) we distinguish between
structural and dynamic properties.
9
On the simulation of container terminal logistics, see e.g. the diploma thesis by Planeth and Willig (2004)
10
The 'gravel pit' example is adopted from Page and Kreutzer (2005, p. 32).
39](https://image.slidesharecdn.com/17180-250225211355-04c51378/85/Process-Oriented-Analysis-and-Validation-of-Multi-Agent-Based-Simulations-1st-Edition-Nicolas-Denz-48-320.jpg)
![2. Modeling and Simulation
Truck
Arrival
Truck
queue
Idle
Loading
Idle
Loading
Begin of
service
End of
service
Loading dock 2
[]
[]
[]
[] []
Loading dock 1
Finished
trucks
Leave
system
Leave
system
End of
service
Begin of
service
Figure 2.6.: A very abstract PN model of a 'gravel pit' with two loading docks. Note that this
model neglects simulation time consumption and queueing strategies.
2.3.2.2. Structural Patterns and Properties
Structural properties are based on the net graph N = (P, T, F), where P is the set of places, T
the set of transitions and F the set of arcs or ow relation. To handle the potential complexity
of general net graphs, we can identify common structural patterns (see e.g. Rölke, 2004, pp. 254)
on the one hand and consider simplied net classes on the other hand.
Figure 2.7.: Basic structural patterns commonly found in Petri nets (adopted with modications
from Rölke, 2004, p. 255 and Baumgarten, 1996, p. 53, 72)
Common structural patterns are displayed in Figure 2.7. The denition of sequences and cycles
(Baumgarten, 1996, p. 72) is straightforward. Cycles of length 1 are called loops (Baumgarten,
1996, p. 53). A conict corresponds to a decision node in an activity diagram (see Section
2.3.1.3. The concurrent pattern splits and re-joins the control ow into parallel threads similar
to fork and join nodes in activity diagrams.
40](https://image.slidesharecdn.com/17180-250225211355-04c51378/85/Process-Oriented-Analysis-and-Validation-of-Multi-Agent-Based-Simulations-1st-Edition-Nicolas-Denz-49-320.jpg)
![This ebook is for the use of anyone anywhere in the United
States and most other parts of the world at no cost and with
almost no restrictions whatsoever. You may copy it, give it away
or re-use it under the terms of the Project Gutenberg License
included with this ebook or online at www.gutenberg.org. If you
are not located in the United States, you will have to check the
laws of the country where you are located before using this
eBook.
Title: Les Bijoux Indiscrets, or, The Indiscreet Toys
Author: Denis Diderot
Release date: May 6, 2017 [eBook #54672]
Most recently updated: October 23, 2024
Language: English
Credits: Produced by Clare Graham Marc D'Hooghe at Free
Literature
(online soon in an extended version, also linking to free
sources for education worldwide ... MOOC's,
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materials,...) Images generously made available by the
Internet Archive.
*** START OF THE PROJECT GUTENBERG EBOOK LES BIJOUX
INDISCRETS, OR, THE INDISCREET TOYS ***](https://image.slidesharecdn.com/17180-250225211355-04c51378/85/Process-Oriented-Analysis-and-Validation-of-Multi-Agent-Based-Simulations-1st-Edition-Nicolas-Denz-56-320.jpg)
![Chap. LI. Thirtieth and last Trial of the Ring, or Mirzoza.
[Transcribers' Note: Chapters I.-XXI. of the second volume of the 1749 publication have
been renumbered XXXI.-LI. Illustrations weren't present in the copy of the English edition
we used, we added those from the original French (at Gallica, Bibliothèque nationale de
France.]
LIST OF ILLUSTRATIONS.
1.Cupid in Bed (frontispiece).
2.Man, Woman and Cupid, or Folly, Imagination, and Love.
3.Evocation of the Genius.
4.Dogs and Lady in Bed.
5.The Mare, c.
6.The Bubble-blower.
7. Women walking on their hands.
8.Man and Lady on a Sopha (Zuleiman).](https://image.slidesharecdn.com/17180-250225211355-04c51378/85/Process-Oriented-Analysis-and-Validation-of-Multi-Agent-Based-Simulations-1st-Edition-Nicolas-Denz-63-320.jpg)
Process Oriented Analysis and Validation of Multi Agent Based Simulations 1st Edition Nicolas Denz
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- 5. Process Oriented Analysis and Validation of Multi Agent Based Simulations 1st Edition Nicolas Denz Digital Instant Download Author(s): Nicolas Denz ISBN(s): 9783832587741, 3832587748 Edition: 1 File Details: PDF, 10.41 MB Year: 2014 Language: english
- 6. Agent Technology Theory and Application Daniel Moldt (Ed.) Nicolas Denz Process-Oriented Analysis and Validation of Multi-Agent-Based Simulations
- 8. Agent Technology Theory and Application Band 7
- 9. Agent Technology Theory and Application Band 7 Daniel Moldt (Ed.)
- 10. Nicolas Denz Process-Oriented Analysis and Validation of Multi- Agent-Based Simulations Logos Verlag Berlin λογος
- 11. Agent Technology. Theory and Application Daniel Moldt (Ed.) Universität Hamburg Fachbereich für Informatik Vogt-Kölln-Str. 30 D-22527 Hamburg moldt@informatik.uni-hamburg.de Bildquelle: Modifiziert nach L. Cabac, N. Knaak, D. Moldt, and H. Rlke: Ana- lysis of Multi-Agent Interactions with Process Mining Techniques, S. 17. In: Proceedings of the 4th German Conference on Multiagent System Technology (MATES 2006 in Erfurt), S. 12-23, Springer, September 2006. Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar. c Copyright Logos Verlag Berlin GmbH 2015 Alle Rechte vorbehalten. ISBN 978-3-8325-3874-3 ISSN 1614-676X Logos Verlag Berlin GmbH Comeniushof, Gubener Str. 47, 10243 Berlin Tel.: +49 (0)30 / 42 85 10 90 Fax: +49 (0)30 / 42 85 10 92 http://www.logos-verlag.de
- 12. Gutachter Prof. Dr.-Ing. Bernd Page (Erstgutachter) Modellbildung und Simulation Fachbereich Informatik MIN-Fakultät Universität Hamburg (Deutschland) Dr. Daniel Moldt Theoretische Grundlagen der Informatik Fachbereich Informatik MIN-Fakultät Universität Hamburg (Deutschland) 3
- 14. Abstract In multi-agent-based simulation (MABS) the behavior of individual actors is modelled in large detail. The analysis and validation of such models is rated as dicult in the literature and requires support by innovative methods, techniques, and tools. Problems include the complexity of the models, the amount and often qualitative representation of the simulation results, and the typical dichotomy between microscopic modeling and macroscopic observation perspectives. In recent years, the application of data mining techniques has been increasingly propagated in this context. Data mining might, to some degree, bear the potential to integrate aspects of automated, formal validation on the one hand and explorative, qualitative analysis on the other hand. A promising approach is found in the eld of process mining. Due to its rooting in business process analysis, process mining shares several process- and organization-oriented analysis perspectives and use cases with agent-based modeling. On the basis of detailed literature research and practical experiences from case studies, this thesis proposes a conceptual framework for the systematic application of process mining to the analysis and validation of MABS. As a foundation, agent-oriented analysis perspectives and simulation-specic use cases are identied and embellished with methods, techniques, and further results from the literature. Additionally, a partial formalization of the identied analysis perspectives is sketched by uti- lizing the concept of process dimensions by Rembert and Ellis as well as the MAS architecture Mulan by Rölke. With a view to future tool support the use cases are broadly related to concepts of scientic workow and data ow modeling. Furthermore, simulation-specic re- quirements and limitations for the application of process mining techniques are identied as guidelines. Beyond the conceptual work, process mining is practically applied in two case studies re- lated to dierent modeling and simulation approaches. The rst case study integrates process mining into the model-driven approach of Petri net-based agent-oriented software engineering (PAOSE). On the one hand, process mining techniques are practically applied to the analysis of agent interactions. On the other hand, more general implications of combining process mining with reference net-based agent modeling are sketched. The second case study starts from a more code-centric MABS for the quantitative analysis of dierent logistic strategies for city courier services. In this context, the practical utility and applicability of dierent process mining techniques within a large simulation study is evaluated. Focus is put on exploratory validation and the reconstruction of modularized agent behavior. 5
- 16. Kurzfassung In der agentenbasierten Simulation wird das Verhalten individueller Akteure detailliert im Mo- dell abgebildet. Die Analyse und Validierung dieser Modelle gilt in der Literatur als schwierig und bedarf der Unterstützung durch innovative Methoden, Techniken und Werkzeuge. Prob- leme liegen in der Komplexität der Modelle, im Umfang und der oft qualitativen Darstellungs- form der Ergebnisse sowie in der typischen Dichotomie zwischen mikroskopischer Modellierungs- und makroskopischer Beobachtungssicht begründet. In den letzten Jahren wurde in diesem Zusammenhang zunehmend der Einsatz von Techniken aus dem Data Mining propagiert. Diese bergen in gewisser Weise das Potenzial, Aspekte der automatisierten, formalen Validierung mit denen der explorativen, qualitativen Analyse zu vere- inen. Einen vielversprechenden Ansatz bietet das sogenannte Process Mining, welches aufgrund seiner Nähe zur Geschäftsprozessmodellierung mit der agentenbasierten Modellierung vergleich- bare prozess- und organisationsorientierte Modellsichten (Perspektiven) und Anwendungsfälle aufweist. Ziel der vorliegenden Arbeit ist es, auf Basis umfangreicher Literaturrecherche und in Fallstu- dien gesammelter Erfahrungen ein konzeptionelles Rahmenwerk für den systematischen Ein- satz von Process Mining zur Analyse und Validierung agentenbasierter Simulationsmodelle vorzuschlagen. Als Grundlage werden agentenspezische Analyseperspektiven und simulation- sspezische Anwendungsfälle identiziert und durch Methoden, Techniken und weitere Ergeb- nisse aus der Literatur ausgestaltet. Darüber hinaus wird ansatzweise eine Teilformalisierung der Analyseperspektiven unter Ver- wendung des Prozessdimensionen-Konzepts nach Rembert und Ellis sowie der auf Referen- znetzen basierenden Architektur Mulan nach Rölke angestrebt. Die Anwendungsfälle wer- den mit Blick auf eine mögliche Werkzeugunterstützung mit Konzepten der wissenschaftlichen Workow- und Datenussmodellierung in Beziehung gesetzt und durch die Identikation sim- ulationsspezischer Anwendungsrichtlinien für das Process Mining ergänzt. Neben der konzeptionellen Arbeit wird der Einsatz von Process Mining praktisch in unter- schiedlichen Modellierungs- und Simulationsansätzen erprobt. Die erste Fallstudie integriert Process Mining konzeptionell und technisch in den modellgetriebenen Ansatz der Petrinetz- basierten agentenorientierten Softwareentwicklung (PAOSE). Dabei wird einerseits der praktis- che Einsatz von Process Mining-Techniken zur Interaktionsanalyse von Agenten beschrieben. Andererseits zeigt die Studie generelle Implikationen der Kombination von Process Mining und Referenznetz-basierter Agentenmodellierung auf. Ausgangspunkt der zweiten Fallstudie ist eine eher Code-zentrierte agentenbasierte Simulation zur quantitativen Analyse verschiedener Logistikstrategien für Stadtkurierdienste. Im Rahmen dieser Fallstudie werden Process Mining-Techniken im Hinblick auf Anwendbarkeit und Nutzen für eine groÿe Simulationsstudie untersucht. Dabei steht die explorative Validierung und die Rekonstruktion modularisierten Agentenverhaltens im Vordergrund. 7
- 18. Acknowledgement I would like to thank my supervisors Prof. Dr.-Ing. Bernd Page and Dr. Daniel Moldt for their support, patience, and inspiration during the long years of work on this thesis. I appreciate the close cooperation with a number of colleagues and (former) students including Dr. Ralf Bachmann, Dr. Lawrence Cabac, Rainer Czogalla, Nils Erik Flick, Dr. Björn Gehlsen, Johannes Haan, Dr. Frank Heitmann, Sven Kruse, Ruth Meyer, Florian Plähn, Thomas Sandu, and Felix Simmendinger, who all made valuable contributions to the presented work. Further thanks go to my former colleagues at the University of Hamburg's Department of In- formatics including (but not limited to) Dr. Marcel Christ, Prof. Dr. Andreas Fleischer, Dr. Jo- hannes Göbel, Dr. Philip Joschko, Arne Koors, Dr. Matthias Mayer, Prof. Dr.-Ing. Matthias Riebisch, Prof. Dr. Volker Wohlgemuth, and Dr. Claudia Wyrwoll. I would also like to thank my co-workers at ifu Hamburg GmbH for their patience with my 'second job' and especially Dr. Dorli Harms for proofreading parts of this thesis. Finally I want to thank my family for their love, support, patience, and belief in me. You know who you are. Love to Kim and Simon, you are my soulmates. 9
- 20. Contents 1. Introduction 15 1.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2. Objectives and Contributions of the Thesis . . . . . . . . . . . . . . . . . . . . 17 1.2.1. Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.2. Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2.3. Techniques, Tools, and Case Studies . . . . . . . . . . . . . . . . . . . . 19 1.3. Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 I. Foundations and State of the Art 25 2. Modeling and Simulation 27 2.1. Basic System Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1.1. Complexity and Emergence . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1.2. Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2. Computer Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.1. Classication of Simulation Models . . . . . . . . . . . . . . . . . . . . . 30 2.2.2. World Views of Discrete Event Simulation . . . . . . . . . . . . . . . . . 32 2.3. Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3.1. UML 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.2. Petri Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.3. Workow Modeling and Patterns . . . . . . . . . . . . . . . . . . . . . . 48 2.4. Experimentation, Analysis, and Validation . . . . . . . . . . . . . . . . . . . . . 50 2.4.1. Experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.4.2. Output Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.4.3. Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3. Agent-Based Simulation 59 3.1. Agents and Multi-Agent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.1.1. Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.1.2. Agent Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.1.3. Multi-Agent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2. The Agent-Based Simulation World View . . . . . . . . . . . . . . . . . . . . . 64 3.2.1. Relations between Agents and Simulation . . . . . . . . . . . . . . . . . 64 3.2.2. Components of Agent-Based Models . . . . . . . . . . . . . . . . . . . . 65 3.2.3. Coparison with other Simulation World Views . . . . . . . . . . . . . . . 69 3.3. Modeling Techniques for Agent-Based Simulation . . . . . . . . . . . . . . . . . 71 3.3.1. Declarative Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.2. UML-Based Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 11
- 21. Contents 3.3.3. Petri Nets and Mulan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4. Implementation of Agent-Based Models . . . . . . . . . . . . . . . . . . . . . . 88 3.4.1. JADE Agent Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.4.2. MadKit Agent Platform and Simulation Framework . . . . . . . . . . . 90 3.4.3. SeSAm Simulation System . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.4.4. FAMOS and DESMO-J . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.4.5. Capa Agent Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.5. The Problem of Analysis and Validation . . . . . . . . . . . . . . . . . . . . . . 95 4. Data Mining and Process Mining 97 4.1. Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.1.1. The KDD Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.1.2. Classication of Data Mining Techniques . . . . . . . . . . . . . . . . . . 99 4.1.3. Model Validity in Data Mining . . . . . . . . . . . . . . . . . . . . . . . 102 4.1.4. Exemplary Data Mining Techniques . . . . . . . . . . . . . . . . . . . . 106 4.1.5. Tools for Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.2. Process Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.2.1. Denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.2.2. Classication of Process Mining Techniques . . . . . . . . . . . . . . . . 119 4.2.3. Control Flow Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.2.4. Organizational Perspective . . . . . . . . . . . . . . . . . . . . . . . . . 148 4.2.5. Further Perspectives and Tasks . . . . . . . . . . . . . . . . . . . . . . . 153 4.2.6. Tools and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 5. Related Work 169 5.1. Analysis and Validation of MABS . . . . . . . . . . . . . . . . . . . . . . . . . . 169 5.1.1. Methodologies for MABS Validation . . . . . . . . . . . . . . . . . . . . 169 5.1.2. Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5.2. Data Mining in Multi-Agent Systems and Simulations . . . . . . . . . . . . . . 186 5.2.1. Relations between Data Mining and MAS . . . . . . . . . . . . . . . . . 186 5.2.2. Data Mining in MABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 5.2.3. Data Mining in Other Simulation World-Views . . . . . . . . . . . . . . 196 5.2.4. Data Mining in MAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 5.3. Process Mining in Software Engineering and Simulation . . . . . . . . . . . . . 200 5.3.1. Process Mining in Software Engineering . . . . . . . . . . . . . . . . . . 200 5.3.2. Mining Message Sequence Graphs . . . . . . . . . . . . . . . . . . . . . . 202 5.3.3. Web Service and Interaction Mining . . . . . . . . . . . . . . . . . . . . 203 5.3.4. Process Mining for Agents and Simulation . . . . . . . . . . . . . . . . . 209 5.4. Scientic Workows for Simulation and Process Mining . . . . . . . . . . . . . . 216 5.4.1. Scientic Workow Support for Process Mining . . . . . . . . . . . . . . 216 5.4.2. Scientic Workow Support for Simulation . . . . . . . . . . . . . . . . 217 12
- 22. Contents II. Concepts, Tools, and Case Studies 221 6. Conceptual Framework 223 6.1. Motivation and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 6.2. Analysis Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 6.2.1. Decision Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 6.2.2. Internal Control Perspective . . . . . . . . . . . . . . . . . . . . . . . . . 229 6.2.3. Structural Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 6.2.4. External Control Perspective . . . . . . . . . . . . . . . . . . . . . . . . 235 6.2.5. Adaptivity Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 6.2.6. Level-Encompassing Perspective . . . . . . . . . . . . . . . . . . . . . . 242 6.2.7. Domain-Specic Perspectives . . . . . . . . . . . . . . . . . . . . . . . . 246 6.3. Use Cases within the Model Building Cycle . . . . . . . . . . . . . . . . . . . . 248 6.3.1. Real System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 6.3.2. Exploratory Analysis of Model Behavior . . . . . . . . . . . . . . . . . . 252 6.3.3. Validation and Verication . . . . . . . . . . . . . . . . . . . . . . . . . 254 6.3.4. Optimization and Calibration . . . . . . . . . . . . . . . . . . . . . . . . 258 6.3.5. Design of Adaptive Agents . . . . . . . . . . . . . . . . . . . . . . . . . . 260 6.3.6. Analysis of the Model Building Cycle . . . . . . . . . . . . . . . . . . . . 263 6.4. Simulation-specic Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 266 6.4.1. Robustness and Degree of Generalization . . . . . . . . . . . . . . . . . 267 6.4.2. Relevant Control Flow Constructs . . . . . . . . . . . . . . . . . . . . . 268 6.4.3. Usability of Mining Techniques for Simulation Practitioners . . . . . . . 268 6.4.4. Handling of Multiple Stochastic Simulation Runs . . . . . . . . . . . . . 269 6.5. Summary and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 7. Process Mining in PAOSE 273 7.1. Process Mining and the Mulan Framework . . . . . . . . . . . . . . . . . . . . . 273 7.1.1. Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . . . . 273 7.1.2. Analysis Perspectives and Mulan . . . . . . . . . . . . . . . . . . . . . 274 7.1.3. Support for Analysis Use Cases . . . . . . . . . . . . . . . . . . . . . . . 281 7.2. Reconstruction of Basic Interaction Protocols . . . . . . . . . . . . . . . . . . . 289 7.2.1. Basic Interaction Mining Chain . . . . . . . . . . . . . . . . . . . . . . . 290 7.2.2. Message Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 7.2.3. Conversation Clustering and Role Mining . . . . . . . . . . . . . . . . . 293 7.2.4. Control Flow Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 7.2.5. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 7.3. Reconstruction of Higher Order Protocols . . . . . . . . . . . . . . . . . . . . . 304 7.3.1. Extended Interaction Mining Chain . . . . . . . . . . . . . . . . . . . . . 306 7.3.2. Log Segmentation and Role Mining . . . . . . . . . . . . . . . . . . . . . 307 7.3.3. Control Flow Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 7.3.4. Multiple Instantiation and Cardinalities . . . . . . . . . . . . . . . . . . 310 7.3.5. Result Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 7.4. Tool Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 7.4.1. Mulan Snier Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 7.4.2. Analysis Framework and Mining Chains . . . . . . . . . . . . . . . . . . 313 7.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 13
- 23. Contents 8. Process Mining in a Discrete Event Simulation Study 321 8.1. Courier Service Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 8.1.1. Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 8.1.2. Agent-Based Courier Service Models . . . . . . . . . . . . . . . . . . . . 322 8.1.3. Implementation with FAMOS and DESMO-J . . . . . . . . . . . . . . . 328 8.1.4. Data Collection and Result Analysis . . . . . . . . . . . . . . . . . . . . 330 8.1.5. Validation and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 331 8.1.6. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 8.2. Application of Process Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 8.2.1. Objectives and Methodology . . . . . . . . . . . . . . . . . . . . . . . . 341 8.2.2. Analysis Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 8.2.3. Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 8.2.4. Data Collection and Preprocessing . . . . . . . . . . . . . . . . . . . . . 344 8.2.5. Perspectives and Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 348 8.3. Process Mining Experiments and Results . . . . . . . . . . . . . . . . . . . . . . 350 8.3.1. External Control Perspective . . . . . . . . . . . . . . . . . . . . . . . . 350 8.3.2. Internal Control Perspective . . . . . . . . . . . . . . . . . . . . . . . . . 368 8.3.3. Decision Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 8.3.4. Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 379 8.4. Integration into an Experimentation Environment . . . . . . . . . . . . . . . . . 384 8.4.1. Motivation and Introduction . . . . . . . . . . . . . . . . . . . . . . . . 384 8.4.2. Design and Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 385 8.4.3. Scientic Workows with KNIME and ProM . . . . . . . . . . . . . . . 387 9. Summary, Discussion, and Outlook 389 9.1. Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 9.2. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 9.2.1. Attainment of Research Goals . . . . . . . . . . . . . . . . . . . . . . . . 391 9.2.2. Comparison to Related Work . . . . . . . . . . . . . . . . . . . . . . . . 397 9.3. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 14
- 24. 1. Introduction Multi-agent systems (MAS) are a promising theoretical concept to approach practical challenges related to the exibility, adaptivity, and distribution of computer systems. The agent metaphor combines an object-oriented encapsulation of program state and control ow with ideas on the mechanics of [...] decision making (Davis et al., 1989) rooted in articial intelligence, sociology, and economics. 1 One common example of MAS are teams of real or simulated robots competing in the robot soccer league Robo Cup 2 (see e.g. Nair et al., 2004). Accordingly, agent-based abstractions are used in several subelds of computer science; e.g. soft- ware engineering, distributed systems, and robotics. (Page and Kreutzer, 2005, pp. 339). Inde- pendent from the application context, a major problem is posed by the need to analyze and understand the behavior of agent-based systems, and in particular to assess their validity. This term, which will be dened precisely later, means in short that a system fullls its intended functions in an appropriate way. An agent-based simulation model should, for instance, represent the microscopic agent-level as well as the macroscopic system-level of the corresponding original system in detail to allow for reliable conclusions about reality. The increasing application of agent technology in domains with high safety or real-time requirements (e.g. manufacturing control) calls for particularly powerful validation techniques. The call for appropriate methods and tools to support the analysis and validation of agent-based systems has been uttered in early publications on agent- based software engineering already (e.g. Gasser and Huhns, 1989) and apparently not been answered suciently (see e.g. Guessoum et al., 2004, pp. 440). Therefore, the aim of this thesis is to shed light on innovative techniques to validate agent-based models. 1.1. Motivation For a number of reasons, the analysis and validation of MAS poses severe problems that are inherent to the approach. The distributed system state and high sensitivity of ABS [agent-based simulations] often results in an unmanageable and unpredictable global behaviour. (Knaak, 2007, p. 29, see also Klügl, 2008, Sec. 2.2). Minor deviations in the system's initial conditions might give rise to strong deviations in behavioral trajectories (Rand et al., 2003, p. 2) 3. Due to the microscopic modelling perspective, global [system] properties are not inuenced directly (Knaak, 2007, pp. 29-30), but only by specifying the behavior of individual agents. Since relations be- tween microscopic causes and macroscopic eects are generally hard to determine in distributed 1 A paragraph with similar content also forms the introduction to our pre-publication (Cabac et al., 2006c). 2 http://robocup.org, last visit 2012-11-17 3 page numbers relate to the version of the article downloadable at http://masi.cscs.lsa.umich.edu/ sluce/publications/sluce-abs.pdf (last visit 2012-10-06) 15
- 25. 1. Introduction systems, this situation often complicates tasks like calibration and optimization (Klügl, 2000, p. 205). Certain uses of the agent metaphor even prohibit an a-priori specication of the system's behavior as in traditional software engineering: Innovative elds such as social simulation, swarm intelligence (Kennedy, 2001) or the engineering of self-organizing systems (Potgieter, 2004) explicitly strive to investigate or benet from self-organizing or emergent eects observed in certain MAS (David et al., 2002, p. 91). For the analysis and validation of MAS several approaches reaching from formal to simulation-based techniques have been proposed. Formal verication is based on representations using formalisms such as Petri nets or modal logic. Due to their conciseness, formal methods are increasingly applied in agent-oriented software-engineering. However, as noted in (Cabac et al., 2006b, Sec. 1) only simple and often practically irrelevant classes of MAS (Edmonds and Bryson, 2004) can be analyzed with formal methods alone. The simulation-based approach relies on the empirical observation of operational MAS and an a-posteriori analysis of the observed behavior. The empirical analysis of MAS and agent behavior is an important means for validation, often outperforming the application of formal methods (see e.g. Cohen, 1995 and Guessoum et al., 2004). According to Uhrmacher (2000, p. 39) the development of software agents is [...] mainly an experimental process 4. However, as cited in (Cabac et al., 2006b, Sec. 1) the observation of even simple multi-agent systems might produce large and complex amounts of data (Sanchez and Lucas, 2002), the interpretation of which requires complex, computer-supported analysis techniques. The literature provides complementary approaches for analyzing and validating MAS based on empirical observations: While conrmatory techniques such as statistical hypothesis tests or model-based trace-analysis (e.g. Howard et al., 2003) allow for the falsication of a-priori specications or hypotheses, exploratory techniques serve to investigate and better understand previously unknown aspects of MAS behavior (e.g. Botía et al., 2004). Due to the experimental character of MAS development (Uhrmacher, 2000, p. 39), exploratory analysis techniques seem well-suited to foster analysis and validation tasks. Several MAS development tools support exploratory analysis by means of powerful visualization techniques (e.g. Ndumu and Nwana, 1999). To overcome inherent drawbacks of visualization (e.g. in handling large amounts of high-dimensional data) the additional use of data mining (DM) in MAS analysis and validation has increasingly been proposed in the last years (e.g. Remondino and Correndo, 2005). 5 The notion of data mining will be introduced later in detail. For the moment it is used as an umbrella term for computer supported methods from machine learning and exploratory statis- tics that automatically generate models from large amounts of data. In MAS analysis, data mining is in particular suited to nd implicit interaction patterns and relations between pro- cesses at multiple levels of a system. Such patterns can serve as meaningful high-level system descriptions supporting data-intensive analysis tasks such as validation (see also Remondino and Correndo, 2005). This has some tradition in simulation analysis where simulation out- put is aggregated to more abstract meta models used in result interpretation, validation, and optimization (e.g. Barton and Szczerbicka, 2000). 4 All literal citations from German sources were translated by the author of this thesis. 5 see also Cabac et al. (2006b, Sec. 1) 16
- 26. 1.2. Objectives and Contributions of the Thesis Since processes are an important aspect and event logs an important data source in ABS, a class of highly appropriate techniques is found in a DM subeld called process mining (PM) (Aalst and Weijters, 2004). These techniques are typically applied in workow management and serve to reconstruct process models from workow execution logs. Similar to ABS, PM research considers multiple system views with a focus on concurrent control ow and organisational models. Despite these similarities, relations between both elds have not been considered in the literature often. There are only few explicit entries (e.g. Hiel, 2005) and [...] recent [...] case example[s] ([e.g.] Dongen et al., 2006b). (Knaak, 2007, p. 30) However, process mining has been applied in 'MAS-like' domains, such as inter-organizatio- nal workows (e.g. Aalst, 2004), computer-supported cooperative work (Aalst, 2005a), or web services (e.g. Gombotz et al., 2005). Related techniques such as grammar inference have been applied to the analysis of MAS as well (e.g. Mounier et al., 2003). Summarizing as will be substantiated later the 'research landscape' in this eld has evolved rapidly within the last years on the one hand (see also Dongen et al., 2006b). On the other hand, the approaches appear heterogeneous and sometimes far from being applicable to real world scenarios in MAS and simulations. 1.2. Objectives and Contributions of the Thesis Though the spectrum of topics and applications discussed in this thesis is quite broad, the presented work is positioned in the eld of multi-agent-based simulation (MABS). More specic, the main objective is to evaluate and methodologically enhance the applicability of process mining and related techniques to the analysis and validation of MABS. This restriction seems sensible for several reasons: Firstly, the motivation for this work origi- nates from the lack of appropriate validation techniques in agent-based simulation that became apparent to the author during a research project on courier service logistics (Bachmann et al., 2004; Deecke et al., 2004; Knaak et al., 2003). Secondly, analyzing and validating simulation output is a restricted problem characterized by good data quality and a need for semi- (instead of fully) automated techniques. Considering the current state of process mining techniques, this problem seems manageable, and developments from this context can be extended in the future towards more complex tasks such as autonomous learning. Thirdly, the presented approach can straightforwardly be transfered to the more general but closely related eld of agent-oriented software engineering (AOSE). 1.2.1. Research Questions To rene the general objective stated above, the following research questions will be discussed in the thesis: 1. Q1 - State-of-the-art: In which way have process mining and related techniques already been applied to MABS and similar domains? What aspects of the systems have been analyzed and which analysis tasks (such as validation or calibration) have been supported? 17
- 27. 1. Introduction 2. Q2 - Conceptual foundations: What is an appropriate conceptual foundation for the integration of process mining, simulation, and MAS? What are the general possibilities and limitations of this integration and in what way does it contribute to the respective elds? 3. Q3 - Techniques for interaction mining: How can process mining algorithms and re- lated techniques be combined and extended to foster the complex task of analyzing and validating simulated agents' interactions? 4. Q4 - Tool integration: How can process mining techniques and tools be embedded into software environments for simulation studies? 5. Q5 - Practical benet: What is the practical value of process mining in model-driven and code-centric simulation approaches? 6. Q6 - Level-encompassing validation: How can process mining be combined with advanced techniques from simulation (e.g. simulation-based optimization) in order to support the task of analyzing and validating processes at multiple levels of a (simulated) MAS? 6 Note that the scope of the research questions Q2 to Q4 covers most constituents of an approach (i.e. tools, applications, techniques, and methods, Cabac, 2010, p. 23) according to the denition by Moldt (1996, p. 30, cited in Cabac, 2010, p. 23). 1.2.2. Conceptual Framework The rst question is tackled by means of a literature review, where the objective is to evaluate the current state-of-the-art in analysis and validation of MA(B)S 7. Due to the broad applica- bility of the agent metaphor, this review has to take into account several neighboring elds such as distributed systems, software reverse engineering, and social network analysis. In order to answer the second question, a conceptual framework for the integration of process mining and MABS will be derived from the literature review. The framework includes comple- mentary dimensions of analysis perspectives (i.e. what aspects of MAS can be analyzed), use cases (i.e. when and how automated analysis techniques can be applied in the dierent phases of a simulation study), techniques (i.e. what mining, representation, and support techniques can be applied, and how they can be combined), as well as simulation-specic requirements and limitations. Despite the large body of case examples, there are only few general attempts to integrate auto- mated analysis techniques into AOSE or MABS (e.g. Arroyo et al., 2010; Köster, 2002; Ndumu and Nwana, 1999; Remondino and Correndo, 2005) that the presented framework combines and extends. The contribution is therefore twofold: On the one hand, it allows to classify the heterogeneous work found in the literature in a coherent way and point out directions for further research. On the other hand, it serves as a guideline for the practical application of process mining techniques during a simulation study. 6 Note that the thesis by Chen (2009), which was published in parallel to the work on the thesis at hand, is solely dedicated to this question. This work will be cited and related to the presented approach in many places in the following (e.g. Sections 5.2.2.4 and 6.2.6). 7 This notation is used when both multi-agent systems (MAS) and multi-agent-based simulation (MABS) are addressed. 18
- 28. 1.2. Objectives and Contributions of the Thesis A novel aspect [of the framework] is the use of the Petri net-based Mulan model (MULti Agent Nets, Rölke, 2004) as a formal foundation (Knaak, 2007, p. 30) for integrating process mining into MA(B)S. Mulan is a Petri net-based MAS architecture that builds upon the Reference net formalism by Kummer (2002). Petri nets are a common means for result representation in process mining. Mulan provides further structure by distinguishing multiple Petri net-based views of a MAS. Thereby, it might help to formalize the framework's analysis perspectives in order to perform more MAS-specic analyses. Reference nets can also be used to formalize the use cases in the style of scientic workows. 1.2.3. Techniques, Tools, and Case Studies After dening the conceptual frame, the scope of the discussion is narrowed down to the appli- cation and extension of specic process mining techniques and tools for MABS analysis (and thereby refer to research questions 3, 4, and 5). From the various perspectives discussed be- fore, the focus is put on agent behavior and interactions. Two complementary modeling and simulation approaches developed at the University of Hamburg will be chosen as case examples for an integration of process mining. These will be explained in the following. 1.2.3.1. Process Mining in the PAOSE Approach The rst is the model-driven Petri net-based AOSE (Paose, see e.g. Cabac, 2010) approach developed at the University of Hamburg's theoretical foundations group (TGI). In Paose, simulation is mainly used to validate the developed applications. Since process mining appears as a promising support technique due to its strong relation to the Petri net formalism, an integration is attempted in cooperation with members of this group (mainly Dr. Lawrence Cabac and Dr. Daniel Moldt). At the conceptual level, it will be shown that the Mulan model (Rölke, 2004) with its related development process and tools (Cabac, 2010) is an appropriate basis for realizing the analysis and validation tasks described in the framework. This is mainly due to the fact, that a com- mon executable formalism is available to represent the conceptual and computer model, the meta-models extracted from observed data, and the experimentation and analysis processes themselves. At the technical level, an approach towards the reconstruction of agent interaction protocols from message logs observed during simulation is presented. Agent interaction mining is a complex task that requires to combine and extend several existing process mining techniques. While the interaction mining approach is closely related to parallel work from the web service context (e.g. Gaaloul, 2005; Gombotz et al., 2005), it contains some novel aspects indicated in the following. A processing chain will be presented as an extension of work by Schütt (2003) that allows to reconstruct models of basic interactions between pairs of agents. One central part is a simple algorithm to mine process models with non-unique activity labels from event-based message logs. Schütt (2003) proposes a hybrid algorithm consisting of a subsequent grammar inference and concurrency detection stage. The grammar inference is, however, restricted to cycle-free models and the concurrency detection is only described conceptually. 19
- 29. 1. Introduction The grammar inference is therefore extended towards cyclic models by using the well-known k- RI algorithm (Angluin, 1982), the concurrency detection is operationalized, and the algorithm is compared to related approaches based on log preprocessing (e.g. Gu et al., 2008) and the theory of regions (e.g. Rubin et al., 2006). Furthermore, a preceding log segmentation and role mining stage is integrated (based on work from, among others, Dustdar and Gombotz, 2006; Greco et al., 2004; Schütt, 2003; Srinivasa and Spiliopoulou, 2000; Vanderfeesten, 2006) that clusters similar courses of interaction in the absence of unique conversation and protocol identiers. The basic interaction mining chain is conceptually expanded towards the reconstruction of hierarchical and multicast protocols. Multicast protocols are special hierarchical protocols closely related to the multiple instantiation workow pattern, where a variable number of instances of the same activity (or message) are executed (or sent) in parallel (see e.g. Guabtni and Charoy, 2004). While several workow patterns can be detected by process mining algorithms (see e.g. Gaaloul et al., 2004), rst (and partly rather preliminary) approaches to reconstruct control ow models containing multiple instantiation constructs have only been presented recently (e.g. Canbaz, 2011; Kikas, 2011; Kumar et al., 2010; Lou et al., 2010b). In this thesis, an algorithm for reconstructing multicast protocols and detecting synchronizations between the participating agents will be sketched and compared to the related approaches. At the tool level, the plugin-based architecture of the Petri net simulator Renew (Kummer et al., 2006) and the lightweight component mechanism of net components (Cabac, 2002) are employed to model analysis and validation processes (called mining chains here) as hierarchical scientic workows (see e.g. Guan et al., 2006). At a small example it is shown how validation and roundtrip engineering can be supported. 1.2.3.2. Process Mining in a Discrete Event Simulation Study The second case study is conducted on the basis of a research project on the simulation of sustainable logistics strategies for large city courier services (Deecke et al., 2004). The author of this thesis started to work on this project during his diploma thesis (Knaak, 2002) and developed parts of the employed software framework. As a domain for process mining, the courier service study complements the Paose approach in several respects: (1) The software development is mainly code-centric, based on the discrete event simulation framework DESMO- J (Lechler and Page, 1999) and its extension FAMOS for agent-based simulation (Knaak, 2002; Meyer, 2008). (2) The study employs discrete event simulation to perform a quantitative analysis of a target system. (3) The number of agents in the model is relatively high, and large amounts of log data are produced. The applicability of process mining to this example is investigated in an aliated bachelor thesis by Haan (2009). Beyond the results gained from this study, the author of this thesis presents a rst, strongly simplied implementation of the complex interaction mining procedure mentioned above and discusses ways to further continue the integration of MABS with process mining techniques and tools. In particular, it is sketched how process mining-based analysis workows can be integrated into a generic simulation environment (Czogalla et al., 2006) that helps users to perform experiments 20
- 30. 1.3. Outline of the Thesis with (in principle) arbitrary simulators based on the programming language Java (e.g. Arnold et al., 2000). The environment is conceptually rooted in experimentation and analysis tools developed earlier at the University of Hamburg's simulation group (MBS) such as DISMO (Gehlsen, 2004), CoSim (Bachmann, 2003), and MOBILE (Hilty et al., 1998). The tool is implemented in the form of plugins for the well-known Eclipse platform 8. A prototypical integration of process mining algorithms implemented in the tool ProM (Don- gen et al., 2005) is tackled with the aid of the scientic workow system KNIME (Chair for Bioinformatics and Information Mining at Konstanz University, 2007) and might in the future employ Renew as an alternative, possibly more exible, workow engine (Simmendinger, 2007; Simmendinger et al., 2007). Beyond that, it will be discussed how the environment relates to recent similar eorts like the framework WorMS (Workows for Modeling and Simulation) by Rybacki et al. (2011). 1.3. Outline of the Thesis Due to the relatively broad scope of the thesis, the presentation is grouped into two parts: (1) foundations and state of the art, (2) concepts and case studies. An overview of the structure of the thesis is shown in Figure 1.1. 9 The rst part starts with an introduction of concepts from modeling and simulation in Chapter 2. This chapter introduces basic modeling techniques from the domains of discrete event simulation (DES), Petri net theory, and workow modeling. A particular way of using the UML 2 notation (e.g. Jeckle et al., 2002) for simulation modeling is introduced and related to the DES world views 10 and the reference net formalism. Beyond that, the chapter reviews the later stages of the modeling process (Edmonds, 2000, p. 23) including experimentation, analysis, and validation as the main focus of this thesis. Chapter 3 reviews basic concepts from multi-agent systems and agent-based simulation, cov- ers modeling and implementation techniques from MABS and AOSE, and nally focuses on the problem of analysis and validation (i.e. ultimately understanding) of agent-based models. With respect to the techniques used in the thesis, the focus is put on UML 2 and the refer- ence net-based Mulan architecture. Besides providing the reader with the thesis' conceptual foundations, a main objective of the chapter is to motivate the need for advanced analysis and validation techniques. Chapter 4 completes the foundations by presenting data mining and especially process mining as promising candidate methods. After introducing foundations concerning the validation of agent-based simulations in general, Chapter 5 brings together both elds by presenting an extensive review of related work on MABS analysis and validation with the aid of data mining, process mining, or similar techniques. The second part of the thesis elaborates on the author's contributions described in Section 1.2. Based on the literature review, Chapter 6 presents the conceptual framework for integrating process mining and MABS. It closes by classifying (small parts of) the previously reviewed 8 http://www.eclipse.org, last visit 2012-11-17 9 It is no surprise that several theses on topics related to modeling use precedence graphs to display dependencies between chapters (e.g. Klügl, 2000, p. 5; Medeiros, 2006, p. 12). This thesis is no exception. 10 based on pre-publications like Page and Kreutzer (2005, Sec. 4) and Knaak (2006) 21
- 31. 1. Introduction Figure 1.1.: Overview of the chapters of this thesis in the form of a precedence graph. A directed edge in the graph indicates that a chapter largely builds upon the results of a previous chapter. work along the framework's dimensions in order to present a coherent view on the 'research landscape' and identify promising directions for the development of new techniques. Chapter 7 reports the rst case study in the Paose approach with a focus on agent interaction mining techniques as well as architectural integration into Mulan. Chapter 8 reviews the procedure and results of the second case study in the DESMO-J context with a focus on evaluating the practical value of process mining in a large simulation project. Chapter 9 concludes the thesis by deriving implications from the two case studies, critically discussing their results and pointing out directions for further research. As a nal remark it should be emphasized that the work presented in this thesis (like most similar projects) was neither developed 'in isolation', nor written down 'in one go'. Therefore, several parts were developed in cooperation with colleagues, and some of the texts were previ- ously published as part of conference and journal papers as well as a textbook on simulation. Though these pre-publications were partly written together with other authors, this monograph naturally focuses on those parts that the author of this thesis contributed to most. In particular, parts of the Chapters 2 and 3 are based on Chapters 4 (UML modeling), 8 (model validation) and 11 (multi-agent-based simulation) of the Java Simulation Handbook (Page and Kreutzer, 2005), as well as on articles about simulation modeling with UML 2 by (Knaak and Page, 2005, 2006). The practical application of UML 2 to discrete event simulation modeling was investigated together with Thomas Sandu. 22
- 32. 1.3. Outline of the Thesis As already mentioned, much of the research presented in Chapters 6 and 7 was conducted together with Dr. Daniel Moldt and Dr. Lawrence Cabac from the Department of Informatics' theoretical foundations group (TGI). The monitoring tool presented in Chapter 7 was imple- mented by Frank Heitmann and Florian Plähn. Intermediate results were pre-published as conference papers and technical reports (Cabac et al., 2006a,b,c, 2008a; Knaak, 2006, 2007). Several parts of the second case study from Chapter 8 were conducted as part of the bachelor thesis by Johannes Haan (2009) and the study project by Sven Kruse (2005). The simula- tion system described in the latter Sections of this chapter was developed together with Rainer Czogalla and several (former) students including Felix Simmendinger and Philip Joschko. Inter- mediate results were pre-published in conference papers by Czogalla et al. (2006), Simmendinger et al. (2007), and the diploma thesis by Simmendinger (2007). To emphasize this embedding of an individual dissertation project into a larger community (including you as a reader), the rst person plural narrative mode 11 ('we') will often be preferred in the following. 12 11 http://en.wikipedia.org/wiki/First-person_narrative, last visit 2012-11-17 12 for a similar discussion see Eagleman (2011, p. 266) 23
- 34. Part I. Foundations and State of the Art 25
- 36. 2. Modeling and Simulation This chapter reviews relevant foundations from system theory and simulation and brings out their connotations in the context of this thesis. After an introduction to fundamental terms, we focus on the later stages of the modelling process (Edmonds, 2000, p. 23) including experimen- tation, output analysis, and validation, as the thesis' main topics. The presentation is largely based on the simulation handbook by Page and Kreutzer (2005, Chs. 1, 2, 4, 5, 7, 8, and 9). Chapters 4 and 8 of that book were co-written by the author of this thesis. 2.1. Basic System Theory According to Page and Kreutzer (2005, p. 4) a system is a subset of reality which we study to answer a question; i.e. its boundary to the environment in which it is embedded will be determined by the question we wish to ask. Important points of this denition are that (a) the term is generic, i.e. anything can be regarded as a system, and that (b) system identication is a constructive act, since systems are always considered in relation to an observer and an observation goal. Further following Page and Kreutzer (2005, p. 5), a system must have a number of distinct and clearly identiable components which may themselves be considered as systems at a lower level. Systems are decomposed hierarchically to perform a complexity reduction (Kouvastos, 1976, p. 1081). We distinguish between elementary components with basic properties (such as position or velocity, see also Page and Kreutzer, 2005, p. 25) and non-elementary sub-systems whose properties emerge from the interplay of their components. The set of all properties observed at a certain instant is called system state (Page and Kreutzer, 2005, p. 5). The system theoretical stance is characterized by a duality of structure and behaviour (London, 2004, p. 166). Structure refers to the statical aspects of a system, i.e. the network of relations between the existing elements and their roles within this network (see e.g. Wikipedia, 2007). System behavior is described in terms of one or more processes, where a process is understood as a chronological sequence of state variable vectors (Page and Kreutzer, 2005, p. 5). System structure and behavior are closely linked and mutually dependent (Wikipedia, 2007). Whereas the system structure sets up boundary conditions for the processes running within it, the processes can modify the structure, thus giving rise to new boundary conditions for future behavior. Due to such complicated interrelations, system behavior often appears counter intuitive and hard to predict (Page and Kreutzer, 2005, p. 5). 2.1.1. Complexity and Emergence Auyang (1998, p. 13) notes that there is no precise denition of complexity and degree of com- plexity in the natural sciences, and continues by identifying two dierent meanings of the term. 27
- 37. 2. Modeling and Simulation On the one hand, it is applied in an intuitive way to describe self-organized systems that have many components and many characteristic aspects, exhibit many structures in various scales, undergo many processes in various rates, and have the capability to change abruptly and adapt to external environments (Auyang, 1998, p. 13). In the same manner, Page and Kreutzer (2005, p. 5) state that system complexity depends on the number of state variables (properties) and the density of their connections. On the other hand, formal approaches from computer science dene the term more concisely. A well-known measure is the computational complexity of a problem, i.e. the number of steps (computation time complexity) and the amount of memory (computation space complexity) needed to algorithmically solve the problem in relation to the size of its encoding (see e.g. Auyang, 1998, p. 13 or Gruska, 1997, Ch. 5). Another formal measure is the information content complexity 1 of a character sequence dened as the length in bits of the smallest program capable of specifying it completely to a computer (Auyang, 1998, p. 13). This measure assigns the lowest complexity to very regular sequences, and the highest complexity to purely random sequences without any patterns (Auyang, 1998, p. 13). While the former seems plausible, the latter might appear counter-intuitive, since complexity is not commonly understood as a complete lack of structure. Formal denitions of complexity seem less useful in the context of this thesis due to their limited scope: Computational complexity is a dierent concept than complexity in system theory. Information content complexity might be interpreted to that eect that a more complex system (program) is able to generate more variable patterns of behavior (character sequences). A purely random sequence contains so many variations that it cannot be described more compactly than by stating the sequence itself (Auyang, 1998, p. 13). In system theory, we are often interested in phenomena with a medium information content complexity, i.e. systems that exhibit behavioral variety, but still allow for the recognition of patterns. 2 The possibility to aggregate system behavior to a more compact description is of great importance for the applicability of data mining techniques described below. A related quality of complex systems is emergence. This concept is based on the observation that systems include multiple levels with at least a macroscopic level of the system as a whole and a microscopic level of the basic components. According to Jones (2003, p. 418), the term is applied to the appearance of novel, coherent objects [at the macroscopic level] that are not predictable from the system's [microscopic] parts. The notion of emergence is used quite ambiguously, since for some authors, it denotes an invocation of something mystical (Jones, 2003, p. 418), while others use it as a shorthand ex- planation for multi-level phenomena within a reductionist world view (Jones, 2003, p. 421). Cariani (1991, p. 771) 3, for instance, subsumes the fact that complex global forms can arise from local computations under the notion of computational emergence. This includes deterministic phenomena like swarm formation in articial life simulations or the appearance of identiable shapes in cellular automata. In this thesis, we use the term complexity in the intuitive way for systems that 1 which is also called Kolmogorov complexity, see e.g. Gruska (1997, p. 398) 2 See also the discussion on pattern-formation by Gribbin (2005, p. 135), who uses the term edge of chaos. 3 cited in Jones (2003, p. 418) 28
- 38. 2.2. Computer Simulation • consist of a large number of components, where each component itself exhibits a certain behavioral variability and exibility (i.e. complex micro-level processes), • contain a large number of relations and interactions between the components (includ- ing feedback) and possibly a variable structure (i.e. complex macro-level structures and processes), • can be viewed at multiple levels, where relations between the levels are often obscured due to distributed and sensitive cause-eect dependencies (i.e. complex inter-level relations). We will avoid using the term emergence due to its non-scientic connotations. However, we will regard multi-agent systems that exhibit computational emergence where macroscopic patterns emerge from microscopic interactions through deterministic computations. Data mining will be applied to expose such patterns and the rules that generated them from observed data. 2.1.2. Models The term model describes a simplied image of a system. As a main benet, a model allows to conduct controlled experiments that might be inconvenient or impossible with the real system (see Niemeyer, 1977, p. 57 cited in Page and Kreutzer, 2005, p. 5). The complexity of the system under analysis is reduced by considering only the most relevant parts in the model and by putting them in a simplied form (see e.g. Heinrich, 2002, p. 1046). This abstraction and idealization (Page and Kreutzer, 2005, p. 6) needs to preserve structural similarity between the model and the real system (Heinrich, 2002, p. 1046) with regard to a certain purpose or set of questions [... the model] can answer (Page and Kreutzer, 2005, p. 5). Given this similarity, the model is considered as valid and its analysis allows to draw conclusions on the real system. The notion of models is also central to statistics and data mining. In this context, Hand et al. (2001, p. 9) dene a model (structure) as a global summary of a data set. According to Han and Kamber (2000, p. 24), one main purpose of data mining is nding models [...] that describe and distinguish data classes or concepts [...] The derived model is based on the analysis of a set of training data [...]. Large data sets are thus algorithmically aggregated to abstract models that describe the data more compactly. This is somehow similar to modeling in simulation with the exception that the abstraction is performed automatically. One important property of models in statistics and machine learning is generalization. To be useful for prediction and classication tasks (see Han and Kamber, 2000, p. 24), a model should not only describe the specic training data set that it has been derived from, but a possibly large range of data that the underlying system might be able to generate. We will continue this discussion in Section 4.1.2. 2.2. Computer Simulation To understand complex systems we analyze abstract models and draw conclusions on the origi- nal. The analysis of formal models can be performed either with analytical methods that allow to compute a closed-form solution 'in one go', or by using simulation, where the model state is 29
- 39. 2. Modeling and Simulation advanced step by step in order to emulate the temporal development of the real system (Page and Kreutzer, 2005, p. 10). Simulation can thus be dened as the process of describing a real system and using this model for experimentation with the goal of understanding the system's behaviour or to explore alternative strategies for its operation (Shannon, 1975, cited in Page and Kreutzer, 2005, p. 9). This general denition ts many activities in computer science such as the stepwise execution of a computer program for the purpose of debugging or the token-game in Petri nets (see Section 2.3.2.1). Though this general meaning is sometimes referred to here, we mostly draw to the more specic denition of Page and Kreutzer (2005, p. 9), who use the term to denote the eld of computer simulation as well as the execution of a computer simulation study. In this context, the model building process is explicitly mentioned, and simulation is characterized as the modelling of dynamic processes in real systems, based on real data and seeking predictions for a real system's behaviour [. . . where] models are represented by (simulation) programs, and simulation experiments (runs) are performed by a models's execution for a specic data set. (Page and Kreutzer, 2005, p. 9) This denition emphasizes the embedding of the actual 'simulations' into a scientic or indus- trial research study, where activities like data acquisition, model validation, experimentation, result analysis, and presentation are of equal importance than the modeling and simulation itself. 2.2.1. Classication of Simulation Models Typical dimensions for the classication of models in simulation, which may also apply to other elds, are shown in Figure 2.1 (e.g. form of analysis, purpose, etc.). From these dimensions, Page and Kreutzer (2005, pp. 6) emphasize the purpose, the representation medium, and the type of state changes occurring in the model. 4 2.2.1.1. Purpose of Models Models are used to better explain and understand the represented system, to predict its fu- ture behavior, to support the design of a planned system or to optimize the operation of an existing one (Page and Kreutzer, 2005, p. 7): The purpose of a model strongly inuences its properties. Explanatory models should represent the system's structure and behavior in an appropriate and interpretable way to allow for an understanding of the observed phenomena. For predictive models it might be sucient to mimic the system's behavior closely enough for successful predictions, even if the model's behavior is generated by unrealistic or not explicitly understandable structures. We will take up this point in Section 4.1.2. 2.2.1.2. Representation Forms Models are represented in dierent forms ranging from physical and verbal models to graphical and mathematical models (Page and Kreutzer, 2005, p. 6). One might additionally consider the explicitness and conciseness of model representation (Page and Kreutzer, 2005, p. 6): Mental 4 Brade (2003, Sec. 1.2) focuses on the latter two dimensions as well. 30
- 40. 2.2. Computer Simulation models only exist in the modeller's mind while external models are represented in some other medium for means of communication. Formal models are described in a language with a concise formal semantics which permits their operationalization. In this thesis we further dierentiate between explicit formal models represented in a modeling language such as UML or Petri nets, and implicit formal models 'hidden' in programming language code. While this criterion is somewhat fuzzy, explicit models are deemed more understandable and veriable than implicit models. Figure 2.1.: Common dimensions for the classication of models. Compiled with modications from Brade (2003); Klügl (2001); Lechler and Page (1999); Page and Kreutzer (2005). Model types treated in this thesis are shaded in grey. 2.2.1.3. Types of State Changes An important criterion to characterize dynamic simulation models is the type of state changes, which might occur continuously or instantaneously at discrete points in time. The next model state can be determined by its predecessor in a deterministic or stochastic fashion (Page, 1991, p. 6). Concerning discrete simulation models we distinguish two kinds of simulation time advance (Page et al., 2000, p. 6): In time-driven models, the clock proceeds in equidistant intervals and the model state is permanently re-computed. In event-driven models, time advance is triggered by a sequence of events that occur in arbitrary intervals. Since the model state is only updated 'when something has happened', event-driven models often exhibit a lower computational complexity (Page et al., 2000, p. 6). 31
- 41. 2. Modeling and Simulation 2.2.1.4. Modeling Point of View A complementary dimension for simulation model classication is the modeling point of view. According to Klügl (2000, p. 42) a macroscopic model represents the whole system as a single object, describes its state by means of variables and relates them to each other with respect to certain parameters, while a microscopic model consists of multiple components whose interactions generate the model's overall behavior. A multi-level model is composed of multiple micro models at dierent levels of aggregation (Klügl, 2000, p. 44). While macroscopic models are mostly formulated in terms of dierential equations (Klügl, 2000, p. 42), microscopic modeling styles are more diverse, ranging from cellular automata to discrete event as well as individual- and agent-based models. 5 By comparison, microscopic modeling allows for a more detailed and straightforward representation of real systems consisting of multiple components, and is better suited for the explanation of their behavior (Klügl, 2000, p. 72). Problems are the models' high computational complexity and the diculty to nd an appropriate level of detail (Klügl, 2000, pp. 73). 6 This thesis is, on the one hand, concerned with agent-based simulation models, i.e. microscopic discrete event models whose overall behavior is encoded by an (often implicit) algorithmic description of the components. On the other hand, explicit formal and graphical models at dierent levels are reconstructed from observations of the models' behavior to aid analysis and validation. 2.2.2. World Views of Discrete Event Simulation The traditional world views in discrete event simulation (DES) are event-, process-, activity-, and transaction-orientation (see e.g. Page and Kreutzer, 2005, Ch. 5). These are characterized by dierent, but closely akin concepts for relating model state and simulation time (Page and Kreutzer, 2005, pp. 24) depicted in Figure 2.2. The basic unit in discrete modeling is the event. Events describe instantaneous system state changes at discrete but arbitrary points in (simulation) time. At the next level of aggregation, we consider time-consuming activities, where each activity consists of a start and end event. Multiple related activities can be aggregated to a process describing an entity's life-cycle. Each concept builds the foundation for one or more modeling styles. In event-orientation (see e.g. Page and Kreutzer, 2005, Ch. 5.2.2), we identify relevant entities and events of the system. In the model, each event is represented by an event class with an event routine that algorithmically describes the caused state changes. This modeling style often (but not necessarily) takes in a top-down view in that each event describes the set of all transformations of all relevant entities at specied points in time (Page and Kreutzer, 2005, p. 108). In contrast, the process-oriented world view takes in a bottom-up view where all state changes concerning an entity are aggregated into a single algorithmic description, i.e. the entities lifecycle executed as a simulation process (Page and Kreutzer, 2005, p. 98). During simulation, a 5 For an overview see e.g. Klügl (2000, Ch. 3.2) 6 In fact, this author discusses agent-based versus macroscopic models, but many arguments apply to micro- scopic models in general. 32
- 42. 2.3. Modeling Techniques Figure 2.2.: Relations between events, activities, and processes with a possible interpretation in a DES model (adopted with modications from Page, 1991, p. 27). process undergoes alternating phases of computational activity and passiveness. Active phases correspond to events where the process instantaneously modies its own or other entities' states. Simulation time only passes during the passive phases. These either represent conceptually active states, where the process executes an activity after which it re-activates itself, or passive states, where the process waits for re-activation by another process (Page and Kreutzer, 2005, p. 100). Process interaction is often limited to untyped activation signals, but might also include typed signals to represent interrupt conditions (Page and Kreutzer, 2005, p. 105). Activity-oriented models (Page and Kreutzer, 2005, pp. 131) are described in terms of time consuming activities together with preconditions for their invocation (see the level 'activities' in Figure 2.2). Their execution somehow resembles rule-based systems: A scheduler chooses the next activity whose preconditions hold and executes it by advancing the simulation clock to its end time and performing the assigned state changes. Transaction-oriented models consist of a net of permanent resources (blocks) that transient entities (transactions) ow through (Page and Kreutzer, 2005, p. 129). Page and Kreutzer (2005, p. 129 and p. 132) show how both modeling styles can be mapped to process-oriented models. 2.3. Modeling Techniques Executable simulation models are often stated implicitly in the form of program code while conceptual models are specied using explicit graphical notations. To narrow this semantic gap (see e.g. Klügl, 2000, p. 76) several formal and semi-formal notations are applied. In the following, we introduce the Unied Modeling Language (UML) and reference nets as notations used to explicitly represent simulation models in this thesis. 33
- 43. 2. Modeling and Simulation 2.3.1. UML 2 As noted in (Knaak and Page, 2006, p. 33), UML is quite commonly used as a simulation modeling language today. Several applications (see e.g. De Wet and Kritzinger, 2004) and extensions (see e.g. Oechslein et al., 2001) are reported in the literature (Knaak and Page, 2006, p. 33). Page and Kreutzer (2005, Ch. 4) as well as Knaak and Page (2006) present our way of applying and extending UML 2 for discrete event simulation that is briey reviewed below. 2.3.1.1. The Unied Modeling Language In (Page and Kreutzer, 2005, p. 60) 7 we have introduced the Unied Modeling Language by determining what UML is and of equal importance what it is not. According to the UML reference manual, it is a general-purpose visual modeling language that is used to specify, visualise, construct, and document the artifacts of a software system. As Jeckle et al. (2002, p. 10) point out, UML is not complete, not a programming language, not a formal language, not specialized to an application area and [...] rst of all not a method or software process. Further following the shorter presentation in (Knaak and Page, 2006, pp. 34-35): UML 2.0 contains a total of 13 diagram types to visualise dierent aspects of object- oriented modelling (Jeckle et al., 2002, p. 15). According to Jeckle et al. (2002, p. 16) these diagrams can be broadly divided into three classes [mirroring the dualism of structure and behavior mentioned in Section 2.1]: • Structural diagrams model the static structure of a system. Among them are class diagrams, object diagrams, package diagrams, component diagrams, composition struc- ture diagrams and deployment diagrams. • Behaviour diagrams serve to display the [...] behaviour of objects or components at dierent levels of detail. This [...] includes use case diagrams, activity diagrams, statechart diagrams and several interaction diagram types. • Interaction diagrams are special behaviour diagrams that focus on the interactions going on between [...] objects in a system. [... They] can be divided into sequence diagrams and timing diagrams that emphasise the temporal order of interaction events on the one hand and communication diagrams that highlight the general structure of the cooperation between partners in an interaction on the other hand (Jeckle et al., 2002, p. 391). [...] interaction overview [...] diagrams represent a mixture between activity diagrams and interaction diagrams showing the causal and temporal interplay among dierent interaction scenarios (Jeckle et al., 2002, p. 419). [...] the concepts and notations of the UML are [...] dened in [a so-called meta] model that is [itself] expressed in terms of the UML (Born et al., 2004, p. 12). This object-oriented language denition makes extensions of the UML quite easy. [...] Such extensions are either stated as extensions of the metamodel itself, or by using a lightweight extension mechanism called stereotyping (Born et al., 2004, p. 245). According to Jeckle et al. (2002, p. 95) a 7 and similarly in (Knaak and Page, 2006) 34
- 44. 2.3. Modeling Techniques stereotype is a a class in the metamodel that is able to further specify other classes [...] by extension. [... As an example, we might] represent entity types in DES models [by extending] the meta class Class [...] with a stereotype entity. [...] Now entity types in class diagrams are marked by attaching the term entity in angle brackets to the respective model elements. 2.3.1.2. UML in Simulation A main feature that makes UML suitable for the DES domain [... is] the event-based communication model underlying all behaviour diagrams (see Jeckle et al., 2002, pp. 172) (Knaak and Page, 2006, p. 36). Similar to DES, an event in UML is a relevant occurrence such as sending a message or invoking an operation (Jeckle et al., 2002, p. 173). Dierent from DES, a UML event has a lifecycle consisting of creation, distribution and consumption, and its occurrence in a real system might consume time (Jeckle et al., 2002, p. 173). We can, however, abstract from these aspects and regard UML events in DES models as instantaneous. Simulation practitioners benet from UML diagrams as a common and simulation-software inde- pendent basis for documenting, visualizing and understanding the model structure (Richter and März, 2000, p. 2). The dierent UML diagrams provide multiple views focusing on [... complementary] aspects of the model. (Knaak and Page, 2006, p. 36) In an industrial or non-computer-science context, the diagrams might be understood more easily than more abstract formal languages like Petri nets (see Section 2.3.2.1). Nevertheless, the quite concise semi-formal semantics of UML 2 behaviour diagrams [...] provide support for the task of model validation and verication as well as code generation (Knaak and Page, 2006, p. 36). Current approaches towards model driven software development apply transformation rules that map UML models to executable code. 8 In the following, we briey introduce UML activity and interaction diagrams for modeling the dynamics of discrete simulations. The presentation is based on Page and Kreutzer (2005, Ch. 4) and Knaak and Page (2006). Basic concepts of object orientation (such as inheritance) and their representation in class, object and package diagrams are taken for granted (for an overview see e.g. Jeckle et al., 2002, Chs. 3, 4, 5). 2.3.1.3. Activity Diagrams In (Page and Kreutzer, 2005, pp. 77), we introduced activity diagrams with a focus on DES: According to Jeckle et al. (2002, p. 199) activity diagrams are [an appropriate] notation [...] for modelling [...] operations, use cases, and business processes. [... Consequently, they] are particularly well suited for modelling lifecycles of simulation processes in [... DES]. Since they provide features such as concurrency, object ow[,] and message passing they are convenient for showing the synchronization of two or more processes. [...] In UML 2.0, the statechart-like event-handling semantics of [UML 1.x ...] has been replaced by a Petri net-like token semantics [see also Section 2.3.2.1]. 8 On the application of model driven software development in the simulation context see Sandu (2007). 35
- 45. 2. Modeling and Simulation In (Knaak and Page, 2005, p. 404) we observed that the synchronization operations of the process-oriented world view (see Section 2.2.2) map quite obviously to send- and receive-signal actions [...] (Jeckle et al., 2002, p. 214). [...] Generally any time consumption is modelled using receive-signal actions, whereas normal action nodes correspond to active process phases without passing of simulation time. Figure 2.3 shows [an example of] two process classes [...] that synchronize via sending and reception of activation signals. Figure 2.3.: Synchronisation of [... simulation processes in an imaginary] Gravel Pit model via sending and reception of signals. Figure and caption adopted from Knaak and Page (2006, p. 38). The separation by activity regions (Jeckle et al., 2002, pp. 245) makes it possible to display multiple interacting processes in a single diagram. As carried out in (Knaak and Page, 2006, p. 38) we denote process activations by a send-signal action (Jeckle et al., 2002, p. 214) with the stereotype activate. [...] The passive state is indicated by a receive-signal action (Jeckle et al., 2002, p. 214) with the stereotype passive. [...] [In compliance with ...] Jeckle et al. (2002, p. 215) [... the hold operation is] modelled using a time signal reception node depicted by an hour glass symbol [...] with the additional stereotype hold [... that] delays incoming tokens for a specied duration. Further following Knaak and Page (2006, p. 39), data ow is displayed with the aid of object nodes depicted by rectangles (Jeckle et al., 2002, pp. 218). When the outgoing edge of an action node is connected to an object node, execution of the action produces a so called data token that contains the result object of the execution. The data token is stored in the object node and might serve as input to another action [... Object nodes can 36
- 46. 2.3. Modeling Techniques be] used as synchronisation constructs in [... process- and transaction-oriented] models [see Figure 2.3]. We use the stereotype queue to indicate that an object node has a queue semantic. A mapping of UML activity diagrams to further DES-specic constructs (e.g. interrupts) and modeling styles (e.g. transaction orientation) is presented by Knaak and Page (2006) and Page and Kreutzer (2005, Ch. 4 and 5). 2.3.1.4. Interaction Diagrams Figure 2.4.: An example of using basic sequence diagrams in DES (adopted from Page and Kreutzer, 2005, p. 89) In (Page and Kreutzer, 2005, pp. 87-91) we described UML interaction diagrams as follows: [While] the main purpose of [... activity] diagrams is the description of individual [...] behaviour [...] interaction diagrams are often better suited to model the interplay between multiple entities. [...] basic [...] sequence diagrams display timely ordered message sequences describing an interaction scenario [...] Figure 2.4 shows an [...] example [...that] can be regarded as a possible [rened] execution sequence of the activity diagrams shown in Figure 2.3. 37
- 47. 2. Modeling and Simulation [...] the dierent [...] roles [...] taking part in an interaction are plotted along the horizontal axis, while the vertical axis represents time (Jeckle et al., 2002, p. 327). The main diagram elements are the lifelines of the interaction partners and what messages pass between them. [...] UML distinguishes several communication modes, each of which is symbolized by a dierent arrow-head (Jeckle et al., 2002, p. 346). A lled black arrowhead indicates a synchronous message, where the sender waits [...] until the message has been processed by the receiver. The receiver answers by sending a response message, represented by a dashed arrow with lled arrowhead. [...] Asynchronous messages are symbolized by an open arrowhead. [... Here] the sender con- tinues its lifecycle without waiting for the message to be processed by the receiver. [We model method calls as synchronous messages and process interactions including passivation as asynchronous messages.] [...] Conditions ensuring the correctness of a scenario [...] can be expressed by [...] state invariants (Jeckle et al., 2002, p. 356) [...] symbolized by using rounded rectangles [...] [...] Time constraints can be inserted at any place in the diagram where they are meaningful (Jeckle et al., 2002, p. 352). [...] in UML 2 it is also possible to represent alternative, optional, parallel, and repeated sequences of interaction [using block-structured interaction fragments]. Furthermore, dia- grams might contain references to other sequence diagrams that contain a rened descrip- tion of particular interaction steps. Due to their derivation from [...] High Level Message Sequence Charts (Jeckle et al., 2002, p. 332), we will refer to this notation as high level sequence diagrams. Like activity diagrams [...], high level sequence diagrams do not display a single scenario but rather a class of possible interaction sequences. A drawback of the extended notation is that such diagrams can become [...] dicult to understand. (Page and Kreutzer, 2005, pp. 87-91) :Dispatcher :AGV 3[idle]:Accept(transport order) 3[not idle]: Reject(transport order) :Truck 2:Request(transport order) 1:Arrival Truck Arrival sd Figure 2.5.: A communication diagram displaying an interaction at an imaginary container terminal. A more detailed description of UML 2 sequence diagrams including a comparison with the similar AgentUML interaction diagrams is provided in Section 3.3.2.1. An alternative view upon communicating entities is provided by communication diagrams as shown in Figure 2.5 (see also Jeckle et al., 2002, pp. 391). The example shows a possible interaction taking place 38
- 48. 2.3. Modeling Techniques at a container terminal. 9 On the arrival of a truck, the order dispatcher generates a transport order to fetch a certain container and dispatches it to an automatic guided vehicle (AGV) that might accept or reject the order depending on its state. Note that communication diagrams do not focus on control ow (Jeckle et al., 2002, p. 392) but display relations between communication partners similar to a social network Aalst and Song (see e.g. 2004b). Nevertheless it is possible to indicate the order of messages by consecutive numbering. While alternatives are expressed using the UML guard notation, other interaction fragments (e.g. loops) are not supported (Jeckle et al., 2002, pp. 400). 2.3.2. Petri Nets Despite several attempts to formalize and execute UML models, the UML remains a semi- formal language without an explicit operational semantic. In contrast, Petri nets (PN) are formal models to represent concurrent processes. In the following, we will focus on the reference net formalism by Kummer (2002) and its relations to simulation and UML. 2.3.2.1. Petri Nets Rölke (2004, p. 251) informally introduces a PN as a directed graph with two dierent node types: places and transitions. A place [drawn as a circle] is a passive element corresponding to a storage [. . . ] while a transition [drawn as a rectangle] represents an action or processing step. Arcs can only connect a place with a transition or vice versa. The PN formalism was proposed by Petri (1962) to model distributed system states and con- currency (Rölke, 2004, p. 253). A set of events or actions are concurrent if they are not causally interrelated and might therefore be executed in an arbitrary order or even simultane- ously (Rölke, 2004, p. 253). The state of a PN is indicated by a marking of its places with tokens (Rölke, 2004, p. 251), where each place can contain a number of tokens up to a certain (possibly unlimited) capacity. The behavior of a PN is realized by the ring of transitions. A transition's ability to re depends on its local environment, i.e. the input places connected via incoming arcs and the output places connected via outgoing arcs (Rölke, 2004, pp. 251). The transition is activated if all input places contain enough tokens (with respect to the incoming arcs' weights) and the ring of the transition does not exceed any output place's capacity (with respect to the outgoing arcs' weights) (Jessen and Valk, 1987, p. 39). The ring removes tokens from the input places and puts tokens into the output places (Rölke, 2004, p. 252). Figure 2.6 exemplies a PN representing a 'gravel pit' model with two loading docks. 10 Since places and arcs do not contain numerical inscriptions, each place capacity is unlimited and each arc weight is 1 by default. In the following, we review further aspects of PNs that will be relevant later in this thesis. As usual (see e.g. Baumgarten, 1996 or Bause and Kritzinger, 1996) we distinguish between structural and dynamic properties. 9 On the simulation of container terminal logistics, see e.g. the diploma thesis by Planeth and Willig (2004) 10 The 'gravel pit' example is adopted from Page and Kreutzer (2005, p. 32). 39
- 49. 2. Modeling and Simulation Truck Arrival Truck queue Idle Loading Idle Loading Begin of service End of service Loading dock 2 [] [] [] [] [] Loading dock 1 Finished trucks Leave system Leave system End of service Begin of service Figure 2.6.: A very abstract PN model of a 'gravel pit' with two loading docks. Note that this model neglects simulation time consumption and queueing strategies. 2.3.2.2. Structural Patterns and Properties Structural properties are based on the net graph N = (P, T, F), where P is the set of places, T the set of transitions and F the set of arcs or ow relation. To handle the potential complexity of general net graphs, we can identify common structural patterns (see e.g. Rölke, 2004, pp. 254) on the one hand and consider simplied net classes on the other hand. Figure 2.7.: Basic structural patterns commonly found in Petri nets (adopted with modications from Rölke, 2004, p. 255 and Baumgarten, 1996, p. 53, 72) Common structural patterns are displayed in Figure 2.7. The denition of sequences and cycles (Baumgarten, 1996, p. 72) is straightforward. Cycles of length 1 are called loops (Baumgarten, 1996, p. 53). A conict corresponds to a decision node in an activity diagram (see Section 2.3.1.3. The concurrent pattern splits and re-joins the control ow into parallel threads similar to fork and join nodes in activity diagrams. 40
- 50. 2.3. Modeling Techniques Restricted sub classes of net graphs considered in this thesis are workow, free-choice, and causal nets. According to Aalst and Hee (2002, p. 271) a workow-net (WF net) serves to model the control ow of workow instances (cases). 11 Its transitions are interpreted as the basic activities (tasks) occurring in the workow, while arcs and places represent the causal relations and states of the workow (Aalst and Hee, 2002, p. 271). Book Ticket Book Seat No further requests Further requests Customer calls Advise customer i o Book Ticket Book Seat No further requests Customer calls Advise customer i o Workflow-net Causal-net Figure 2.8.: Left: A WF net representing a simple ticket reservation workow. The grey section mixes an alternative split and a parallel join but nevertheless has the free-choice property. Right: A causal net representing a single ticket reservation case without cycles and conicts. Example model adopted with modications from Page (1991, pp. 46). A WF net comprises a single input place i (i.e. a place without input transitions) and a single output place o (i.e. a place without output transitions) to indicate a well-dened begin and end of the represented workow (Aalst and Hee, 2002, p. 272). As a further condition, all places and transitions of a WF net must be on a path from the input to the output place to prevent the modeling of unused tasks and states (Aalst and Hee, 2002, p. 272). An example is shown in Figure 2.8. A WF net strongly resembles an activity diagram with an initial and nal node. However, Aalst and Hee (2002, p. 277) note that most control ow notations (including activity diagrams) do not model conditions as explicit places but as an implicit part of the decision nodes. Therefore, it is not possible to include a routing construct like the grey area of Figure 2.8. It is nevertheless possible to build an equivalent structure composed from decision and fork/join nodes. 11 on workow modeling see Dumas et al. (2005) and Section 2.3.3 41
- 51. Another Random Scribd Document with Unrelated Content
- 55. The Project Gutenberg eBook of Les Bijoux Indiscrets, or, The Indiscreet Toys
- 56. This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title: Les Bijoux Indiscrets, or, The Indiscreet Toys Author: Denis Diderot Release date: May 6, 2017 [eBook #54672] Most recently updated: October 23, 2024 Language: English Credits: Produced by Clare Graham Marc D'Hooghe at Free Literature (online soon in an extended version, also linking to free sources for education worldwide ... MOOC's, educational materials,...) Images generously made available by the Internet Archive. *** START OF THE PROJECT GUTENBERG EBOOK LES BIJOUX INDISCRETS, OR, THE INDISCREET TOYS ***
- 57. Les Bijoux Indiscrets. OR, The Indiscreet Toys. By
- 58. Denis Diderot. Translated from the Congese Language. Printed at Monomotapa. In Two Volumes. Adorned with Copper-Plates. TOBAGO: Re-printed for Pierrot Ragout, with the Approbation of M——l S——xe, MDCCXLIX. And sold by R. Freeman, near St. Paul's; and at all the Booksellers.
- 60. Frontispiece French edition 1749 TO ZIMA. Zima, embrace the moment. The Aga Narkis entertains your mother, and your governess is upon the watch in a balcony for your father's return: take, read, fear nothing. But even tho' the Bijoux indiscrets should be found behind your toilet, do you think it would be a matter of wonder? No, Zima, no; it is well known, that the Sopha, the Tanzai, and the Confessions have been under your pillow. Do you hesitate still? Know then, that Aglaé has not disdained to set her hand to the work, which you blush to accept. Aglaé, say you, the sober Aglaé!—The same. While Zima was straying with, or perhaps contriving how to get rid of the young Bonza Alleluia; Aglaé amused herself innocently, by relating to me the adventures of Zaide, Alphana, Fannia, c.—furnished me with the few strokes, which please me in the history of Mangogul, revised it, and pointed me out the means of making it better: for if Aglaé is one of the most virtuous and least edifying women in Congo; she is likewise one of the least jealous of wit, and one of the most witty. Can Zima now think, that it becomes her to play the scrupulous? Once more, Zima, take, read, read all; even without excepting the narrative of the Rambling Toy, which may be interpreted to you, without any expence to your virtue, provided the interpreter be neither your spiritual director nor your lover. CONTENTS. Preface Chap. I. Birth of Mangogul.
- 61. Chap. II. Education of Mangogul. Chap. III. Which may be regarded as the first of this History. Chap. IV. Evocation of the Genius. Chap. V. Mangogul's dangerous temptation. Chap. VI. First Trial of the Ring, or Alcina. Chap. VII. Second Trial of the Ring, or the Altars. Chap. VIII. Third Trial of the Ring, or the private Supper. Chap. IX. The state of the Academy of Sciences at Banza. Chap. X. Less learned and less tedious than the preceding. Continuation of the Academical Sitting. Chap. XI. Fourth Trial of the Ring, or the Echo. Chap. XII. Fifth Trial of the Ring, or Play. Chap. XIII. Sixth Trial of the Ring, or the Opera at Banza. Chap. XIV. Orcotomus's Experiments. Chap. XV. The Bramins. Chap. XVI. The Muzzles. Chap. XVII. The two Devouts. Chap. XVIII. The Toyman's Return. Chap. XIX. Seventh Trial of the Ring, or the stifled Toy. Chap. XX. Eighth Trial of the Ring, or the Vapors. Chap. XXI. Ninth Trial of the Ring, or Things lost and found. Chap. XXII. A sketch of Mangogul's Moral Philosophy. Chap. XXIII. Tenth Trial of the Ring, or the Dogs. Chap. XXIV. Eleventh Trial of the Ring, or the Pensions. Chap. XXV. Twelfth Trial of the Ring, or a Law-Case. Chap. XXVI. Mirzoza's Metaphysical Essay, or the Soul. Chap. XXVII. Sequel of the preceding Conversation. Chap. XXVIII. Thirteenth Trial of the King, or the little Mare.
- 62. Chap. XXIX. Mangogul's Dream, or a Voyage into the Region of Hypotheses. Chap. XXX. Fourteenth Trial of the Ring, or the Mute Toy. Chap. XXXI. Was Mangogul in the right? Chap. XXXII. The fifteenth Trial of the Ring, or Alphana. Chap. XXXIII. Sixteenth Trial of the Ring, or the Petits-maitres. Chap. XXXIV. Seventeenth Trial of the Ring, or the Comedy. Chap. XXXV. Conversation on Literature. Chap. XXXVI. Eighteenth and nineteenth Trials of the Ring, or the flatted Spheroïd, and Girgiro the entangled. Chap. XXXVII. Mirzoza's Dream. Chap. XXXVIII. Twenty-first and twenty-second Trials of the Ring, or Fricamona and Callipiga. Chap. XXXIX. Dreams. Chap. XL. Twenty-third Trial of the Ring, or Fannia. Chap. XLI. The History of Selim's Travels. Chap. XLII. Twenty-fourth and twenty-fifth Trials of the Ring, or, the Masquerade, and Sequel of the Masquerade. Chap. XLIII. Selim at Banza. Chap. XLIV. Twenty-sixth Trial of the Ring, or the Rambling Toy. Chap. XLV. Cydalisa. Chap. XLVI. Twenty-seventh Trial of the Ring, or Fulvia. Chap. XLVII. Prodigious Events of the Reign of Kanaglou, Mangogul's Grand-father. Chap. XLVIII. Twenty-eighth Trial of the Ring, or Olympia. Chap. XLIX. Twenty-ninth Trial of the Ring, or Zuleiman and Zaide. Chap. L. Platonic Love.
- 63. Chap. LI. Thirtieth and last Trial of the Ring, or Mirzoza. [Transcribers' Note: Chapters I.-XXI. of the second volume of the 1749 publication have been renumbered XXXI.-LI. Illustrations weren't present in the copy of the English edition we used, we added those from the original French (at Gallica, Bibliothèque nationale de France.] LIST OF ILLUSTRATIONS. 1.Cupid in Bed (frontispiece). 2.Man, Woman and Cupid, or Folly, Imagination, and Love. 3.Evocation of the Genius. 4.Dogs and Lady in Bed. 5.The Mare, c. 6.The Bubble-blower. 7. Women walking on their hands. 8.Man and Lady on a Sopha (Zuleiman).
- 65. Imagination takes the feather from the hand of folly, and love dictates. The Indiscreet Toys. CHAP. I. Birth of Mangogul. Hiaouf Zeles Tanzai had already reigned long in great Chechianea, and this voluptuous prince still continued to be the delight of his subjects. Acajou king of Minutia had undergone the fate predicted by his father: Zulmis was no more: the Count De —— was still living: Splendidus, Angola, Misapouf and some other potentates of the Indies and Asia were carried off by sudden deaths. The people tired of obeying weak sovereigns, had shaken off the yoke of their posterity; and the descendants of those unfortunate monarchs rambled unknown, or not regarded, in the provinces of their empires. The grandson of the illustrious Scheherazad was the only one who maintain'd his throne: and he was obeyed in Indostan by the name of Schach Baam, at the time when Mangogul was born in Congo. Thus it appears, that the death of several sovereigns was the mournful epoch of his birth. His father Erguebzed did not summon the Fairies round the cradle of his son; because he had observed, that most of the princes of his time, who had been educated by these female intelligences, were no better than fools. He contented himself with ordering his nativity to be calculated by one Codindo, a person fitter for a portrait than an acquaintance. Codindo, was head of the college of Soothsayers at Banza, the ancient capital of the empire. Erguebzed had settled a large pension on him, and had granted to him and his descendants, on account of the merit of their great uncle, who was an excellent cook, a magnificent castle on the frontiers of Congo. Codindo was appointed
- 66. to observe the flight of birds, and the state of the heavens, and to make a report thereof at court: which office he executed very indifferently. If it be true, that they had at Banza the best theatrical pieces, and the worst play-houses in all Africa; in return they had the most beautiful college in the world, and the most wretched predictions. Codindo, informed of the business for which he was summoned to Erguebzed's palace, set out much embarrassed; for the poor man could no more read the stars than you or I. He was expected with impatience. The principal lords of the court were assembled in the appartment of the great Sultana. The ladies, magnificently dress'd, stood round the infant's cradle. The courtiers were hurrying to congratulate with Erguebzed on the great things, which he was undoubtedly on the point of hearing concerning his son. Erguebzed was a father, and thought it quite natural, to discern in the unform'd lines of an infant, what he was to be. In fine, Codindo arrived. Draw near, says Erguebzed to him: as soon as heaven had granted me the prince before you, I ordered the instant of his birth to be exactly registered, and without doubt you have been informed of it. Speak sincerely to your Master, and tell him boldly the destiny which heaven has reserved for his Son. Most magnanimous Sultan, answered Codindo, the prince, born of parents equally illustrious and happy, can have no other than a great and fortunate destiny: but I should impose on your highness, if I plumed myself with a science which I do not possess. The stars rise and set for me as for the rest of mankind; and I am not more enlightened in futurity by their means, than the most ignorant of your subjects. But, replied the Sultan, are you not an astrologer? Magnanimous prince, answered Codindo, I have not that honour. What the devil are you then? says the old, but passionate Erguebzed. An Aruspex! By the heavens I did not imagine, that you had so much as thought of it. Believe me, Seigneur Codindo, suffer
- 67. your poultry to feed in quiet, and pronounce on the fate of my son, as you lately did on the cold of my wife's parrot. Codindo immediately drew a glass out of his pocket, took the infant's left ear, rubb'd his eyes, turn'd his spectacles again and again, peep'd at that ear, did the like to the right ear, and pronounced, that the young prince's reign would be happy, if it proved long. I understand you, replied Erguebzed: my son will do the finest things in the world, if he has time. But, zounds! what I want to have told me is, that he will have time. What matter is it to me, after he is dead, that he would have been the greatest prince upon earth, had he lived. I have sent for you to cast my son's horoscope, and you make me his funeral oration. Codindo assured the prince, that he was sorry he was not more knowing; but beseeched his highness to consider, that his knowledge was sufficient for the little time he had been a conjurer. In effect, the moment before, what was Codindo? CHAP. II. Education of Mangogul. I will pass lightly over Mangogul's first years. The infancy of princes is the same with that of the rest of mankind; with this difference, however, that princes have the gift of saying a thousand pretty things, before they can speak. Thus before Erguebzed's son was full four years old, he furnished matter for a volume of Mangogulana. Erguebzed, who was a man of sense, and was resolved that his son's education should not be so much neglected as his own had been, sent betimes for all the great men in Congo; as, painters, philosophers, poets, musicians, architects, masters of dancing, mathematicks, history, fencing, c. Thanks to the happy dispositions of Mangogul, and to the constant lessons of his masters, he was
- 68. ignorant in nothing of what a young prince is wont to learn the first fifteen years of his life; and at the age of twenty he could eat, drink, and sleep, as completely as any potentate of his age. Erguebzed, whose weight of years began to make him feel the weight of his crown, tired with holding the reins of the empire, frighted at the disturbances which threatened it, full of confidence in the superior qualifications of Mangogul, and urged by sentiments of religion, sure prognostics of the approaching death or imbecility of the great, descended from the throne, to seat his son thereon: and this good prince thought he was under an obligation of expiating, by a retirement, the crimes of the most just administration, of which there is any account in the annals of Congo. Thus it was, that in the year of the world 15,000,000,032,000,021, of the empire of Congo 390,000,070,003, began the reign of Mangogul, the 1,234,500 of his race in a direct line. Frequent conferences with his ministers, wars carried on, and the management of affairs, taught him in a very short time what remained for him to know at getting out of the hands of his pedagogues; and that was somewhat. However, in less than ten years Mangogul acquired the reputation of a great man. He gained battles, stormed towns, enlarged his empire, quieted his provinces, repaired the disorder of his finances, restored arts and sciences, raised edifices, immortalized himself by useful establishments, strengthened and corrected the legislative power, even founded academies; and, what his university could never comprehend, he executed all these great things, without knowing one word of Latin. Mangogul was not less amiable in his Seraglio than great on the throne. He did not take it into his head to regulate his conduct by the ridiculous customs of his country. He broke the gates of the palaces inhabited by his women; he drove out those injurious guards of their virtue; he prudently confided in themselves for their fidelity: the entrance into their appartments was as free for men as into those of the canonesses of Flanders; and doubtless their behaviour
- 69. as decent. Oh! how good a Sultan he was! There never was his equal, but in some French romance. He was mild, affable, chearful, gallant, of a charming figure, a lover of pleasures, cut out for them, and contained more wit and sense in his head, than had been in those of all his predecessors put together. 'Tis easy to judge that, with such uncommon merit, a number of the sex aspired to make him their conquest: Some few succeeded. Those who miss'd his heart, endeavour'd to console themselves with the grandees of the court. Young Mirzoza was of the number of the former. I shall not amuse myself with detailing the qualities and charms of Mirzoza: the work would be without end, and I am resolved that this history shall have one. CHAP. III. Which may be regarded as the first of this history. Mirzoza had already fixed Mangogul for some years. These lovers had said, and a thousand times repeated, all that a violent passion suggests to persons who have the most wit. They were got as far as confidences, and they would impute it to themselves as a crime, to conceal the most minute circumstance of their lives from each other. These singular suppositions, If heaven, which has placed me on the throne, had given me an obscure low birth, would you have deign'd to descend down to me, would Mirzoza have crown'd me? Should Mirzoza happen to lose the few charms which she is thought to have, would Mangogul love her still? These suppositions, I say, which exercise the fancy of ingenious lovers, which sometimes make tender lovers quarrel, and frequently oblige the most sincere lovers to tell untruths, were quite worn out between our pair. The favorite, who possess'd in a supreme degree, the necessary and uncommon talent of making a good narrative, had drained the
- 70. scandalous history of Banza. As she had not the best constitution, she was not always disposed to receive the Sultan's caresses, nor he always in the humour of offering them. In short, there were some days, in which Mangogul and Mirzoza had little to say, hardly any thing to do, and in which, without any diminution of love, they amused themselves but indifferently. Those days were rare indeed, but there were some; and this was one of them. The Sultan was carelessly stretch'd on a sopha, opposite to the favorite, who was knotting in silence. The weather did not permit them to take a walk. Mangogul would not venture to propose a party of piquet; and this posture had lasted near a quarter of an hour, when the Sultan, yawning several times, said, It must be allowed, that Geliotta sung like an angel. And that your highness is tired to death, answered the favorite. No, Madam, replied Mangogul, endeavouring to smother a yawn, the minute that one sees you, is not that of tiresomeness. If that is not a polite compliment, 'tis no body's fault but your own, rejoin'd Mirzoza: but you ponder, you are absent, you yawn. Prince, what ails you? I know not, said the Sultan. But I guess, continued the favorite. I was eighteen, when I had the good fortune to please you. It is full four years since you began to love me. Eighteen and four make twenty-two. Therefore I am now very old. Mangogul smiled at this calculation. But if I am no longer worth any thing for pleasure, added Mirzoza, I will at least demonstrate that I am very good for advice. The variety of amusements which attend you, has not been able to secure you against disgust. You are disgusted. Prince, there is your disease. I do not allow, that you have hit it off, says Mangogul: but supposing you have, do you know a remedy? Mirzoza answered the Sultan, after a moment's pause, that his highness seem'd to take so much pleasure at the narratives she made him of the gallantries of the town, that she was sorry she had no more to relate to him, or that she was not better informed of those of the court; that she would have tried that expedient, till she thought of somewhat better. I think it a good one, says Mangogul: But who knows the stories of all those fools; and tho' they were known to any, who could relate
- 71. them like you? Let us learn them however, replied Mirzoza. Whosoever it be that tells them, I am certain that your highness will gain more by the matter, than you will lose by the form. I shall join with you, if you please, in fancying the adventures of the court ladies very diverting, says Mangogul: but tho' they were to be a hundred times more so, what does that avail, if it be impossible to come at them? There may be a difficulty in it, answers Mirzoza, but in my opinion, that is all. The Genius Cucufa, your relation and friend, has done greater things. Why do you not consult him? Ah, joy of my heart! cried the Sultan, you are an admirable Creature. I make no doubt but the Genius will employ all his power in my favour. This moment I shut myself up in my closet, and invoke him. Accordingly Mangogul arose, kissed the favorite on the left eye, pursuant to the custom of Congo, and departed.
- 73. Evocation of the Genius. CHAP. IV. Evocation of the Genius. The Genius Cucufa is an old hypochondriac, who fearing lest the concerns of the world, and dealings with the rest of the genii, might prove an obstacle to his salvation, took refuge in the Void; in order to employ himself quite at leisure on the infinite perfections of the great Pagoda, to pinch, scratch and make notches in his flesh, to fret himself into madness, and starve himself to death. In that place he lies on a straw mat, his body tuck'd up in a sack, his flanks squeez'd with a cord, his arms crossed on his breast, and his head sunk into a hood, which suffers nothing to issue but the end of his beard. He sleeps, but one would think him in contemplation. All his company is an owl which nods at his feet, some rats which gnaw his mat, and bats which hover round his head. The manner of evoking him, is, by repeating, to the sound of a bell, the first verse of the nocturnal office of the Bramins: then he lifts up his hood, rubs his eyes, puts on his sandals, and sets out. Figure to yourself an old Camaldolian Monk carried in the air by two large horn-owls, which he holds by the legs. In this equipage it was, that Cucufa appear'd to the Sultan. May the blessing of Brama be within these walls, says he, bowing. Amen, answered the prince. What do you want, my son? A very small matter, says Mangogul; to procure me some pleasure at the expence of the court ladies. Oh, my son! replied Cucufa, you have a larger appetite than a whole monastery of Bramins. What do you pretend to do with this troop of extravagants? To learn from themselves their present and past adventures, that is all. But that is impossible, says the Genius. To have women confess their adventures, is a thing that never was, nor ever will be. Yet it must be, added the Sultan. At these words, the Genius scratching his ear,
- 74. and combing his long beard with his fingers, fell to thinking. His meditation was short. My child, said he to Mangogul, I love you, you shall be satisfied. Instantly he plunged his right hand into a deep pocket made under his arm-pit on the left side of his frock, and, together with images, bless'd beads, little leaden pagoda's, and musty sweatmeats, drew out a silver ring, which Mangogul at first took for one of St. Hubert's rings. You see this ring, said he to the Sultan, put it on your finger, my child: every woman, at whom you shall level the stone, will relate her intrigues in a plain, audible voice. Do not imagine however, that 'tis by the mouth that they are to speak. By what then will they speak? says Mangogul. By the frankest part about them, and the best instructed in those things which you desire to know, says Cucufa; by their Toys. By their Toys, replies Mangogul bursting into laughter; that is particular. Talking Toys! That is an unheard extravagance. My son, said the Genius, I have performed many greater prodigies for your grandfather: therefore depend on my word. Go, and may Brama bless you. Make a good use of your secret, and remember that there are ill-placed curiosities. This said, the old hypocrite nodded his head, pull'd his hood over his face, took his horn-owls by the legs, and vanish'd in the air. CHAP. V. Mangogul's dangerous Temptation. Scarcely was Mangogul in possession of Cucufa's mysterious ring, when he was tempted to make the first trial of it on the favorite. I forgot to mention, that besides the vertue of obliging the Toys of those women, on whom he turn'd the stone, to speak, it had that also of rendering the person invisible, who wore it on the little finger. Thus could Mangogul transport himself in the twinkling of an eye to a thousand places where he was not expected, and with his own
- 75. eyes see many things, which are frequently transacted without witnesses. He had nothing more to do than to put on his ring, and say I desire to be in such a place, and he was there in an instant. Behold him then in Mirzoza's bed-chamber. Mirzoza, who gave over all hopes of the Sultan's company, was in bed. Mangogul approach'd her pillow softly, and saw by the glimmering light of a night taper, that she was asleep. Good, say he, she sleeps, let us quickly shift the ring on another finger, resume our natural shape, turn the stone on this fair sleeper, and awake her Toy a little while.—But what stops me?—I tremble.—Is it possible that Mirzoza?—No, it is not possible, Mirzoza is faithful to me. Fly from me, injurious suspicions, I will not, I ought not to heed ye. He said, and put his fingers on the ring: but taking them off as hastily as if it had been fire, he cried within himself. What do I do, wretched man! I insult Cucufa's advice. For the sake of satisfying a silly curiosity, I am going to run the hazard of losing my mistress and my life. If her Toy should be in the humor of talking extravagantly, I should never see her more, and I should dye of grief. And who knows what a Toy may have in its soul? Mangogul's agitation made him in some measure forget himself: he pronounced these last words pretty loud, and the favorite awoke. Ah, Prince, said she, less surprized than charmed at his presence, you are here. Why did you not send me notice? Must you condescend to wait for my awaking? Mangogul answered the favorite by relating the success of his interview with Cucufa, shew'd her the ring, and did not conceal one of its properties from her. Ah! what a diabolical secret has he given you! cry'd Mirzoza. But pray, Prince, do you intend to make any use of it. How, said the Sultan, do I intend to use it? I shall begin by you, if you argue with me. At these terrible words the favorite turn'd pale, trembled, recover'd herself, and conjured the Sultan by Brama, and all the Pagoda's of the Indies and Congo, not to try the experiment on her of a secret power, which indicated a diffidence of her fidelity. If I have been constantly honest, continued she, my Toy will not speak a word, and you will have done me such an injury
- 76. as I shall never forgive. If it happens to speak, I shall lose your esteem and heart, and that will make you run distracted. Hitherto you have, in my opinion, found your account in our connection; why would you run the risk of breaking it off? Prince, believe me. Follow the advice of the Genius; he has had great experience, and advices of Genius are always good to follow. This is exactly what I was saying to myself, answered Mangogul, when you awoke. And yet if you had slept two minutes longer, I cannot answer for what might have happened. What would have happened, says Mirzoza, is, that my Toy would have given you no information, and that you would have lost me for ever. That may be, replied Mangogul; but now that I have a full view of the danger which I incurred, I solemnly swear to you by the eternal Pagoda, that you shall be excepted from the number of those, on whom I shall turn the ring. At these words Mirzoza brightened up, and fell to joking at the expence of the Toys which the Prince should hereafter interrogate. Cydalisa's Toy, said she, has many stories to tell, and if it be as indiscreet as its mistress, it will not require much intreaty. Haria's Toy is no longer of this world, and your highness will obtain no tales from it of fresher date than the days of my grandmother. As for that of Glauce, I believe it is a proper one to be consulted. She is a coquet and pretty. And for that reason precisely it is, replied the Sultan, that her Toy will be mute. Why then, said the Sultana, apply to that of Phedima, she is ugly, and loves gallantry. Yes, continued the Sultan; and so ugly, that one must be as ill-natured as you, to accuse her of gallantry. Phedima is sober; 'tis I who say it, and who know something of the matter. As sober as you please, replied the favorite, but she has a sort of grey eyes that speak the contrary. Her eyes belye her, said the Sultan warmly. You tire my patience with your Phedima. Might not one say, that there is no other Toy but this to examine. But may I presume, without offending your highness, added Mirzoza, to ask which is the first
- 77. you intend to honour with your choice. We shall see anon, said Mangogul, in the circle of the Manimonbanda, (the Congese name of the great Sultana). We shall have a good deal of work upon our hands and when we happen to be tired of the Toys of my court, we may chance make a tour thro' Banza. Possibly we may find those of the city women more reasonable than those of dutchesses. Prince, said Mirzoza, I have some acquaintance with the former, and can assure you, that they are only more circumspect. We shall soon hear from them: but I cannot refrain from laughter, continued Mangogul, when I think on the confusion and surprize of these women at the first words of their Toys, ha, ha, ha! Remember, delight of my soul, that I shall expect you at the great Sultana's, and that I shall make no use of my ring till you are come. Prince, said Mirzoza, I rely on the promise you have made me. Mangogul smiled at her allarm, reiterated his promise, sealed them with kisses, and retired. CHAP. VI. First Trial of the Ring. Alcina. Mangogul arrived before her at the great Sultana's, and found all the ladies very busy at cards. He survey'd all those, whose reputation was established, fully resolved to try his ring on one of them, and his only difficulty was in the choice. While, he was in suspence by whom to begin, he spied a young lady of the household of the Manimonbanda in a window. She was toying with her husband; which appear'd singular to the Sultan, inasmuch as they had been married above eight days. They had made their appearance in the same box at the Opera, in the same coach at the Bois de Boulogne, they had finished their visits; and the fashion of the times exempted
- 78. them from loving or even meeting each other. If this Toy, says Mangogul, is as silly as its mistress, we shall have a diverting soliloquy. At this instant the favorite appear'd. Welcome, said the Sultan to her in a whisper. I have cast my lead, waiting for you. And on whom? ask'd Mirzoza. On that couple which you see sporting in that window, answer'd Mangogul with a wink. Well set out, replied the favorite. Alcina, for that was the young lady's name, was sprightly and pretty. The Sultan's court had few women more amiable, and not one of a gayer disposition. One of the Sultan's Emirs had filled his head with her. He was not left in ignorance of what the chronicle had published concerning Alcina: the report alarm'd him, but he followed the custom: he consulted his mistress about it. Alcina swore, that it was pure calumny invented by some coxcombs, who would have been silent, if they had had any reason for talking; but however, that there was no harm done, and that he was at full liberty to believe it or not, as he thought proper. This answer, delivered with an air of confidence, convinced the amorous Emir of his mistress's innocence. He closed the affair, and assumed the title of Alcina's husband with all its prerogatives. The Sultan levelled his ring at her. A loud burst of laughter, which seized Alcina at some comical saying of her husband, was suddenly cut short by the operation of the ring; and immediately a murmuring noise was heard under her petticoats. Well, now I am titled. Truly I am glad on't. Nothing like having a rank. If my first advices had been heeded, I should have been provided with something better than an Emir: but yet an Emir is better than nothing. At these words all the ladies quitted the game, to seek from what quarter the voice issued. This movement made a great noise. Silence, says Mangogul, this deserves attention. They obeyed, and the Toy continued. One would be apt to think, that a husband is a guest of great importance, by the precautions which are taken to receive him. What preparatives! What profusion of myrtle water! Another fortnight of this regimen would have demolished me. I had disappear'd, and the Emir might have sought lodgings elsewhere, or
- 79. have shipped me off for the island Jonquille. Here my author says, that all the ladies grew pale, look'd at each other in deep silence, and grew vastly serious; which he ascribes to their fear, lest the conversation should grow warm, and become general. Yet, continued Alcina's Toy, in my opinion the Emir did neither require nor stand in need of so many formalities: but I must still acknowledge the prudence of my mistress. She guarded against the worst, and I was treated for the great lord as for his little page. The Toy was on the point of continuing its extravagant harangue, when the Sultan, observing that this strange scene shock'd the modest Manimonbanda, interrupted the orator by turning off the ring. The Emir had vanish'd at the first words of his wife's Toy. Alcina, without being disconcerted, pretended to take a nap: mean while the ladies whispered that she had the vapours. Yes, says a Petit-maitre, —— Vapours: Ch——y calls them hysterics, as much as to say, things which come from the lower region. For this case he has a divine elixir; it is a principle, principiating, principiated, which revives——which——I will propose it to the lady. The company laugh'd at this gibberish, and our Cynic resumed. Nothing more true, ladies: I, who speak, have used it for a deperdition of substance. A deperdition of substance, good marquiss, said a young person, pray what is that? Madam, replied the marquiss, it is one of those casual accidents which happen——but every body knows it. By this time the pretended drowziness went off. Alcina sat down to play with as much intrepidity as if her Toy either had not spoken a word, or had made the finest speech in the world. Nay, she was the only lady that play'd without distraction. This sitting was worth a considerable sum to her. The rest did not know what they were about, could not count the dots on the cards, forgot their reckonings, neglected their good luck, dealt wrong, and committed a hundred other mistakes, of which Alcina took the advantage. In fine, they broke up play, and every one withdrew.
- 80. This adventure made great noise not only at court and in town, but all over Congo. Epigrams were handed about on it. The discourse of Alcina's Toy was published, revised, corrected, enlarged and commented by the Agreeables of the court. The Emir was lampoon'd, and his wife immortalized. She was pointed at in the play-house, and followed in the public walks. People flock'd about her, and she heard them buzzing: Yes, 'tis she: her Toy made a discourse two hours long. Alcina bore her new reputation with admirable tranquillity. She listened to these expressions, and many more, with a serenity, which the rest of the women could not shew. They were every moment under apprehensions of some indiscretions being committed by their Toys: but the adventure of the following chapter compleated their confusion. As soon as the company had broke up, Mangogul gave his hand to the favorite, and conduced her to her appartment. She was far from having that lively chearful air, which seldom quitted her. She had lost considerably at play, and the effect of the dreadful ring had plunged her into a pensiveness, out of which she was not yet thoroughly recovered. She knew the Sultan's curiosity, and she had not sufficient confidence in the promises of a man less amorous than despotic, to be free from uneasiness. What ails you, my soul's delight? said Mangogul. You are pensive. I played with bad luck without example, answered Mirzoza. I lost the possibility. I had twelve tableaux, and I don't think I mark'd three times. That is vexatious, replied Mangogul; but what think you of my secret? Prince, said the favorite, I persist in deeming it diabolical. Doubtless it will amuse you, but that amusement will be attended with dismal consequences. You are going to spread discord in every family, undeceive husbands, throw lovers into despair, ruin wives, dishonour daughters, and raise a thousand other hurly-burlys. Ah! Prince, I conjure you.—— By the light, said Mangogul, you moralize like Nicole! I would be glad to know why the concern for your neighbour touches you so to the quick. No, no, madam; I will keep my ring. And what do I matter those husbands undeceived, those lovers thrown into despair, those wives ruined, those
- 81. daughters dishonoured, provided I amuse myself. Am I then a Sultan for nothing? Good night, madam, we must hope that future scenes will be more comic than the first, and that you will take more pleasure in them by degrees. I do not believe it, sir, replied Mirzoza. And for my part, I promise you, that you will find pleasant Toys, nay, so pleasant, that you cannot refuse giving them audience. And what would you do, if I sent them to you in quality of ambassadors? I will if you desire it, spare you the trouble of their harangues; but as to the recital of their adventures, you shall hear it either from their own mouths or mine. 'Tis a determined point; and I can abate nothing of it. Resolve to familiarize yourself with these new speech-makers. At these words he embraced her, and went into his closet, reflecting on the trial he had made, and devoutly thanking the Genius Cucufa. CHAP. VII. Second trial of the Ring. The Altars. The next evening there was to be a private supper in Mirzoza's appartment. The persons invited came early. Before the prodigy of the preceding day, people came by inclination; this night they came purely out of politeness. All the ladies had an air of constraint, and spoke in monosyllables. They were upon the watch, and expected every moment, that some Toy would join in conversation. Notwithstanding their itch of bringing Alcina's odd adventure on the carpet, none of them dared to undertake opening the topic. Not that they were restrained by her presence: tho' included in the supper- list, she did not appear; it was judged that she had a swimming in her head. However, whether it was that they became less apprehensive of danger, as the whole day long they had heard no
- 82. body speak but from the mouth; or whether they affected to appear courageous, the conversation revived, the women most suspected composed their countenances, put on an air of assurance, and Mirzoza ask'd the courtier Zegris, if he knew any entertaining news. Madam, replied Zegris, you have been informed of a match between the Aga Chazour and young Siberina: I assure you it is broke off. Upon what account? interrupted the favorite. On account of a strange voice, continued Zegris, which Chazour says he heard at the toilet of his princess. Since yesterday, the Sultan's court is full of people, who go with their ears cock'd, in hopes of catching, I can't say how, such declarations, as most certainly the persons concerned have no inclination to make them. That is silly, replied the favorite. Alcina's misfortune, if it be one, is far from being averred. We have not got to the bottom—— Madam, interrupted Zelmaida, I have heard her most distinctly. She spoke without opening her mouth. The facts were well articulated, and it was not very difficult to guess whence this extraordinary sound issued. I assure you, that I should have died, were I in her place. Died! replied Zegris. Folks survive other sorts of accidents. How? cried Zelmaida. Can there be a more dreadful one than the indiscretion of a Toy? Well, there is no medium left. One must either renounce gallantry, or resolve to pass for a woman of pleasure. Indeed, said Mirzoza, the option is severe. No, no, madam, replied another lady, you will see that women will fix their resolution. They will allow Toys to prate as much as they please; and will go their own way, without troubling themselves with what the world shall say. And after all, what does it signify, whether it be a woman's Toy or her lover that proves indiscreet? Are things less exposed? Upon a serious consideration of the whole affair, continued a third, if a woman's adventures must be divulged, 'tis better it should happen by her Toy than her lover.
- 83. The notion is singular, said the favorite; and true, replied she who had broach'd it: for, pray, observe that a lover is generally dissatisfied, before he becomes indiscreet, and therefore tempted to be revenged by exaggerating every thing: whereas a Toy talks without passion, and adds nothing to the truth. For my part, said Zelmaida, I am not of that opinion. In this case it is not so much the importance of the depositions, as the strength of the evidence, that ruins the criminal. A lover, who by his discourse dishonours the Altar, on which he has sacrificed, is a kind of impious person, who deserves no credit: but if the altar lifts up its voice, what answer can be made. That the altar knows not what it says, replied the second. Monima, hitherto mute, broke silence, in order to say in a dragging, lazy tone: Ah! let my Altar, since you call it so, speak or be silent, I fear nothing from its talk. Mangogul enter'd that very instant, and Monima's last words did not escape him. He levell'd his Ring at her, and her Toy was heard to cry out: Do not believe her, she lies. Her female neighbours, gazing at each other, ask'd whose Toy it was that made this answer. 'Tis not mine, said Zelmaida; nor mine, said another; nor mine, said Monima; nor mine, said the Sultan. Every one, and the favorite among the rest, persisted in the negative. The Sultan, taking the advantage of this incertainty, and addressing the ladies, said: You have Altars then? Pray, how are they feasted? As he was speaking, he nimbly turn'd his Ring successively on all the women except Mirzoza; and every one of their Toys answering in its turn, these words were heard in different tones. I am frequented, batter'd, abandon'd, perfum'd, fatigu'd, ill serv'd, disgusted, c. They all spoke their word, but so precipitately, that no just application could be made. Their jargon, sometimes rumbling, sometimes yelping, accompanied with loud laughs of Mangogul and his courtiers, made a noise of a new kind. The ladies agreed with a very grave air, that it was very diverting. How, said the Sultan, sure we are too happy, that the Toys deign to speak our language,
- 84. and furnish half the expence of the conversation. Society must be a considerable gainer by this duplication of organs. Possibly we men shall speak also in our turn, by something else besides our mouths. Who knows? What agrees so perfectly well with Toys, may happen to be destin'd to make questions and responses to them: nevertheless my anatomist is of a different opinion. CHAP. VIII. Third trial of the Ring. The Private Supper. Supper was served up, the company sate down at table, and at first they diverted themselves at Monima's charge: all the women unanimously agreed that her Toy had spoke first; and she must have sunk under this confederacy, had not the Sultan taken her part. I do not pretend, said he, that Monima is less gallant than Zelmaida; but I believe her Toy has more discretion. Besides, when the mouth and Toy of a woman contradict each other, which to believe? Sir, replied a courtier, I know not what Toys will say hereafter; but hitherto they have explain'd themselves on a subject, which is very familiar to them. As long as they shall have the prudence to speak of nothing but what they understand, I shall believe them as so many oracles. Others, said Mirzoza, of greater authenticity might be consulted. Pray, madam, replied Mangogul, what interest can these have in disguising the truth? Nothing but a chimæra of honour could be their motive: but a Toy has none of these chimæras. That is not the place of prejudices. A chimera of honour, said Mirzoza, prejudices! If your highness had been exposed to the same inconveniences with us, you would become sensible, that whatever touches virtue, is far from being chimærical. All the ladies, encouraged by the Sultana's answer, insisted that it was superfluous
- 85. to put them to certain proofs; and Mangogul, that these proofs were generally dangerous at least. This conversation ushered in the champagne: it moved briskly round, they plied it close, and it warmed the Toys. Then it was that Mangogul had intended to resume his frolicks. He turn'd his ring on a very gay sprightly young lady, who sate pretty near him, and directly opposite to her husband: and immediately issued from under the table a plaintive noise, a weak languishing voice, which said: Oh, how I am harrassed! I can bear it no longer, I am at death's door. How, by the Pagoda Pongo Sabiam, cried Husseim, my wife's Toy speaks, and what can it say? We are going to hear, answered the Sultan.——Prince, you will permit me not to be of the number of its auditors, replied Husseim; for if any thing ridiculous drop'd from it, do you think?——I think you are a fool, said the Sultan, to alarm yourself at the prattle of a Toy: do we not know a good part of what it can say, and may we not guess the rest? Sit down, then, and endeavour to divert yourself. Husseim sat down, and his wife's Toy began to prate like a magpye. Shall I eternally have this huge Flandrian Valanto? I have seen some who have made an end; but this man——At these words Husseim arose in a fury, snatch'd up a knife, sprang to the other side of the table; and would have pierced his wife's breast, if his neighbours had not prevented him. Husseim, said the Sultan, you make too much noise: the company cannot hear. Might not one say, that your wife's Toy is the only one that has not common sense? And what would become of these ladies, if their husbands were of your humour? How! you are out of your wits for a pitiful little adventure of one Valanto, who never made an end. Return to your seat, behave like a man of honour; see that you watch yourself, and not commit a second failure before a prince, who admits you to his pleasures. While Husseim, stifling his rage, was leaning on the back of a chair, his eyes shut, and his hand on his forehead; the Sultan dexterously levell'd his Ring, and the Toy went on. Valanto's young page would
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