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Andrew Greasley
Simulating Business Processes for Descriptive, Predictive and Prescriptive Analytics

Andrew Greasley
Simulating Business Processes
for Descriptive, Predictive
and Prescriptive Analytics

ISBN 978-1-5474-1674-5
e-ISBN (PDF) 978-1-5474-0069-0
e-ISBN (EPUB) 978-1-5474-0071-3
Library of Congress Control Number: 2019937567
Bibliographic information published by the Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie;
detailed bibliographic data are available on the Internet at http://dnb.dnb.de.
© 2019 Andrew Greasley
Cover image: Matveev_Aleksandr/iStock/Getty Images and PonyWang/E+/Getty Images
Typesetting: Integra Software Services Pvt. Ltd.
Printing and binding: CPI books GmbH, Leck
www.degruyter.com

Preface
Analytics has received much interest in recent years reflecting the opportunities
presented by approaches such as machine learning. Many of the techniques of ana-
lytics have been used for some time, often classified using the term artificial intelli-
gence (AI), but the recent increase in the availability of data has led to an upsurge
in the use and capability of analytic techniques. Computer simulation is now in
widespread use as a tool to look into the future and test designs. In fact, simulation
is now an essential element in technological development and is an important way
in which what is called the scientific method, how discoveries are made, can be em-
ployed. While simulation has a vast area of application, this text will focus on the
use of simulation to analyze business processes.
This book uses the term analytics in two ways. Firstly, analytics can be consid-
ered in terms of outcomes that represent an approach to the measurement of perfor-
mance. Analytic outcomes can be categorized into three types: descriptive analytics
describes what is happening in order to understand, predictive analytics shows us
what will be happening for different future scenarios in order to plan and prescrip-
tive analytics recommends what should be happening in order to achieve our aims.
The ability of simulation to study the current and future behavior of business pro-
cesses and provide a course of action makes it an ideal tool for all three types of
analytic outcomes. Secondly, analytics can be used as a term to represent the proc-
essing of large data sets (often termed big data) using statistical techniques such as
machine learning. In terms of an analysis approach, analytics can be defined as
a data-driven method which uses large data sets to develop predictive algorithms
and is contrasted with the model-driven method of simulation. As a model-driven
approach, simulation uses domain knowledge (knowledge of people who under-
stand how the system works) to move from the real system to a simplification
termed the conceptual model. The conceptual model is then implemented on
a computer using simulation software. This enables us to “run” the model (simu-
late) into the future, thus providing a descriptive, predictive and prescriptive ana-
lytic capability.
The text will explain the use of simulation and analytics for analysis, show how
to undertake a simulation study and provide a number of case studies to demon-
strate the use of simulation in a business setting to undertake descriptive, predic-
tive and prescriptive analytics. Chapter 1 introduces the three main areas covered of
simulation modelling, business processes and analytics. The model-driven ap-
proach of simulation and the data-driven approach of analytics are covered and the
relationship between the two is defined. Chapter 2 covers how business processes
can be redesigned and performance measured. Chapter 3 covers the first main stage
in simulating business processes which entails defining the conceptual model
which is a simplification of the real business process. Chapter 4 discusses the con-
version of the conceptual model into a computer model using simulation modelling
https://doi.org/10.1515/9781547400690-201

software. A simple example is used to demonstrate the steps involved. Chapter 5
covers the interpretation of the simulation model results. Due to the variability in-
herent in the simulation model output this requires the use of statistical analysis.
Chapters 6–19 aim to show the potential of simulation and provide guidance on
how it can be used by the presentation of a number of manufacturing and service
case study examples.
Andrew Greasley
January 2019
VI Preface

Acknowledgments
I would like to recognize the contributions from many individuals to the contents of
this book and the case studies in Part 2. I would specifically like to thank Anand Assi,
Yucan Wang, David Smith, Melissa Venegas Vallejos, Chris M. Smith, Emmanuel
Musa, Stuart Barlow, Emmanuel Thanassoulis, Chris Owen and John S. Edwards.
I would also like to thank Steve Hardman for his support and Jeffrey M. Pepper
and Jaya Dalal at De Gruyter.

About the Author
Andrew Greasley lectures in Simulation Modeling and Operations Management at Aston Business
School, Birmingham, UK. He has taught in the UK, Europe, and Africa at a number of institutions.
Dr. Greasley has over 100 publications with 13 books including Operations Management, Wiley;
Operations Management: Sage Course Companion, Sage; Simulation Modeling for Business,
Ashgate; Business Information Systems, Pearson Education (co-author); and Enabling a Simulation
Capability in the Organisation, Springer Verlag. He has provided a simulation modeling
consultancy service for 30 years to a number of companies in the public and private sectors
including ABB Transportation Ltd. (now Bombardier), Derbyshire Constabulary, GMT Hunslet Ltd.,
Golden Wonder Ltd., Hearth Woodcraft Ltd., Luxfer Gas Cylinders Ltd., Pall-Ex Holdings Ltd., Rolls
Royce Ltd. (Industrial Power Group), Stanton Valves Ltd., Tecquipment Ltd., Textured Jersey Ltd.,
and Warwickshire Police.

Contents
Preface V
Acknowledgments VII
About the Author VIII
Part 1: Understanding Simulation and Analytics
Chapter 1 Analytics and Simulation Basics 3
Chapter 2 Simulation and Business Processes 52
Chapter 3 Build the Conceptual Model 67
Chapter 4 Build the Simulation 110
Chapter 5 Use Simulation for Descriptive, Predictive and Prescriptive
Analytics 154
Part 2: Simulation Case Studies
Chapter 6 Case Study: A Simulation of a Police Call Center 195
Chapter 7 Case Study: A Simulation of a “Last Mile” Logistics System 206
Chapter 8 Case Study: A Simulation of an Enterprise Resource Planning
System 214
Chapter 9 Case Study: A Simulation of a Snacks Process Production
System 230
Chapter 10 Case Study: A Simulation of a Police Arrest Process 239
Chapter 11 Case Study: A Simulation of a Food Retail Distribution
Network 249
Chapter 12 Case Study: A Simulation of a Proposed Textile Plant 259

Chapter 13 Case Study: A Simulation of a Road Traffic Accident Process 271
Chapter 14 Case Study: A Simulation of a Rail Carriage Maintenance
Depot 280
Chapter 15 Case Study: A Simulation of a Rail Vehicle Bogie Production
Facility 289
Chapter 16 Case Study: A Simulation of Advanced Service Provision 298
Chapter 17 Case Study: Generating Simulation Analytics with Process
Mining 308
Chapter 18 Case Study: Using Simulation with Data Envelopment
Analysis 321
Chapter 19 Case Study: Agent-Based Modeling in Discrete-Event
Simulation 325
Appendix A 336
Appendix B 337
Index 338
X Contents

Part 1: Understanding Simulation and Analytics

Chapter 1
Analytics and Simulation Basics
Organizations need to provide goods and services that meet customer needs such
as low price, fast delivery, wide range and high quality. In order to do this, these
organizations operate as complex systems with many internal parts interacting
with an external environment that is ever changing in response to forces such as
technological advances. Because of this increasing complexity, organizations re-
quire tools that can help them both understand their current business processes
and plan for future changes in response to their internal and external environment.
This book is about the how simulation modeling of business processes for descrip-
tive, predictive and descriptive analytics can attempt to explain behavior and thus
help make decisions in the face of an uncertain future. Figure 1.1 shows these three
areas in context and also shows how they work together.
Simulation can take many forms, but the type of simulation that is the focus of
this text is based on a mathematical model that can implemented on a computer.
Operations research/
Management science
Operations
management
Business
process
management
Information systems
Mathematical
models
Simulation
Optimization Performance
measures
Business
processes
Analytics
Simulating business
processes for descriptive,
predictive and
prescriptive analytics
Figure 1.1: Simulating business processes for descriptive, predictive and prescriptive analytics.

These models can be used to represent a simplified version of a real system in
order to aid its understanding and to provide a prediction of its future behavior.
The use of models allows us to overcome the drawbacks of predicting future be-
havior with the real system which can be costly, time-consuming, unfeasible
while testing many design options and in some cases dangerous for safety criti-
cal systems. In order to determine the “best” option for future actions, we may
use optimization techniques. Both mathematical modeling and optimization
techniques fall under the areas of operations research as the focus on business
applications has expanded management science. These terms are often used in-
terchangeably or under the umbrella terms operations research/management sci-
ence (OR/MS). Optimization may also come under the information systems area
when the optimization is enabled by program code in the form of machine-
learning algorithms.
The type of simulation can vary and so can its application range into physics,
chemistry, biology and many other areas. This text is focused on the application
of simulation to analyze processes within business organizations. The process
perspective is associated with the area of operations management, which consid-
ers the transformation of materials, information and customers into goods and
services. This transformation is undertaken by processes that require the alloca-
tion of resources such as people and equipment. Business process management
(BPM) is a discipline that is focused on the use of business processes as a way of
improving organizational performance. Deriving and using process performance
measures is a key aspect of both operations management and BPM. In operations
management performance is often measured using the metrics of cost, quality,
speed, flexibility and dependability. These measures not only provide an indica-
tion of performance but the identification and pursuit of a subset of these meas-
ures provide a way of connecting the strategic direction of the company with its
operational decisions.
Analytics or business analytics can be seen as incorporating the use of model-
ing and statistics from OR/MS and information systems capabilities such as the stor-
age of big data in order to transform data into actions through analysis and insights
in the context of organizational decision making. A key part of analytics is the use
of performance measures to assess business performance.
Analytics is usually associated with the use of large data sets termed big
data and computer programs running algorithms to process that data in what is
known as data-driven analysis. This text is focused on the use of a model-driven
approach using simulation to analyze business processes to produce analytic
outcomes. So before describing simulation in more detail, the data- and model-
driven perspectives for the analysis of business processes will be covered. This
analysis will include the possibility of combining the data- and model-driven
approaches.
4 Chapter 1 Analytics and Simulation Basics

Data- and Model-Driven Analysis
In the context of analyzing organizational business processes, analytics can be clas-
sified into the following:
Descriptive Analytics
– This is the use of reports and visual displays to explain or understand past
and current business performance.
– Descriptive data-driven reports often contain statistical summaries of met-
rics such as sales and revenue and are intended to provide an outline of
trends in current and past performance. Model-driven techniques are often
used for descriptive analysis in the context of the design of new products
and processes when little current data exists.
Predictive Analytics
– This is the ability to predict future performance to help plan for the future.
– Data-driven models often do this by detecting patterns or relationships in
historical data and then projecting these relationships into the future.
Model-driven approaches use domain knowledge to construct a simplified
representation of the structure of the system that is used to predict the
future.
Prescriptive Analytics
– This is the ability to recommend a choice of action from predictions of fu-
ture performance.
– Data-driven models often do this by recommending an optimum decision
based on the need to maximize (or minimize) some aspect of performance.
Model-driven approaches may use optimization software to try many differ-
ent scenarios until one is found that best meets the optimization criteria.
A data-driven modeling approach aims to derive a description of behavior from ob-
servations of a system so that it can describe how that system behaves (its output)
under different conditions or scenarios (its input). Because they can only describe
the relationship between input and output, they are called descriptive models. One
approach is to use pattern recognition as a way to build a model that allows us to
make predictions. The idea of pattern recognition is based on learning relationships
through examples. Pattern recognition is achieved through techniques such as as-
sociations, sequences, classification and clustering of the data. These techniques
are implemented in models that use equations, logical statements and algorithms
to find the patterns. In essence, this approach produces a model that imitates real
behavior based on past observations of that behavior termed a descriptive model.
This imitation can be achieved by defining a relationship that relates model input
to model output. Generally, the more data (observations) that can be used to form
the description, the more accurate the description will be and thus the interest in
big data analytics that uses large data sets. Machine learning uses a selection of
Data- and Model-Driven Analysis 5

learning algorithms that use large data sets and a desired outcome to derive an al-
gorithm that can be used for descriptive, predictive and prescriptive analytics.
A model-driven modeling approach aims to explain a system’s behavior not just
derived from its inputs but through a representation of the internal system’s struc-
ture. The model-driven approach is a well-recognized way of understanding the
world based on a systems approach in which a real system is simplified into its essen-
tial elements (its processes) and relationships between these elements (its structure).
Thus in addition to input data, information is required on the system's processes, the
function of these processes and the essential parts of the relationships between these
processes. These models are called explanatory models as they represent the real sys-
tem and attempt to explain the behaviour that occurs. This means that the effect of
a change on design of the process can be assessed by changing the structure of the
model. These models generally have far smaller data needs than data-driven models
because of the key role of the representation of structure. For example, we can repre-
sent a supermarket by the customers that flow through the supermarket and the pro-
cesses they undertake—collecting groceries and paying at the till. A model would
then not only enable us to show current customer waiting time at the supermarket
tills (descriptive analytics) but also allow us to change the design of the system such
as changing the number of tills and predict the effect on customer waiting time (pre-
dictive analytics). We can also specify the target customer waiting time based on the
number of tills required (prescriptive analytics). However most real systems are very
complex—a supermarket has many different staff undertaking many processes using
different resources—for example, the collection and unpacking of goods, keeping
shelves stocked, heating and ventilation systems, etc. It is usually not feasible to in-
clude all the elements of the real system, so a key part of modeling is making choices
about which parts of the system should be included in the model in order to obtain
useful results. This simplification process may use statistics in the form of mathemat-
ical equations to represent real-life processes (such as the customer arrival rate) and
a computer program (algorithm) in the form of process logic to represent the se-
quence of activities that occur within a process.
Simulation for Descriptive, Predictive, and Prescriptive Analytics
Simulation is not simply a predictive or even a prescriptive tool but can also be used in
a descriptive mode to develop understanding. Here the emphasis is not necessarily on develop-
ing accurate predictive models but on using the simulation model to help develop theories re-
garding how an organizational system works. In this role simulation is used as an experimental
methodology where we can explore the effect of different parameters by running the simulation
under many different conditions. What we do is start with a deductive method in which we have
a set of assumptions and test these assumptions and their consequences. We then use an experi-
mental method to generate data which can be analyzed in an inductive manner to develop theo-
ries by generalization of observations. In fact the simulation analyst can alternate between
a deductive and inductive approach as the model is developed.

Data-Driven Analysis Techniques
In general terms, there are many analysis techniques that can be considered as
data-driven techniques including regression analysis, econometric modeling, time
series experiments and yield management. However, data-driven techniques con-
sidered here are most often associated with big data analytics. These techniques re-
late to those that are used for the analysis on large-scale data sets termed big data.
A brief description follows of each of the main categories of big data-driven analyt-
ics techniques.
Data Mining
In a general sense, data mining can be defined as identifying patterns in complex
and ill-defined data sets. Particular data mining techniques include the following:
– Identifying associations involves establishing relationships about items that
occur at a particular point in time (e.g., what items are bought together in
a supermarket).
– Identifying sequences involves showing the order in which actions occur (e.g.,
click-stream analysis of a website).
– Classification involves analyzing historical data into patterns to predict future
behavior (e.g., identifying groups of website users who display similar visitor
patterns).
– Clustering involves finding groups of facts that were previously unknown (e.g.
identifying new market segments of customers or detecting e-commerce fraud).
There are various categories of mining depending on the nature of the data that is
being analyzed. For example, there is text mining for document analysis and web
mining of websites.
Machine Learning
Machine learning uses an iterative approach for the analysis of prepared training and
test sample data in order to produce an analytical model. Through the use of itera-
tion, learning algorithms build a model that may be used to make predictions. This
model may be in the form of a mathematical equation, a rule set or an algorithm.
Thus, machine learning does not refer to actual learning by a machine (computer)
but the use of algorithms that through iteration provide an ability to predict outcomes
from a data set. The main steps involved in machine learning are preprocessing of
the data set, creation of a training set (usually 80% of the data) and a test set (usually
20% of the data) and selection of a learning algorithm to process the data.
Data-Driven Analysis Techniques 7

Supervised machine learning relates to learning algorithms that build models
that can be used to make predictions using classification and regression techniques
while unsupervised machine learning relates to identifying similar items using clus-
tering techniques. In supervised machine learning, our training data sets have values
for both our input (predictor) and output (outcome) variables that are known to us so
that we can use classification techniques such as support vector machines (SVMs)
and regression techniques such as linear regression, decision trees (DTs) and neural
networks for prediction. In unsupervised learning our training data sets have values
for our input (predictor) variables but not for our output (outcome) variables so this
approach involves examining attributes of a data set in order to determine which
items are most similar to one another. This clustering function can be achieved using
techniques such as K-Means algorithms and neural networks. In addition to the cate-
gories of supervised and unsupervised machine learning, Reinforcement Learning is
a subfield of machine learning that uses learning algorithms that explore options and
when they achieve their aim, deduce how to get to that successful endpoint in the
future. A reinforcement approach can be implemented by the use of a reward and
penalty system to guide a choice from a number of random options. Simulation is
particularly relevant for this type of machine learning as it can provide a virtual envi-
ronment in which the reinforcement training can take place safely and far quicker
than in a real system.
Some examples of machine learning algorithms used are:
– Association rules mining uses a rules-based approach to finding relationships
between variables in a data set.
– DTs generate a rule set that derive the likelihood of a certain outcome based on
the likelihood of the preceding outcome. DTs belong to a class of algorithms
that are often known as CART (classification and regression trees). Random for-
est DTs are an extension of the DT model in which many trees are developed
independently and each “votes” for the tree that gives the best classification of
outcomes.
– SVMs are a class of machine-learning algorithms that are used to classify data
into one or another category.
– k-Means is a popular algorithm for unsupervised learning that is used to create
clusters and thus categorize data.
– Neural networks or artificial neural networks represent a network of connected
layers of (artificial) neurons. These mimic neurons in the human brain that
“fire” (produce an output) when their stimulus (input) reaches a certain thresh-
old. They have recently become a popular approach due to the development of
the backpropagation algorithm which makes it possible to train multi-layered
neural networks. Multilayered neural networks have one or more intermediary
("hidden") layers between the input and output layers to enable a wider range
of functions to be learnt. Neural networks with more than two hidden layers are
generally known as deep neural networks or deep learning systems.

Simulation vs Machine Learning for Prediction
The model-driven approach of simulation requires the model builder to understand causations
and codify them in the model. The model then permits prediction by running the model into the
future—simulation. Machine Learning’s great promise is by using a data-driven approach it can
generate algorithms that may provide predictions. However there are a number of challenges
for the Machine Learning approach when used for prediction
– Although the prediction algorithm is generated, the learning algorithm and training method
must be devised to enable this. This task can be challenging.
– We often do not understand how the prediction algorithm has arrived at its prediction.
Thus algorithms based on approaches such as neural networks are “black box” and are
thus difficult to validate.
– The data used to train and test the algorithm is based on a fixed period of time (i.e.
a sample) and thus may not cover all required learning examples—this is termed
incompleteness.
– There is a need to distinguish natural variation in the data from changes in the data due to
rare or infrequent behavior not representative of typical behavior—this is termed noise
– As the context of the prediction widens the number of potential variables impacting on the
prediction increases vastly. Thus there is a need for increasingly massive data sets to
cover the “state space” of the effects of these variables.
Process Mining
The use of process mining involves obtaining and extracting event data to pro-
duce an event log and transforming the event log into a process model termed pro-
cess discovery. The process model can then be used to check conformance of the
system with the process design and to measure the performance of the process. In
terms of event log construction, the data required to make an event log can come
from a variety of sources including collected data in spreadsheets, databases and
data warehouses or directly from data streams. The minimum data required to
construct an event log consists of a list of process instances (i.e., events), which
are related to a case identification number and for each event a link to an activity
label such as “check ticket.” Activities may reoccur in the event log, but each
event is unique and events within a case need to be presented in order of execu-
tion in the event log so that casual dependencies can be derived in the process
model. It is also usual for there to be a timestamp associated with each event in
the event log. Additional attributes associated with each event may also be in-
cluded such as the association of a resource required to undertake the event and
the estimated cost of the event.
Once we are satisfied that the process model does provide a suitable representa-
tion of behavior, then we can use the model in a normative mode and judge discrepan-
cies in terms of deviations from the ideal behavior shown by the model. Undesirable
behavior is when deviations occur due to unwanted actions (for example, not
Data-Driven Analysis Techniques 9

obtaining authorization for a purchase) and desirable deviations occur when actions
occur that are outside normal parameters but show flexibility in meeting the process
objectives (for example, providing additional customer service). Conformance checking
of processes against a normative model is a major use of process mining. In addition
to conformance checking, process mining can be used to assess performance across
a number of dimensions by providing additional information in the event log, which is
subsequently incorporated into the process model. For example, performance can be
reviewed by associating resources to the people undertaking the activities. The interac-
tions between people can be mapped in a social network to provide an organizational
perspective. In addition, a cost perspective can be achieved by associating costs with
activities.
Visual Analytics
The basic idea of visual analytics is to present large-scale data in some visual form,
allowing people to interact with the data to understand processes better. In order to
facilitate better understanding of data, software that provides a visual representation
of data is available in the form of applications such as spreadsheets, dashboards and
scorecards. In conjunction with their statistical and forecasting capabilities, spread-
sheets are particularly useful at providing graphical displays of trends such as sales for
analysis by an organization. To meet the needs of managers who do not use computers
frequently, a graphical interface, called a dashboard (or a digital dashboard), permits
decision makers to understand statistics collated by an organization. A dashboard dis-
play is a graphical display on the computer presented to the decision maker, which
includes graphical images such as meters, bar graphs, trace plots and text fields to con-
vey real-time information. Dashboards incorporate drill-down features to enable data
to be interrogated in greater detail if necessary. Dashboards should be designed so that
the data displayed can be understood in context. For example, sales figures can be dis-
played against sales figures for the previous time period or the same time period in the
previous year. Figures can also be compared against targets and competitors. For ex-
ample, quality performance can be benchmarked against best-in-class competitors in
the same industry. The visual display of data can also be used to show the amount of
difference between performance and targets both currently and the trend over time.
Visual indicators, such as traffic lights, can be used to show when performance has
fallen below acceptable levels (red light) is a cause for concern (amber light) and is
acceptable (green light).
While dashboards are generally considered to measure operational performance,
scorecards provide a summary of performance over a period of time. Scorecards may
be associated with the concept of the balanced scorecard strategy tool and examine
data from the balanced scorecard perspectives of financial, customer, business pro-
cess and learning and growth.

Data Farming
Data farming is the purposeful generation of data from computer-based models, in-
cluding simulation models. Large-scale simulation experiments can be initiated by
varying many input variables, examining many different scenarios or both. Data
farming offers the possibility of using simulation to generate big data, with the ad-
vantage that the data generated is under the control of the modeler. However, the
implementation of data farming may require the use of simulation software with
a relatively fast execution speed.
People Analytics
Some of the pitfalls around data driven analytics are shown by the use of people analytics in
organizations. People analytics deals with perceptual data and data based on intangible varia-
bles rather than the factual data used in finance for example. Historically data on people within
a business has been used for applications such as workforce modeling in order to match the
supply of people and skills to planned workload. Performance measurement of people has also
taken place in the context of the business itself. However the use of big data to drive analytics
has seen the development of people analytic models that provide measurement based on data
gathered on a massive scale. The idea is that the sheer scale of data will improve the accuracy
of the analytical process and allow “fact-based” decisions to be made on people at the individ-
ual level. However as Cathy O’Neil (2016) found, the complexity of people has led to a number
of pitfalls with the use of people analytic methods, including:
Proxy measures are used to attempt to measure complex human behaviors that may not be
an accurate representation.
The algorithms have inbuilt feedback loops that reinforce the assumptions of the model
leading to self-fulfilling results.
There is inbuilt bias by model builders reflecting their viewpoint on people’s behaviors.
There is a lack of transparency of the workings of the models leading to a lack of knowledge
around the limitations of the results of the models and a lack of accountability regarding the
model’s validity.
Model-Driven Analysis Techniques
Model-driven analysis techniques use a model that can be defined as a simplified
representation of a real system that is used to improve our understanding of that
real system. The representation is simplified because the complexity of most sys-
tems means that it is infeasible to provide all details of the real system in the
model. Indeed, the simplification process actually benefits understanding, where it
allows a focus on the elements of the system that are relevant to the decision. For
this reason, a model should be as simple as possible, while being valid, in order to
meet its objectives. The modeling process thus involves deciding what is relevant
and should be included in the model to meet the aims of the current investigation.
Model-Driven Analysis Techniques 11

The model then provides information for decision making that can be used to make
predictions of real-world system behavior (Figure 1.2).
There are many different approaches to modeling, but mathematical models repre-
sent a system as a number of mathematical variables (termed state variables) with
mathematical equations used to describe how these state variables change over
time. An important distinction between mathematical models is the classification
between static (fixed in time) or dynamic (change over time), with dynamics sys-
tems being modeled using a continuous or discrete approach (Figure 1.3).
Static Mathematical Models
Static models include the use of a computer spreadsheet, which is an example of
a numerical static model in which relationships can be constructed and studied for
different scenarios. Another example of a static numerical model is the Monte Carlo
Simplification by domain expert
Information for decision making
Real world system Computer model
Figure 1.2: The modeling process.
Mathematical
Models
Static
Dynamic
Continuous
Discrete
Linear programming
Spreadsheets
Monte Carlo simulation
System dynamics
Discrete-event simulation
agent-based simulation
Figure 1.3: Categories of mathematical models.

simulation method. This consists of experimental sampling with random num-
bers and deriving results based on these. Although random numbers are being
used, the problems that are being solved are essentially determinate. The Monte
Carlo method is widely used in risk analysis for assessing the risks and benefits
of decisions. Linear programming is a modeling technique that seeks defined
goals when a set of variables and constraints are given. A linear programming
technique is data envelopment analysis (DEA), which is a method for calculating
efficiency. DEA can be used as a benchmarking tool to generate a score that in-
dicates the relative distance of an entity to the best practices so as to measure its
overall performance compared with its peers. This overall performance measured
by DEA can be manifested in the form of a composite measure that aggregates
individual indicators. Chapter 18 shows how DEA may be used in conjunction
with simulation.
Dynamic Mathematical Models
A dynamic mathematical model allows changes in system attributes to be derived
as a function of time. A classification is made between continuous and discrete
model types. A discrete system changes only at separate points in time. For exam-
ple, the number of customers in a service system is dependent on individual arriv-
als and departures of customers at discrete points in time.
Continuous systems vary over time; for example, the amount of petrol in
a tanker being emptied is varying continuously over time and is thus classi-
fied as a continuous system. In practice most continuous systems can be mod-
eled as discrete and vice versa at different levels of detail. Also, systems will
usually have a mixture of both discrete and continuous elements. In general,
continuous models are used at a high level of abstraction, for example, inves-
tigating cause-and-effect linkages in organizational systems, while discrete
models are used to model business processes. The system dynamics (SD) ap-
proach is described as an example of a continuous mathematical model, while
discrete-event simulation (DES) is described as a discrete mathematical model-
ing approach.
Simulation
Simulation is a particular kind of dynamic modeling in which the model (usually
represented on a computer) is “run” forward through (simulated) time. This book
is focused on the use of simulation in an organizational context to measure busi-
ness process performance. In order to use simulation, we must represent a theory
of how the organization works (conceptual model) and transform that into
Simulation 13

a procedure that can be represented as a computer program (simulation model).
Simulation has an experimental methodology in that we can explore the effect of
different parameters by running the simulation under many different conditions.
From these observations, we can refine our theory about how the organization
works and can make predictions about how it might work in the future. Thus sim-
ulation can be used to:
– Understand past and current behavior of business processes (descriptive
analytics).
– Predict the future behavior of business processes (predictive analytics).
– Recommend action based on the future behavior of business processes (pre-
scriptive analytics).
The Need for Simulation When Studying a Dynamic System
When studying organizational systems we are studying a dynamic system—one that changes
over time and reacts to its environment and thus shows both structure and behavior. This
means that the model must also be dynamic and it can be represented by a mathematical equa-
tion, a logical statement (such as a series of if-then statements) or as a computer program (in
the form of an algorithm). There are two aspects of dynamic systems are addressed by
simulation:
Variability
Most business systems contain variability in both the demand on the system (e.g., customer
arrivals) and in durations (e.g., customer service times) of activities within the system. The
use of fixed (e.g., average) values will provide some indication of performance, but simulation
permits the incorporation of statistical distributions and thus provides an indication of both
the range and variability of the performance of the system. This is important in customer-
based systems when not only is the average performance relevant, but performance should
also not drop below a certain level (e.g., customer service time) or customers will be lost. In
service systems, two widely used performance measures are an estimate of the maximum
queuing time for customers and the utilization (i.e., percentage time occupied) for the staff
serving the customer. If there is no variability, there will be no queues as long as the arrival
rate is less than or equal to the service time. However, Figure 1.4 shows that the higher the
variability, the higher the average queue length for a given utilization. It is difficult to elimi-
nate variability entirely, so it is recommended to try to keep utilization (of staff and equip-
ment) below 80%.
Variability can be classified into customer-introduced variability and internal process vari-
ability. Customer-introduced variability includes factors such as the fact that customers don’t
arrive uniformly to a service and customers will require different services with different service
times. Also not all customers appreciate the same thing in a service; some like self-service and
some do not. In addition customer-introduced variability can arise from internal processes
within the organization such as variability in staff performance (this includes both variability
between different people's performance and variability in process performance by one person
over time). Variability can also be caused by equipment and material variations.

Interdependence
Most systems contain a number of decision points that affect the overall performance of the
system. The simulation technique can incorporate statistical distributions to model the likely
decision options taken. Also the “knock-on” effect of many interdependent decisions over time
can be assessed using the model’s ability to show system behavior over a time period.
To show the effect of variability on systems, a simple example will be presented. An owner of
a small shop wishes to predict how long customers wait for service during a typical day. The
owner has identified two types of customer, who have different amounts of shopping and so
take different amounts of time to serve. Type A customers account for 70% of custom and take
on average 10 minutes to serve. Type B customers account for 30% of custom and take on aver-
age 5 minutes to serve. The owner has estimated that during an 8-hour day, on average the
shop will serve 40 customers. The owner then calculates the serve time during a particular day:
Customer A = 0.7 × 40 × 10 minutes = 280 minutes
Customer B = 0.3 × 40 × 5 minutes = 60 minutes
Therefore, the total service time = 340 minutes and gives a utilization of the shop till of 340/
480 × 100 = 71%
Thus, the owner is confident that all customers can be served promptly during a typical day.
A simulation model was constructed for this system to estimate the service time for customers.
Using a fixed time between customer arrivals of 480/40 = 12 minutes and with a 70% probabil-
ity of a 10 minutes service time and a 30% probability of a 5 minutes service time, the overall
service time for customers (including queuing time) has a range of between 5 and 10 minutes
and no queues are present in this system.
Service Time for Customer (minutes)
Average 8.5
Minimum 5
Maximum 10
However, in reality customers will not arrive, equally spaced at 12-minute intervals, but will ar-
rive randomly with an average interval of 12 minutes. The simulation is altered to show a time
Average
number in
queue
Average utilization (arrival rate/service time)
High
variability
Low variability
Figure 1.4: Average number in queue against average utilization.
Simulation 15

between arrivals following an exponential distribution (the exponential distribution is often
used to mimic the behavior of customer arrivals) with a mean of 12 minutes. The owner was
surprised by the simulation results:
Service Time for Customer (minutes)
Average 17
Minimum 5
Maximum 46
The average service time for a customer had doubled to 17 minutes, with a maximum of 46
minutes!
The example demonstrates how the performance of even simple systems can be affected
by randomness. Variability would also be present in this system in other areas such as
customer service times and the mix of customer types over time. Simulation is able to in-
corporate all of these sources of variability to provide a more realistic picture of system
performance.
Deterministic and Stochastic Models
Another way of classifying models is between deterministic and stochastic models. A deterministic
model does not represent uncertainty and so for a given set of conditions and parameters will al-
ways produce the same outcome. This implies that given a well enough detailed snapshot of
a system we should be able to forecast the system’s dynamic behavior perfectly. Thus these types
of models are analytically tractable and may be expressed as mathematical formulae. Stochastic
models include some random components such as variable demand rate or variation of processing
rates due to natural variability. The inclusion of stochasticity typically makes even simple models
intractable but increases their realism. This is because few systems show no variation over time or
can be perfectly understood and measured. However a stochastic model only allows us to quote
a probability of a future prediction.
The Role of Simplification in Data-Driven and Model-Driven Analysis
In order to be used for prediction, both data- and model-driven analysis methods need to sim-
plify the real world in order to reduce complexity.
In the area of data-driven machine learning, the terms overfitting and underfitting are used to
describe the simplification process. Overfitting is when the learning algorithm “tries too hard” to
fit the data, approximating nearly all the points in the data set. This means there is a lack of gen-
eralization and the algorithm only explains behavior that directly derives from the training data.
In this case, any noise such as missing or incorrect data in the test data set will cause
a misleading prediction. The algorithm will produce a number of different mistakes, termed high
variance. Underfitting is when the algorithm is “not trying hard enough” to fit the data, leading to
the same mistakes repeated, termed high bias. This means there is too much generalization and
the algorithm predicts behavior that does not derive from the training data. The solution to over-
fitting is to try a less flexible learning algorithm or to obtain more data. The solution to underfit-
ting is to try a more flexible learning algorithm or try a different learning algorithm. The issue of
simplification in machine learning is about guiding the learning algorithms to provide a balance
between underfitting and overfitting the data, which is a difficult task.

In the area of model-driven simulation, simplification is about providing a specification
for a conceptual model that contains a suitable level of detail to meet the predictive needs
of the model. Too little simplification will lead to an overly complex model, which may hin-
der understanding of the effects being studied. Too much simplification will lead to inaccu-
rate results as important elements of the system that have an effect on the predictive
metrics of interest have been omitted from the model.In data-driven machine learning, the
simplification process is coded into the design of the learning algorithm by the data scien-
tist, whereas in model-driven simulation the simplification process is achieved using the
domain knowledge of the modeler. Both approaches need careful application of the model
and interpretation of model results by personnel with the requisite technical (quantitative)
and domain knowledge (qualitative) skillsets.
Data- and Model-Driven Analysis with Simulation and Analytics
So far we have defined data- and model-driven approaches to the analysis of busi-
ness processes. Analytics is categorized as a data-driven approach and simulation
is categorized as a model-driven approach. There are instances, however, of the use
of analytics techniques that are driven by data generated from a model that will be
termed model-driven analytics and simulations that are data driven, termed data-
driven simulation.
Simulation and analytics and thus each of these combinations attempt to cod-
ify the real world into a computer model that can be used for understanding and
prediction of the real system. This reality will usually be based on knowledge of
only a part of all the data that exists (or ever existed) about the real system. The
relationship between data-driven, model-driven, analytics and simulation is pre-
sented in this context. Figure 1.5 shows how the four combinations of simulation
and analytic analysis can be represented by four types of reality that reflect their
different emphasis in terms of the use of a subset of all the data that exists that is
related to a system.
Selected reality
Data (raw)
Farmed reality
Data (simulated)
Digital reality
Data (analyzed)
Simplified reality
Data (sampled)
Data-driven Model-driven
Analytics
Simulation
Figure 1.5: Data- and model-driven analysis with simulation and analytics.
Data- and Model-Driven Analysis with Simulation and Analytics 17

The categories in Figure 1.5 cover the following:
– Data-driven analytics techniques that use raw data to learn from the past to
represent a selected reality based on the variables and observations included.
This is the data-driven approach described earlier and is represented by analyt-
ics techniques such as data mining, machine learning and process mining.
Data-driven analytics represent a selected reality in that no matter how large
the data sets used for analysis they will only present a selected view of all the
data generated by a process over time.
– Model-driven simulation techniques that use sampled data from the past to rep-
resent a simplified reality. This is the model-driven approach described earlier
and is represented by the technique of simulation. This is termed a simplified
reality as the modeling process employs a simplification of reality by removing
elements that are not considered relevant to the study objectives.
– Data-driven simulations that use analyzed data to drive simulation to provide
a digital reality. These applications allow data, which may be processed through
analytic techniques such as process mining, data mining and machine learning,
to advance the capability of simulation model development and experimentation.
The use of a data-driven approach to provide model-building capabilities and
thus enable recoding of the model to reflect the actual state of a system is
a particularly important advance represented by the use of applications such as
digital twins. This is termed digital reality as the approach is used to construct
a real-time digital replica of a physical object.
– Model-driven analytics that use simulated data to drive analytics techniques to
provide a farmed reality. This enables simulation to be used for training and
testing machine-learning algorithms and facilitating the use of analytic techni-
ques for future system behaviors and for systems that do not currently exist.
This is termed a farmed reality in reference to the term data farming, which re-
fers to the use of a simulation model to generate synthetic data.
Data-Driven Simulation
Usually a simulation model will take some time to develop with a custom model built for each
application and collection of data over a period of time by methods such as observation and
interviews with personnel involved in the process. This relatively long development time and
use of historical data can limit the use of simulation to medium- to long-term decisions based
on steady-state operation. To enable simulation for short-term operational decision making,
there is a need for continuous updating of both the data that is used by the model and in some
instances of the model itself.
This can be now be achieved in a number of ways including:
1. The use of historical process data from factories such as those provided using the
manufacturing execution systems (MES) standard to provide automated collection and
faster updating of data values to configure a simulation model.

2. Real-time information on the status of machines and production schedules in the factory to
provide automated model regeneration to reflect changes in the physical system as they
occur.
3. Data from the simulation model used in conjunction with machine-learning analytics to
flow back to the physical system to control its actions.
All three of these options could be referred to as data-driven simulations and their use should
be based on the complexity of the system being modeled and the objectives of the simulation
study. In terms of the use of historical process data, MES systems are used to track and
control production systems and provide a scheduling capability. For example, the Simio
simulation software package provides facilities to extract data directly from an MES and build
and conﬁgure a Simio model from that data. Simio includes a feature to auto-create model
components and their properties based on the contents of the imported tables, which can
then be used to build complete models from external data. These models would normally
provide a base model, which could then be reﬁned if necessary. This option thus provides the
ability to generate a model much faster than traditional simulation approaches.
Digital Twins
The term digital twin is used to refer to a data-driven simulation that makes use of real-time
data flows and requires a number of components which together in a manufacturing context are
implemented in a Smart Factory. These components include:
– Data infrastructure such as the internet of things (IoT) to provide data collection through
sensors and data connection through the internet.
– Machine-learning techniques to provide an analytics capability.
– Robotics to provide automated control.
Digital twins can be categorized by the level of data integration between the simulation and
real-world object counterpart and by the organizational scope of the simulation.
In terms of the level of data integration there are three possible levels of integration be-
tween the simulation and its real-world object counterpart. When there is no automated data
exchange between the simulation and real-world object, when there is an automated one-way
data flow from the real-world object which leads to a change in state of the simulation and
when data flows are fully integrated in both directions. Digital twins require a two-way data
flow to provide a control capability to take action in response to predicted behavior.
Corrective actions are often implemented using analytics techniques based on machine-
learning algorithms that provide appropriate methods of process control actuation. The devel-
opment of digital twins with fully integrated data flows in both directions is complex and is
still in its infancy.
In the context of the organization, the scope of a digital twin can be at the product, process
and enterprise level.
Digital Twins of Products
This type of digital twin relates to the emulation of physical objects such as machines, ve-
hicles, people and energy. They can be considered as an extension of computer-aided design
(CAD) and computer-aided engineering systems, which capture data that can then be used to

detect issues and generate information that can be used to improve performance. They often
have a focus on improving the efficiency of product life-cycle management, which is important
for successful product-as-a-service business models. Digital twins allow monitoring of multi-
ple products and resources in different operating conditions and different geographic
locations.
Digital Twins of Processes
These emulate processes over time and so require a dynamic simulation engine based on
methods such as DES covered in this book. Depending on the application, process data may
be collected in real time or near real time. Near real-time collection either allows for a delay
for data processing or collects data at set time points and may provide greater feasibility in
execution.
Digital Twins of Enterprises
At the enterprise level, the objective of a digital twin is to capture the business-operating
model for control and management purposes. Enterprise digital twins can be implemented
by using multiple digital twins that are in use at the process level. Applications include con-
nection of the digital twin to an enterprise resource-planning system in order to improve fac-
tory scheduling.
By combining the classification of digital twins by level of data integration and organiza-
tional scope we can see that the concept covers a wide range of applications. Figure 1.6
shows that a key consideration between these different applications is the complexity implied
in the application, with a full digital twin of the enterprise representing the most complex.
No integration
One-way integration
Both-way integration
Product Process Enterprise
Level
of
data
integration
Organizational scope
Complexity
Figure 1.6: Level of data integration and organizational scope of a digital twin.

An Example of a Digital Twin
An example of the use of data-driven simulation combined with machine learning is for predictive
maintenance for a welding machine. Here a simulation provides a virtual representation in real
time of the manufacturing process through data connections over the IoT. The current status of the
welding machine is known by the digital twin. A machine-learning algorithm is used to provide
a prediction of the remaining useful life of the manufacturing equipment based on its current
usage and historical data of the process. The digital twin can be run into the future and predict
machine failure based on its current status and scheduled future usage. The digital twin can then
communicate back to the equipment to instigate a maintenance operation at the appropriate time.
The digital twin thus provides an intelligent and automated predictive maintenance capability.
Model-Driven Analytics
One use for simulation is to generate data to train and test machine-learning algorithms. For
example, in scheduling manufacturing systems, a simulation can be used to randomly generate
combinations of control attributes (such as work-in-progress and utilization). The simulation
can then compare the scheduling performance of the trained machine-learning-based algo-
rithms and further traditional scheduling rules such as shortest process time. Using simulation
in this way offers the possibility of its use for training algorithms for current and planned sys-
tems and for systems that do not currently exist.
The categories in Figure 1.5 cover data-driven analytics techniques that use raw data
to learn from the past to represent a selected reality based on the variables and obser-
vations included; and model-driven simulation techniques that use sampled data
from the past to represent a simplified reality. The predictive capabilities of both of
these approaches are limited by the transient nature of organizational processes. No
matter how large the dataset used in a data-driven approach it may not describe
a future behavior owing to changes in the system causing that behavior. This will
occur at least until the new behavior has been incorporated into the data provided to
the learning algorithms. For model-driven approaches no matter how large the model
we may not incorporate a future behavior owing to the simplified representation of
the model, at least until we have recoded the model to incorporate the cause of that
behavior. Two further categories are shown in Figure 1.5, data-driven simulation that
use data from analytics to drive simulation to provide a digital reality; and model-
driven analytics that use data from simulation to drive analytics techniques to pro-
vide a farmed reality. In terms of data-driven simulation, practitioners need to take
into account the limitations of the data-driven approach in terms of the use of histori-
cal data to represent the future of a transient system. In terms of model-driven analyt-
ics simulation, here the limitation is based around the use of a sampled dataset that
is a simplification of the raw data generated by the real system.
A barrier to the combined use of simulation and analytics is the different back-
grounds and skillsets of simulation and analytics practitioners. Simulation practi-
tioners typically combine the technical knowledge required to undertake simulation

such as model building and statistical methods with an understanding of an applica-
tion domain such as manufacturing or healthcare. In a business setting analytics
may be undertaken by teams consisting of data scientists with data, statistical and IT
skills, business analysts with deep domain knowledge and IT professionals to de-
velop data products. Many simulation practitioners began their simulation careers
coding models in simulation languages such as SIMAN and using languages such as
FORTRAN for file processing. However in the light of the development of drag and
drop interfaces in such tools as Arena, recent users may find it a particular challenge
to adapt to the need for coding when developing a machine learning algorithm in
Matlab, R or Python. One way of addressing this issue may be to emphasize the need
for training of simulation practitioners in data science techniques and the adoption
of a multi-disciplinary approach to research and training.
Comparing the Use of Model-driven Simulation and Data-driven Analytics for Prediction
Simulation and analytics techniques such as machine learning represent two different perspec-
tives on how we can attempt to predict the future. Simulation applies our domain knowledge to
define a relationship between cause and effect which is codified in a conceptual model.
Machine Learning applies our domain knowledge to the design of a learning algorithm that
uses statistics to generate an algorithm that defines a relationship between cause and effect.
Both methods require abstraction methods to simplify reality to produce a relationship between
cause and effect that is generalizable in different applications. In simulation a model-driven ap-
proach requires the definition of the model scope and level of detail in order to meet the simu-
lation objectives. Validation is achieved by significance tests of a comparison between the real
and simulated system. In machine learning a data-driven approach is required which limits
what is termed the state-space; the number of attributes and number of possible outcomes for
the learning algorithm. Validation is achieved by significance tests of a comparison between
the training and test data. The advantage of simulation may be that it codifies within the model
the relationship between cause and effect. The statistical approach of machine learning can
only provide a correlation for prediction. As is often quoted correlation is not causation, we can-
not use the strength of correlation between observed and predicted data to infer that a model’s
prediction is valid. We may also have issues with the use of correlation as a measure in itself.
For example if a model systematically under or over-predicts by a roughly constant amount, no
matter how large, then the correlation will be unaffected. Also if there is a lag in the timing of
the prediction the correlation will be low, even if the magnitude of the prediction is reasonably
accurate. Finally very different data can give exactly the same correlation co-efficient and the
use of visual inspection of model outcomes is recommended. Despite this however correlation
analysis may provide all the information we need and we may even take our correlation as
a sign of causation in certain circumstances. Also we may be attempting to predict aspects
such as human behavior that may be difficult or impossible to codify in a simulation model.
Combining Simulation and Analytics
When undertaking simulation and analytics in combination the following approaches are possi-
ble. For data-driven simulation, a non-integrated approach involves the use of analytics to pro-
cess input data for further use in a simulation model. For example, machine learning algorithms

can be used to generate decision trees that can be codified within the simulation which then
runs independently of the analytics application. An integrated approach embeds the analytics
techniques within the simulation model. One approach is to “call” previously trained algorithms
from the simulation during runtime. However in order for the context of the simulation and ana-
lytics algorithms to be synchronized it may be necessary to undertake training of algorithms
simultaneously with each simulation run. This can be undertaken during the warmup period of
the simulation (before execution of the main simulation experiment) or during the simulation
run itself through the use of real-time data streams such as may be used by a digital twin. For
model-driven analytics applications the simulation can either generate data files that are sub-
sequently used by the analytics application or in an integrated approach provide the environ-
ment around which the analytics application operates. An example of this approach could be
the use of simulation to provide the transport environment in which the analytics algorithms
are trained to direct delivery vehicles.
Types of Simulation
There follows a brief overview of the three main simulation approaches, namely,
SD, agent-based simulation (ABS) and DES. The three methods have their own phi-
losophies, communities of users and main areas of application.
System Dynamics (SD)
SD is a modeling technique that was originally developed by Professor Jay Forrester
when it was known as industrial dynamics. In SD models, stocks of variables are con-
nected together via flows. SD has been used extensively in a wide range of application
areas, for example, economics, supply chain, ecology and population dynamics to
name a few. SD has a well-developed methodology in that the main stages and phases
of the construction of a model are defined. SD attempts to describe systems in terms
of feedback and delays. Negative feedback loops provide a control mechanism that
compares the output of a system against a target and adjusts the input to eliminate
the difference. Instead of reducing this variance between actual output and target out-
put, positive feedback adds the variance to the output value and thus increases the
overall variance. Most systems consist of a number of positive and negative feedback
cycles, which make them difficult to understand. Adding to this complexity is the time
delay that will occur between the identification of the variation and action taken to
eliminate it and the taking of that action and its effect on output. What often occurs is
a cycle of overshooting and undershooting the target value until the variance is elimi-
nated. The SD concept can be implemented using computer software such as Stella II.
A system is represented by a number of stocks (also termed levels) and flows (also
termed rates). A stock is an accumulation of a resource such as materials and a flow is
the movement of this resource that leads to the stock rising, falling or remaining
Types of Simulation 23

constant. A characteristic of stocks is that they will remain in the system even if flow
rates drop to zero and they act to decouple flow rates. An example is a safety stock of
finished goods which provides a buffer between a production system which manufac-
tures them at a constant rate and fluctuating external customer demand for the goods.
An SD flow diagram maps out the relationships between stocks and flows. In Stella II,
resource flows are represented by a double arrow and information flows by a single
arrow. Stocks are represented by rectangles. Converters, which are used for a variety
of tasks such as combining flows, are represented by a circle. Figure 1.7 shows
a simple SD model in Stella II format.
Once the diagram is entered, it is necessary to enter first-order difference equations
that compute the changes of a time-slice represented by the time increment dt. At
the current time point (t) the stock value Lev(t) is calculated by the software as
follows:
Lev(t) = Lev (t−dt) + (InRate−OutRate) * dt
This equation translates to the current stock value is a function of the previously
calculated stock value plus the net flow over the time interval since the last calcula-
tion. For a population model, the following equation could be used to express the
POPULATION stock value.
POPULATION (t) = POPULATION (t-dt) + (BIRTHSdt−DEATHSdt) * dt
One difference in the approach of SD compared to the discrete-event approach can
be demonstrated by an example of a simulation of a new product development pro-
cess. Here the discrete-event approach is able to model each customer purchase
(rather than the quantity sold during a time period) and thus model individual pur-
chase decisions through the ability of DES to carry information regarding each
Population
Birth rate
Births Deaths
Death rate
Figure 1.7: System dynamics diagram for population model.

entity (customer) in the system. Also queuing behavior derived from demand ex-
ceeding supply requires the use of the discrete-event method. Thus, rather than as
a substitute for the discrete-event method, SD can be seen as a more complemen-
tary technique particularly suited for analyzing overall cause-and-effect linkages in
human systems.
Agent-Based Simulation (ABS)
The use of agents in the design of simulation models has its origins in complexity
of science and game theory. Agents are components in a system (for example,
a person or an organization) that have a set of rules or behavior that controls how
they take in information, process that information and effect change on their envi-
ronment. ABS refers to the study of the behavior of agents from the bottom up. This
means that agent behaviors are defined, and then the agents are released into the
environment of study. The behavior of the agents then emerges as a consequence of
their interaction. In this sense, the system behavior is an emergent property of the
agent interactions and the main source of structural change in the system itself is in
the form of the relationship between the agents. ABS has been applied across
a wide area, for example, economics, human behavior, supply chains, emergency
evacuation, transport and healthcare. A particular class of agent-based systems
termed multiagent simulations are concerned with modeling both individual agents
(with autonomy and interactivity) and also the emergent system behavior that is
a consequence of the agent’s collective actions and interactions.
Cellular Automata
Cellular automata are simple agent-based systems that consist of a number of identical cells
that are arranged in a grid usually in the form of a rectangular or 3D cube structure. Each cell
may be in one defined state (such as “on” or “off”) that is determined by a set of rules that
specify how that state depends on its previous state and the states of the cell’s immediate
neighbors. The same rules are used to update the state of every cell in the grid. Thus, the tech-
nique is best used to model local interactions, which are governed by rules that are homoge-
neous in respect to the cell population. Most types of agent-based systems now have actors
that are freed from their cells with the ability to perform autonomous and goal-directed
behavior.
Discrete-Event Simulation (DES)
DES takes a process view of the world and individual entities can be represented as
they move between different resources and are processed or wait in queues. It is
hard to estimate the number of global users of DES, but there is little doubt that of

the three types of simulation outlined here, DES has the largest user base. Evidence
for this is provided by the biannual simulation survey carried out by OR/MS Today,
which demonstrates the wide range of applications for which DES has been used.
The main areas of application are manufacturing, supply chain and logistics, mili-
tary and more recently healthcare. DES is concerned with the modeling of systems
that can be represented by a series of events. The simulation describes each individ-
ual event, moving from one to the next as time progresses. When constructing
a DES, the system being simulated is seen as consisting of a number of entities
(e.g., products, people) that have a number of attributes (e.g., product type, age).
An entity may consume work in the form of people or a machine, termed a resource.
The amount and timing of resource availability may be specified by the model user.
Entities may wait in a queue if a resource is not available when required. The main
components of a DES are as follows:
– Event—an instantaneous occurrence that may change the state of the system.
– Entity—an object (e.g., material, information, people) that moves through the
simulation activating events.
– Attribute—a characteristic of an entity. An entity may have several attributes
associated with it (e.g., component type).
– Resource—an object (e.g., equipment, person) that provides a service to an en-
tity (e.g., lathe machine, shop assistant).
For a DES, a system consists of a number of objects (entity) that flow from point to
point in a system while competing with each other for the use of scarce resources
(resource). The approach allows many objects to be manipulated at one time by
dealing with multiple events at a single point in time. The attributes of an entity
may be used to determine future actions taken by the entities. In DES time is moved
forward in discrete chunks from event to event, ignoring any time between those
events. Thus, the simulation needs to keep a record of when future events will
occur and activate them in time order. These event timings are kept on what is
termed as the simulation calendar that is a list of all future events in time order. The
simulation calendar is also known as the future event list. The simulation executes
by advancing through these events sequentially. When an event has been com-
pleted, the simulation time—stored as a data value called the simulation clock—is
advanced in a discrete step to the time of the next event. This loop behavior of exe-
cuting all events at a particular time and then advancing the simulation clock is
controlled by the control program or executive of the simulation. There are three
main methods of executive control.
In an event-based simulation, future events are scheduled on an event list. In
the first phase of the approach, the executive program simply advances the simula-
tion clock to the time of the next event. At the second phase, all events at that par-
ticular clock time are then executed. Any new events that are derived from these
events are added to the simulation calendar. When all events have been executed

at the current time, the executive program advances the simulation clock to the
time of the next event and the loop repeats. The simulation continues until no
events remain on the simulation calendar or a termination event is executed.
The activity-based approach works by scanning activities at a fixed time inter-
val and activities that satisfy the necessary conditions are immediately scheduled.
Unlike the event-based approach, the activity scanning method does not require
event lists to be maintained. However, the method is relatively inefficient and there-
fore slow because of the number of unnecessary scans that are needed when no
events may be occurring. Also an event may be scheduled between two consecutive
scans and thus will not be activated at the correct time.
Most commercial software uses the process-based approach, which allows the
user to enter a program in a more intuitive flowchart format. The simulation pro-
gram is built as a series of process flowcharts that detail the events through which
a class of entity will pass. The use of entity attributes allows decision points to be
incorporated into the flowchart, providing alternative process routes for entity
classes.
A popular method of control is the three-phase approach that combines the
event- and activity-based methods. The three phases are shown in Figure 1.8 and
described as follows:
– The “A” phase involves advances the simulation clock to the next event time.
The simulation calendar is inspected and the clock jumps directly to the event
with the time closest to the current simulation clock time. The clock is held con-
stant during the three phases until the next “A” phase.
– The “B” phase involves execution of all activities whose future time is known
(i.e., bound events). The simulation takes all bound events that are due to
occur at the current simulation time from the calendar and executes them. The
execution of bound events may cause further events to occur. These are placed
on the simulation calendar to be activated at the appropriate time.
– The “C” phase involves execution of all activities whose future time depends on
other events (i.e., conditional events termed C-events). For each “C” phase, all
conditional events are checked to see if the conditions determining whether
they can be executed are met. If the conditions are met, the conditional event is
executed. The execution of a C-event may cause other C-event conditions to be
met. For this reason the C-events are repeatedly scanned until all C-event con-
ditions are not met at this time point.
In general, bound events are events such as the end of a process when time can be
predicted by simply adding the current simulation time to the process duration.
Conditional events are occurrences that are dependent on resource availability
whose future timing can not be predicted (e.g., a customer awaiting service at
a bank). The three-phase approach simply scans all conditional events after the
bound events have been executed to check if the simulation state allows the

Advance to next
event time
Execute bound
events
Execute
conditional
events
Start
Any
conditonal
events
activated?
Finish
No
Yes
Yes
No
Termination
event?
A phase
B phase
C phase
Figure 1.8: The three-phase executive.

conditional event to take place. The operation of the three-phase discrete-event
method can be shown by studying the actions of the next event mechanism on the
simulation clock.
Figure 1.9 illustrates the next-event time advance approach. Arrival times (A1,
A2, . . .) and service times (S1, S2, . . .) will normally be random variables taken from
a suitable distribution. The discrete-event system operates as follows. The simula-
tion clock advances to the first event at time 8. This is an arrival event (A1) where
an entity arrives at the resource. At this time the resource is available (“idle”) and
so is immediately serviced for 16 time units (S1). During this period, the server sta-
tus is set to “busy.” The simulation calculates the service completion time (C1) of 24
units and inserts an event on the calendar at that time. At time 20, a second entity
arrives (A2). Because the server is currently in the “busy” state, the entity waits at
the server queue until the server becomes available. At each future event, the status
of the server is checked using a conditional (C) event. At time 24 the first entity com-
pletes service (C1) and thus changes the server status from “busy” to “idle.” Entity 2
will now leave the queue and commence service, changing the server status back
from “idle” to “busy.” The completion time is calculated as the current time + ser-
vice time (24+12 = 36) and a completion event is entered on the calendar at this
time. At time 30, entity 3 arrives (A3). Again, the server is busy so the entity waits at
the server queue. At time 36, the second entity completes service (C2) and entity 3
can now leave the queue and commence service. The simulation continues until
a termination state is reached. The time in the system for each entity can be calcu-
lated by the addition of the queuing time and service time (Table 1.1).
8
S1 S2
A1 A2 C1 A3 C2
S = Service time
A = Arrival
C = Completion
0 20
6 6
12 4
24 30 36
8
Figure 1.9: Operation of the three-phase approach.
Table 1.1: Queue and Service Times for Entities.
Entity Queue Time Service Time System Time
   
   

This demonstrates how the next-event time mechanism increments the simula-
tion clock to the next (in time order) event on the calendar. At this point the system
status is updated and future event times are calculated. The time between each ad-
vance will vary depending on the pattern of future events.
Hybrid Simulation: Combining SD, ABS and DES
Hybrid simulation refers to the combined used of two or more of the techniques of SD, ABS and
DES in a simulation study. Hybrid Simulation is intended to enable a suitable modeling ap-
proach to different aspects of the problem and avoid complicated model constructs (known as
workarounds) or oversimplification to achieve a valid model. A hybrid simulation study can be
achieved by the following.
Developing multiple models that exchange data between them. An example is the use of an
SD model that exchanges customer flow data with an ABS that is modeling individual customer
behavior.
Using different models for different stages of the simulation study. “A systems thinking
study” in Chapter 3 is an example of the use of system dynamics to understand the causes
around the behavior of a system that was modeled using DES.
A combination of the approaches in a single model. The AnyLogic software package provides
a multimethod modeling platform that allows the three approaches to be combined. For exam-
ple, a supply chain can be modeled using DES to model business processes with each element
of the supply chain at the same time an agent with attributes such as supplier choice, orders
and shipments.
Using Simulation to Model Human Behavior
The modeling of people is becoming increasingly important in the design of business
processes. Thus to provide a realistic basis for decision support, people’s behavior
will need to be included in simulation models if they are to be effective tools. Many
of the systems that we would like to understand or improve involve human actors,
either as customers of the system or as people performing various roles within the
system. Modeling passive, predictable objects in a factory or a warehouse, however,
is very different from trying to model people. Modeling people can be challenging be-
cause people exhibit many traits to do with being conscious sentient beings with free
will. Human beings can be awkward and unpredictable in their behavior and they
may not conform to our ideas about how they should behave in a given situation.
This presents a practical challenge to model builders, i.e. when and how to represent
human behavior in our simulation models. In some situations, the role of human be-
havior in the model may be small and may be simplified or even left out of the
model. In other cases, human behavior may be central to the understanding of the
system under study and then it becomes important that the modeler represents this
in an appropriate way.

Figure 1.10 presents an overview of potential methods of modeling people who
are identified and classified by the level of detail (termed abstraction) required to
model human behavior. Each approach is given a method name and method descrip-
tion listed in the order of the level of detail used to model human behavior. The
overview recognizes that the incorporation of human behavior in a simulation
study does not necessarily involve the coding of human behavior in the simulation
model itself. It is the combination of the simulation model used in conjunction with
the user of that model that will provide the analysis of human behavior required
and so this may be achieved by an analysis ranging from solely by the user to the
detailed modeling of individual human behavior in the simulation model itself.
Thus, the methods are classified into those that are undertaken outside the model
(i.e., elements of human behavior are considered in the simulation study, but not
incorporated in the simulation model), and those that incorporate human behavior
within the simulation model, termed inside the model. Methods inside the model
are classified in terms of a world view. Model abstraction is categorized as macro,
meso or macro in order to clarify the different levels of detail for methods “inside
None
Outside
the
model
Inside
the
model
None
Continuous system
simulation dynamics
Discrete-event
simulation
Discrete-
event
simulation
Agent-based
simulation
Method
name
Simplify
Externalize
Flow
Entity
Task
Individual
Eliminate human
behavior by
simplification
Incorprate human
behavior outside
of the model
Model humans as
flows Continuos macro
Process
Object Micro
Model human as
machine or material
Model human
perfomance
Model human
behavior
Method description Word
view
Model
abstraction
Simulation
approach Abstraction
meso
Figure 1.10: Methods of modeling human behavior in a simulation study.
Using Simulation to Model Human Behavior 31

the model.” The framework then provides a suggested simulation approach for each
of the levels of detail.
The methods of modeling human behavior shown in Figure 1.10 are now de-
scribed in more detail.
Simplify (Eliminate Human Behavior by Simplification)
This involves the simplification of the simulation model in order to eliminate any re-
quirement to codify human behavior. This strategy is relevant because a simulation
model is not a copy of reality and should only include those elements necessary to
meet the study objectives. This may make the incorporation of human behavior un-
necessary. It may also be the case that the simulation user can utilize their knowl-
edge of human behavior in conjunction with the model results to provide a suitable
analysis. Actual mechanisms for the simplification of reality in a simulation model
can be classified into omission, aggregation and substitution and will be considered
under the topic of conceptual modeling (Chapter 3).
Externalize (Incorporate Human Behavior Outside of the Model)
This approach involves incorporating aspects of human behavior in the simulation
study, but externalizing them from the simulation model itself. For example, the
“externalize” approach to represent human decision making is to elicit the decision
rules from the people involved in the relevant decisions and so avoid the simplifica-
tion inherent when codifying complex behavior. Analytic techniques such as ma-
chine learning and neural networks can be interfaced with the simulation and be
used to provide a suitable repository for human behavior.
Flow (Model Humans as Flows)
At the highest level of abstraction inside the model, humans can be modeled as
a group which behaves like a flow in a pipe. In the case of the flow method of
modeling human behavior, the world view is termed continuous and the model ab-
straction is termed macro. The type of simulation used for implementation of the
flow method is usually the SD technique. The flow approach models humans at the
highest level of abstraction using differential equations. The level of abstraction,
however, means that this approach does not possess the ability to carry information
about each entity (person) through the system being modeled and is not able to
show queuing behavior of people derived from demand and supply. Thus, the

simulation of human behavior in customer-processing applications, for example,
may not be feasible using this approach.
Entity (Model Human as a Machine or Material)
This relates to a mesoscopic (meso) simulation in which elements are modeled as
a number of discrete particles whose behavior is governed by predefined rules. One
way of modeling human behavior in this way would mean that a human would be
either a resource, such as a unit of equipment that is either “busy” or “idle.”
Alternatively modeling a human as an entity would mean that they would under-
take a number of predetermined steps, such as the movement of material in
a manufacturing plant. This approach can be related to the process world view,
which models the movement of entities through a series of process steps. The entity
approach models human behavior using the process world view to either represent
people by simulated machines (resources) and/or simulated materials (entities).
This allows the availability of staff to be monitored in the case of resources and the
flow characteristics of people, such as customers, to be monitored in the case of
entities.
Task (Model Human Performance)
This method models the action of humans in response to a predefined sequence of
tasks and is often associated with the term human performance modeling. Human
performance modeling relates to the simulation of purposeful actions of a human as
generated by well-understood psychological phenomenon, rather than modeling in
detail all aspects of human behavior not driven by purpose. The task approach can
be related to the process world view and mesoscopic (meso) modeling abstraction
level that models the movement of entities, in this case people, through a series of
process steps. The task approach is implemented using rules governing the behavior
of the simulation attributes of human behavior. These attributes may relate to factors
such as skill level, task attributes such as length of task and organizational factors
such as perceived value of the task to the organization. Two assumptions of simula-
tion models are seen as particular barriers to modeling knowledge workers. The first
is that all resources are assumed to belong to pools where any worker within the pool
has the ability to carry out the task. Secondly there is an assumption that once a task
is initiated it will be completed. In DES people can be represented as entities, rather
than resource pools, which enable work on a task to be segmented into sessions. At
the end of each session, work priorities are reassessed and work continues either on
the same tasks if priorities have not changed or on an alternative task. Thus, the task
Using Simulation to Model Human Behavior 33

approach attempts to model how humans act without the complexity of modeling the
cognitive and other variables that lead to that behavior.
Individual (Model Human Behavior)
This method involves modeling how humans actually behave based on individual
attributes such as perception and attention. The approach is associated with an ob-
ject world view where objects are not only self-contained units combining data and
functions, but are also able to interact with one another. The modeling approach
can be termed microscopic (micro) and utilizes either the discrete-event or ABS
types. The approach can use cognitive models for modeling human behavior at an
individual level. This approach is implemented by assigning numerical attributes,
representing various psychological characteristics, to the model entities (people).
These characteristics could include patient anxiety, perceived susceptibility, knowl-
edge of disease, belief about disease prevention, health motivation and educational
level for a medical application for example. The individual approach attempts to
model the internal cognitive processes that lead to human behavior. A number of
architectures that model human cognition have been developed. However, the diffi-
culty of implementation of the results of studies on human behavior by behavioral
and cognitive researchers into a simulation remains a significant barrier. There is
a debate about the suitability of DES to model human behavior but a solution could
be the use of DES software to implement agent-based models (see Chapter 19).
The Use of ABS and DES to Model Human Behavior in Practice.
A review undertaken by the author of published work (covering the period 2005–2015) that re-
ported on the use of ABS and DES found the following:
In terms of overall applications, ABS dominates the modeling of people over DES with 90%
of publications.
The level of ABS publications rose to a consistently higher level since 2008.
The majority of ABS applications (73%) were shown to be in the crowd and evacuation cate-
gories, which can be considered as a special category of application. ABS uses a bottom-up
approach to modeling where control mechanisms are embedded in the individual agents and
an overall behavior emerges from the individual decisions taken. Agent-based software gener-
ally includes a visual spatial display to allow this behavior to be observed at an aggregate or
“crowd” level. It may be that the study of crowd behavior is particularly suited to the bottom-up
and visual display features of the agent-based technique, although there are instances of the
use DES for crowd and evacuation applications.
The balance between techniques used when crowd and evacuation applications are excluded
is more balanced with ABS covering 70% and DES 30%. This implies both techniques present
a viable option in modeling people, but more work is required to ascertain the appropriateness
of the two techniques in different contexts when behavioral modeling is required.
The main barriers to further use of the techniques to model human behavior are found in
terms of data collection requirements and the difficulty of validation.

The DES method will now be adopted for the remainder of this book for descriptive,
predictive and prescriptive analytics. Thus DES will now be referred to as simulation.
Enabling a Simulation Capability in the Organization
The use of simulation is both a technical issue involving model development
and analysis and a process of the implementation of organizational change. This
section discusses technical issues such as the selection of simulation software
and organizational issues such as the selection of personnel and the acquisition
of resources required to provide the capability to undertake a simulation project.
It is important that the full costs of introducing simulation are considered, in-
cluding user time and any necessary training activities. The potential benefits of
simulation must also be estimated. One of the reasons simulation is not used
more widely is the benefits from change, undertaken as a result of a simulation
study can be difficult to quantify.
However, simulation may not always be the appropriate tool. Also for providing
a positive cost/benefit analysis, it should be compared to alternative approaches for
solving the problem. Solutions such as spreadsheet analysis and the use of analyti-
cal methods may be faster and cheaper. It may be that the organization lacks the
infrastructure to provide the necessary data required by the simulation model.
Finally some aspects of the organization, such as human behavior and social inter-
actions, may be too complex to represent as a model.
The steps in introducing simulation in the organization are outlined as follows:
1. Select a simulation sponsor
2. Estimate the benefits of simulation
3. Estimate the costs of simulation
4. Select the simulation software
1. Select a Simulation Sponsor
If the organization has not utilized the simulation method previously, then it
may be necessary to assign a person with responsibility for investigating the
relevance and feasibility of the approach. This person will ideally have both
managerial understanding of the process change that simulation can facilitate
and knowledge of data collection and statistical interpretation issues, which
are required for successful analysis. The development of training schemes for
relevant personnel should be investigated, so the required mix of skills and ex-
perience is present before a project is commenced. It may be necessary to use
consultancy experience to guide staff and transfer skills in initial simulation
projects.
Enabling a Simulation Capability in the Organization 35

2. Estimate the Benefits of Simulation
Often the use of simulation modeling can be justified by the benefits accruing from
a single project. However, due to the potentially high setup costs in terms of the
purchase of simulation software and user-training needs, the organization may
wish to evaluate the long-term benefits of the technique across a number of poten-
tial projects before committing resources to the approach. This assessment would
involve the simulation project sponsor and relevant personnel in assessing poten-
tial application areas and covering the following points:
– Do potential application areas contain the variability and time-dependent fac-
tors that make simulation a suitable analysis tool?
– Do the number and importance of the application areas warrant the investment
in the simulation technique?
– Is there existing or potential staff expertise and support to implement the
technique?
– Are sufficient funds available for aspects such as software, hardware, training
and user time?
– Is suitable simulation software available that will enable the required skills to
be obtained by staff within a suitable timeframe?
– Will sufficient management support in the relevant business areas be forthcom-
ing in the areas of the supply of data and implementation of changes suggested
by the technique?
– Are there opportunities for integration with other process improvement tools
such as activity-based costing?
– Does the level of uncertainty/risk in change projects increase the usefulness of
simulation as a technique to accept change and increase confidence in imple-
menting new practices?
Although not always easy to do, simulation can be treated just like any other in-
vestment and its desirability measured by the level of the return on investment
(ROI) it can provide. One way to do this is to estimate the potential savings made
by the analysis of a problem using simulation as opposed to alternatives such as
a spreadsheet analysis. When making substantial investment decisions, the de-
tailed information contained in simulation results that take into account variabil-
ity in the system are likely to prove their worth over the static analysis of
a spreadsheet. For example, a client may wish to know the quantity of equipment
required when planning a new manufacturing plant to meet a certain output ca-
pacity. If each unit of capacity costs £500,000, then £25,000 expenditure on
a simulation to obtain the right amount of capacity represents a high ROI for sim-
ulation. Savings might also be estimated by the reduction in cost elements such
as increased staff efficiency or a reduction in the use of inventory. Improvements
in other aspects of performance such as speed and flexibility will need to be

translated into monetary terms in order for the ROI benefit to be estimated. Also
note that the cost reduction when undertaking a process improved using simula-
tion will be cumulative over time. The longer time period the process is used the
higher the cumulated savings and better the cost/benefit ratio of using simula-
tion will become.
In addition, in an ROI calculation, there are other intangible benefits that can
be considered. For example, the simulation study process requires a detailed ap-
proach to system design that can increase understanding of how the business
works, which may lead to improvements. This benefit may be achieved at the con-
ceptual modeling stage without the need to build the simulation model. Another
aspect is that the simulation animation facilities can also increase understanding of
processes and be used as a marketing tool to demonstrate capability. Even if the
simulation results do not lead to changes in policy, the simulation can increase the
confidence that planned actions will lead to certain outcomes and so can be seen as
a risk management tool.
An Example of the Benefit of Using Simulation
Chapter 12 shows the use of simulation to test the design of a proposed textile manufacturing
plant. Here the emphasis is on ensuring sufficient resources are provided to meet a target for
plant output. The tasks required in the textile plant were well understood and a spreadsheet
analysis provided an estimate of what resources were required for a target production level
for a particular product mix. However a more detailed investigation was required to ensure
the operation of the plant would indeed meet the required level of performance. This is be-
cause of the variability in demand and process duration and interdependence between the
stages of the manufacturing process can lead to unused capacity at certain points in time and
over-allocated capacity at other times leading to queues. Simulation was able to provide
a detailed study of the textile manufacturing process and thus ensure that the operational de-
tails were addressed at the design stage rather than waiting for issues to arise during imple-
mentation and operation.
3. Estimate the Costs of Simulation
The main areas to consider in terms of resource requirements when implementing
simulation are as follows:
Software
Most simulation software has an initial cost for the package and an additional cost
for an annual maintenance contract that supplies technical support and upgrades.
It is important to ensure that the latest version of the software is utilized as changes
in software functionality can substantially enhance the usability of the software
and so reduce the amount of user development time required.

Hardware
Most software runs on a PC under Windows (although software for other operating
systems is available). Specifications for PC hardware requirements can be obtained
from the software vendors.
Staff Time
This will be the most expensive aspect of the simulation implementation and can
be difficult to predict, especially if simulation personnel are shared with other proj-
ects. The developer time required will depend on the experience of the person in
developing simulation models, the complexity of the simulation project and the
number of projects it is intended to undertake. Time estimates should also factor in
the cost of the time of personnel involved in data collection and other activities in
support of the simulation team.
Training
To successfully conduct a simulation modeling project, the project team should
have skills in the following areas:
General skills for all stages of a simulation project
– Project management (ensure project meets time, cost and quality criteria)
– Awareness of the application area (e.g., knowledge of manufacturing techniques)
– Communication skills (essential for the definition of project objectives and data
collection and implementation activities)
Skills relevant to the stages of the simulation study
– Data collection (ability to collect detailed and accurate information)
– Process analysis (ability to map organizational processes)
– Statistical analysis (input and output data analysis)
– Model building (simulation software translation)
– Model validation (ability to critically evaluate model behavior)
– Implementation (ability to ensure results of study are successfully implemented)
In many organizations, it may be required that one person acquires all these skills.
Because of the wide ranging demands that will be made on the simulation analyst,
it may be necessary to conduct a number of pilot studies in order to identify suit-
able personnel before training needs are assessed. Training is required in the steps
in conducting a simulation modeling study as presented in this text, as well as
training in the particular simulation software that is being used. Most software ven-
dors offer training in their particular software package. If possible, it is useful to be
able to work through a small case study based on the trainees’ organization in
order to maximize the benefit of the training. A separate course of statistical analy-
sis may be also be necessary. Such courses are often run by local university and

college establishments. Training courses are also offered by colleges in project man-
agement and communication skills. A useful approach is to work with an experi-
enced simulation consultant on early projects in order to ensure that priorities are
correctly assigned to the stages of the simulation study.
A common mistake is to spend too long on the model-building stage before ade-
quate consultation has been made, which would achieve a fuller understanding of
the problem situation. The skills needed to successfully undertake a simulation
study are varied and one of the main obstacles to performing simulation in-house is
not cost or training but the lack of personnel with the required technical back-
ground. This need for technical skills has meant that most simulation project lead-
ers are systems analysts, in-house simulation developers or external consultants
rather than people who are closer to the process such as a shop-floor supervisor.
However, the need for process owners to be involved in the simulation study can be
important in ensuring on-going use of the technique and that the results of the
study are implemented.
4. Selecting the Simulation Software
Historically simulations were built on general-purpose computer languages such as
FORTRAN, C and C++. Later languages such as Java were employed and there are also
implementations using the Visual Basic for Applications language to employ the tech-
nique on a spreadsheet platform (Greasley, 1998). There are also a number of special-
ist computer languages developed specifically for constructing simulation models
including SIMAN, SIMSCRIPT, SLAM and GPSS. However, for most applications for de-
cision making in an organizational setting, the use of Windows-based software, some-
times referred to as visual interactive modeling systems, are employed. These software
packages include Arena, Simio, AnyLogic, Witness, Simul8 and the Tecnomatix Plant
Simulation. These packages are based on the use of graphic symbols or icons that re-
duce or eliminate the need to code the simulation model. A model is instead con-
structed by placing simulation icons on the screen, which represent different elements
of the model. For example, a particular icon could represent a process. Data is entered
into the model by clicking with a mouse on the relevant icon to activate a screen input
dialog box. Animation facilities are also incorporated into these packages. For most
business applications, these systems are the most appropriate, although the cost of
the software package can be high. These systems use graphical facilities to enable fast
model development and animation facilities. However, these systems do not release
the user from the task of understanding the building blocks of the simulation system
or understanding statistical issues.
When selecting simulation software, the potential user can read the software
tutorial papers from the Winter Simulation Conference available at www.informs-cs
.org/wscpapers.html, which provide information about the available software.

Additional information can be obtained from both vendor representatives (espe-
cially a technical specification) and established users on the suitability of software
for a particular application area.
Vendors of simulation software can be rated on aspects such as:
– Quality of vendor (current user base, revenue, length in business)
– Technical support (type, responsiveness)
– Training (frequency, level, on-site availability)
– Modeling services (e.g. consultancy experience)
– Cost of ownership (upgrade policy, runtime license policy, multiuser policy)
A selection of simulation software supplier details is listed in Table 1.2.
Simulation software can be bought in a variety of forms including single-user cop-
ies and multiuser licenses. Some software allows “run-time” models to be installed
on unlicensed machines. This allows the use of a completed model, with menu op-
tions that allow the selection of scenario parameters. However, run-time versions
do not allow any changes to the model code or animation display. It is also possible
to obtain student versions (for class use in universities) of software that contain all
the features of the full licensed version but are limited in some way such as the size
of the model or have disabled save or print functions. The two packages used within
this book are Arena and Simio.
Simulation is associated with planning and scheduling software. Here schedules
can be analyzed using a probabilistic analysis incorporating variability to estimate the
underlying risks associated with the schedule. Risk measures generated can include
the probability of meeting defined targets with as well as expected, pessimistic and
optimistic results. Commercial software includes Dropboard (by Systems Navigator,
www.systemsnavigator.com/dropboard) and planning and scheduling with Simio
Table 1.2: Simulation Software Vendors.
Vendor Software Web Address
SIMUL Corporation Simul www.simul.com
Adept Scientific Micro Saint Sharp www.adeptscience.co.uk/products/mathsim/
microsaint
ProModel Corporation ProModel https://www.promodel.com/products/ProModel
Lanner Group Ltd. Witness Horizon https://www.lanner.com/en-gb/technology/wit
ness-simulation-software.html
Siemens PLM Tecnomatix www.plm.automation.siemens.com/global/en/
products/tecnomatix/
The AnyLogic Company AnyLogic www.anylogic.com
Simio LLC Simio www.simio.com
Rockwell Software Inc. Arena www.arenasimulation.com

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Then, like an avalanche, a cascade of foam swept completely over
the boat. Frantically Pyecroft strove to grip the gunwale. Torn away
by the rush of water, he was conscious of being pounded on the
shingle. Then came the dreaded undertow.
Vainly he attempted to grasp the rolling shingle. He felt himself
being swept backwards to be again overwhelmed by the next roller,
when his retrograde motion was arrested by a heavy object. It was
the Pip-squeak. Even in the last stages of her existence Jefferson's
boat seemed destined to be of service.
With a final effort as the frothy water slithered past Pyecroft gained
his feet. The hiss of the approaching breaker gave strength to his
limbs. Stumbling, terror-stricken, and well-nigh exhausted, he
contrived to win the race by inches until, realising that the dreaded
enemy had fallen short, he fell on his face on the wet shingle.
For some moments he lay thus until, haunted by the horrible
suspicion that the rising tide would overwhelm him, he staggered a
few paces until he was above high-water mark, and then collapsed
inertly upon the seaweed-strewn shore.
How long he lay unconscious he had no idea; but when he came to
himself the moon was shining dimly through a watery haze. The tide
had fallen, and with it the horrible ground-swell had disappeared.
He was bitterly cold: his limbs were like lead. An effort to rise was
a dismal failure. He tried to shout, but no sound came from his
parched lips. While he had lain unconscious there must have been a
short spell of wind, for he found that he was covered with dried
wrack and seaweed.
"It must be close on daybreak," he thought. "I'll have to stick it a
little longer."
He made an attempt to look at his wristlet watch. The dial was no
longer luminous, while an ominous silence had taken the place of an

erstwhile healthy tick. A prolonged submergence had ruined the
delicate mechanism for all time.
As he lay, too benumbed to move, he became aware that a boat
had grounded on the beach within a few yards of his involuntary
resting-place. The little craft must have come in very silently, for
until the men's boots grated on the shingle he was unaware of their
presence.
Again he tried to shout, but without result. Then, even as he tried
to raise himself, he noticed that with one exception the men wore
unfamiliar uniforms. They were talking softly, with an unmistakable
guttural Teutonic accent.
"Huns," thought Pyecroft. "What's their little game? I've done them
so far, and I'm hanged if I want them to put a half-nelson on me
now. I'll lie doggo."
Which, considering his weak physical state, was an easy matter to
do.
The Huns were evidently in a hurry, for after a few words with a
greatcoated individual, they pushed off and rowed seaward, while
the man they had left ashore lifted a portmanteau from the shingle
and made his way towards the cliff with the air of one who is
confident of his surroundings.
He passed so close to the prone figure lying partly covered by
seaweed that for a brief instant Pyecroft expected the stranger to
stumble against him.
"Good heavens!" ejaculated the astonished Pyecroft. "Where have I
seen that fellow? By Jove—it's Fennelburt. Up to some dirty work: I
wonder what?"

CHAPTER XIV
A DOUBLE DECOY
"Gun-fire!" exclaimed Lieutenant-Commander Morpeth, sniffing the
salt air like an alert terrier scenting a rat.
"Away to the south-east'ard," corroborated Wakefield. "Is this
going to be one of your lucky days, George?"
"It won't be for the want of trying," rejoined the R.N. R. man
grimly; then bending till his lips nearly touched the mouth of the
voice tube, he shouted, "Stand by, below there, to whack her up."
A few crisp orders followed. Men moved swiftly and silently to their
appointed stations, while the course was altered a couple of points
to take Q 171 to the scene of the supposed action.
It was the second day of Wakefield's and Meredith's enforced but
none the less interesting detention on board the mystery ship. Q 171
was well out into the North Sea, bound for a certain position a few
miles to the west'ard of the now famous Horn Reefs Lightship. The
sea was calm, a light breeze blew from the west'ard, while the sky
was filled with small fleecy clouds drifting slowly athwart the lower
air-currents—an indication of a forthcoming change of wind.
The three officers, clad in black oilskins to keep up the rôle of Hun
pirates, had been sitting on the cambered edge of the base of the
dummy conning-tower, yarning of times not long gone and holding
forth wondrous theories of what might happen in the seemingly far
distant epoch after the war.
"Small quick-firers," declared Morpeth, as the rumble of the sharp
reports grew louder and louder. "None of our M.L.'s in action by any

chance, I hope?"
Slinging his binoculars round his neck, Morpeth, with an agility that
his ponderous frame belied, clambered to the domed top of the
conning-tower, reckless of the fact that his weight was causing the
frail metal-work to "give" ominously.
Bringing his glasses to bear upon a faint dot just on the horizon,
Morpeth made a long and steady scrutiny.
"Merchant vessel—tramp, by the look of her—chased by a Fritz," he
reported, "Unhealthy work—for Fritz. I'll keep her on my lee bow a
bit. It's no use butting in too soon. Too much dashed hurry spoils
everything."
At sixteen knots Q 171 held on, with the apparent object of joining
in the chase and cutting off the fleeing merchantman. Quickly the
chase came in sight—a bluff-bowed, wall-sided tramp, with an
elaborately camouflaged hull.
"Confounded scheme that razzle-dazzle," commented Morpeth.
"Meet three or four in a crowded waterway, and you begin to
wonder whether you'll see mother again. Can't tell whether they are
bows on, or what. Fancy we've got her cold, though. For'ard gun, let
her have it."
The bow-chaser spat viciously, sending a shrieking missile within a
hundred yards of the tramp, which, badly on fire aft, was still
proudly flying the Red Ensign. Her funnel, hit about six feet above
the deck, was showing signs of collapse, being supported only by
the wire rope guys. Making a bare eight knots, she was evidently at
the mercy of the pursuing U-boat, which, capable of doing eighteen
on the surface, was slowing down after the manner of a cat playing
with a mouse.
Q 171, firing rapidly, but deliberately planting her shells wide of the
merchant vessel, now turned twelve points to port. This had the

effect of bringing her into a decidedly convergent course with that of
the U-boat. The latter, probably "smelling a rat," or taking exception
to what appeared to be another of her kind "spoiling the game,"
edged away to starboard, at the same time hoisting a signal.
By the aid of the appropriated German Naval Code Book, Q 171's
skipper deciphered the signal. It was a peremptory request for the
pseudo U-boat to make her number and thus proclaim her identity.
This was easily done. A four letter hoist of bunting fluttered from Q
171's mast, giving the information that she was U 251 of the
Imperial German Navy.
"This is my prize," signalled the dog-in-the-manger Fritz.
"I have good reasons for joining in the chase," was Morpeth's reply.
During the lengthy exchange of flag messages, both boats had
maintained a hot fire upon the tramp. From the genuine U-boat the
result of Q 171's shells could not be observed. Had the Huns been
able to do so, they would have expressed considerable surprise at
their supposed consort's decidedly erratic gunnery; but in the heat
of rivalry they became reckless.
Almost imperceptibly, Q 171 lessened the distance between her
and her prey. The tramp was two miles ahead, while barely half a
mile separated the U-boat and the decoy.
"Stand by the tubes!" ordered Morpeth, at the same time
motioning to Wakefield and Meredith to step clear of the rails.
Meredith felt a distinctly unpleasant sensation in his throat.
Perspiration oozed from his forehead. Fascinated, he watched the
alert faces of the men standing by the mechanism that was to lay
bare the deadly torpedo-tubes.
"Let her have it!" shouted Morpeth.

With hardly a rumble, the dummy conning-tower rolled over the
well-oiled rails, revealing the triple tubes trained abeam upon their
prey. The next instant the glistening cigar-shaped missiles leapt over
the side and disappeared in a welter of foam.
Travelling at the rate of an express train under the impulse of small
but powerful electric motors, the torpedoes took very little time to
cover the intervening distance. So intent were the Huns at shelling
the tramp that they failed to notice the tracks of the sinister
weapons until, with an appalling roar, two of them exploded
simultaneously and thirty yards apart against the U-boat's hull.
Morpeth gave a grunt of satisfaction as he watched the tall column
of water break and fall in a shower of smoke-mingled spray.
"Simple—quite simple," he remarked; then, observing Meredith's
white face, he clapped the young officer on the shoulder.
"Cheer up!" he ejaculated. "Nothing to look white about the gills....
When you've been on the game as long as I have, and seen what an
utter bounder Fritz is, you'll understand."
With the discharge of the torpedoes Q 171 altered helm and
resumed her former course. Morpeth meant to take no chances by
revealing his identity to the tramp. He preferred to let the crew of
the merchant vessel think that the disaster of her supposed consort
had effectually put the wind up the second U-boat. Q 171 was a
mystery ship, and once her true character was known the story
would be all over the first port at which the tramp touched. And,
after all, it was not a very far cry from an East Coast port to Berlin in
war time, and benevolent neutrals had an unfortunate liking for
spreading reports, true or otherwise, of what they saw and heard in
British harbours.
A sudden ejaculation from Morpeth attracted Meredith's attention.
The R.N.R. man was pointing with outstretched arm in the direction
of the tramp.

He had good reason for astonishment. The apparently badly
battered tramp had swung round and was forging through the water
at high speed—possibly a good twenty-five knots. The Red Ensign
had been struck, and the White Ensign streamed proudly in the
breeze.
"Look alive there!" shouted Morpeth. "Up with our rag, or they'll be
planking a four-point-seven into us. Hanged if she isn't a Q-boat
too!"
The R.N.R. man was right concerning the rôle of the oncoming
ship; but he was wrong in his surmise as to her intentions. Her
skipper had noticed that the shells fired from the second U-boat had
purposely gone wide, he had spotted the uncovered torpedo-tubes
on her deck, and had seen the sudden disintegration of U-boat No.
1. Metaphorically speaking, he was foaming at the mouth.
A hoist of bunting rose to the masthead of the approaching vessel.
"Heave-to; I wish to communicate," read the signal.
Morpeth rang for "half speed" and then "stop." He turned to
Wakefield.
"Now's your chance to get a lift back," he remarked.
"Fancy I'll hang on," replied the late skipper of M.L. 1071. "A day or
two won't make much difference. Had I been ashore I suppose the
S.N.O. would have packed me off on leaf."
"And you, my festive?" inquired Morpeth, addressing Meredith.
"I'm following my senior officer's lead," replied the Sub promptly.
"As regards your men, I'll put them on board if she'll have 'em,"
continued Morpeth. "It'll relieve the pressure on the grub locker.
Hope they won't kag too much about us, though."

"I don't think so," replied Wakefield, who had great faith in the
sound sense of his crew.
"But after all it won't matter so very much," added the R.N.R.
officer. "By the time they get ashore my little stunt will, I hope, be a
back number. Now, let's see what this camouflaged blighter has to
say."
The Q-boat had now ranged up within fifty or sixty feet of her small
co-worker. Men, rigged out in the nondescript garments affected by
the Mercantile Marine, were clustered for'ard, while a couple of
stalwart individuals, rigged out in pilot-coats, serge trousers and sea-
boots, were leaning over the side abreast the mainmast.
"Dash you, you meddling bounder!" roared one of the latter. "What
d'ye mean by butting in and spoiling our sport? D'ye think we stood
a gruelling for four mortal hours just for the fun of seeing you give
Fritz socks? An' we had her nicely within range when you let rip."
"Sorry," replied Morpeth apologetically, "But how the blazes was I
to know?"
"You'd have known quick enough if we had shown our teeth,"
replied the other grimly. "Three of my men killed and six wounded,
and nothing to show for it."
"So I suppose when I fall in with a genuine tramp being chased by
a Fritz, I'll just carry on?" inquired Morpeth caustically.
"I won't say that," replied the other. His wrath was fast
evaporating. He was beginning to realise that, after all, cooperation
was the thing, and that rivalry, except of the healthy order, was
detrimental to the great work in hand. "When all's said and done, it's
something to think that we took you in. At first I thought you were a
Fritz: your get-up was so good. But I say, isn't your name Morpeth—
Geordie Morpeth?"

"I have a notion that you've hit the right nail on the head," replied
the skipper Of Q 171. "But I'm dashed if I can call your face to
mind!"
"Met you in Rio in January '12," announced the other, with a typical
sailorman's memory for dates. "You were in the Humming-Bird. I
was on the Glaucis, second mate at the time."
"By Jove!" exclaimed Morpeth, "you're Bellairs. I didn't recognise
you; you've altered some."
"Hardly recognise myself at times," remarked Bellairs. "If you want
to age rapidly, try a trick in a Q-boat. I see you're trying it already.
Well, I must be pushing along. I'm making for Newcastle, after three
weeks off the Lofoden Islands. Fritz was pretty busy in Norwegian
waters, but I guess he's put up his shutters for a time at least.
We've driven a few nails into his coffin."
"Left one or two for me, I hope?" remarked Morpeth. "But look
here, can you give a passage to a few hands?"
"A few," agreed Bellairs guardedly. "How many?"
Morpeth told him.
"I've also two officers on board," he added. "They wish to stay and
have a rest cure. I'm doing my best to educate 'em at the same
time."
The other R.N.R. man laughed. "Right-o!" he exclaimed. "If you
educate 'em like you did the youngsters on the Humming-Bird I can
see them writing home to mother about you."
"Hear that?" inquired Morpeth, turning to Wakefield and Meredith.
"Old man Bellairs evidently thinks I'm a tough nut. Hope Fritz'll think
so too; that's the thing that counts."

CHAPTER XV
CONFIRMED SUSPICIONS
"From Sub-lieut. J. McIntosh to S.N.O., Auldhaig. Regret to report X-
lighter No. 5 sunk in collision. Crew saved."
"From Officer Commanding No. Umpteen Group to Air Ministry. I
have to report that the following officers are reported missing,
believed drowned:—Captain R. G. Cumberleigh, Lieut. H. L.
Jefferson, 2/Lieut. W. Pyecroft, Lieut. J. Blenkinson, all of Auldhaig
Air Station; and Captain G. Fennelburt, from Sheerness Air Station,
on detached duty. It is understood that these officers left Auldhaig in
a private boat on a fishing expedition. It is requested that Sheerness
may be informed concerning the officer mentioned above."
"From O.C. Lintieness Coast Guard Station to Inspecting Officer of
C.G., Auldhaig. I have to report that at 4 P.M. a lighter which had
been signalled passing south at 11 A.M. was observed to be derelict
3 miles E. by S. off Lintieness Head. It was afterwards lost in the
haze, drifting to the northward. At 5 P.M. a violent explosion was
heard, apparently from a direction bearing E. by N."
"From O.C. Auldhaig M.L. Flotilla to S.N.O., Auldhaig. Acting upon
instructions, I proceeded in search of X-lighter No. 5. At a position
bearing N.E. by E., five miles from Lintieness Head, quantity of
wreckage discovered floating, including a buoy marked 'X-lighter No.
5.' The debris gave indication of an explosion. Saw no trace of boat
reported missing by Air Station, Auldhaig."
"From Superintendent of Police, Abercuish, to O.C. Auldhaig Air
Station. Report that at 5 A.M. on the — inst. 2/Lieutenant W.

Pyecroft, R.A.F., was discovered in an exhausted condition on the
shore at Abercuish. He was removed to a house in the village, and
thence to the Abercuish Cottage Hospital. According to his
statement, his companions were taken prisoners by a German
submarine from X-lighter No. 5."
"From Air Ministry to O.C. No. Umpteen Group, Auldhaig. Nothing
known of Captain Fennelburt at Sheerness Air Station. Please
ascertain if a mistake has been made in this officer's name, and
report the nature of the detached duty referred to in your telegram
No. 4452 of the — inst."
These messages, written on official forms, lay on the table in the
private room of the Commander-in-Chief's office at Auldhaig.
There were three persons in the room. One, the Commander-in-
Chief, a breezy, dark-featured, clean-shaven naval officer of about
fifty-five; the second, the dapper, boyish-faced lieutenant-colonel
who held the post of Officer Commanding the R.A.F. Air Station. The
third was the Commander-in-Chief's secretary—a silent, almost
taciturn individual whose face was almost the same colour as that of
his gilt aiguillettes. In his head the secretary held knowledge upon
which depended the success of the Grand Fleet and for which
Germany would willingly have paid millions; but that firmly set
mouth was sealed upon all matters appertaining to the war save
when lawful occasion demanded. And in a few months' time John
Elphinhaye would be placed upon the Retired List with a pension
that, with Income Tax deducted, would be little more than the wages
of an artisan.
"The whole business seems a general muck-up, Greyhouse,"
observed the Commander-in-Chief, addressing the lieutenant-
colonel. "There's something wrong somewhere. How can this
confounded lighter be sunk in collision and shortly afterwards be
blown up?"

"There were two lighters, sir," replied Colonel Greyhouse. "It is
quite possible that one was mistaken for the other."
"As a matter of fact there were half a dozen," explained the
Commander-in-Chief. "And all, except No. 5, are accounted for. That
is so, Elphinhaye?"
"Yes, sir," corroborated the secretary.
"But the main reason why I came to see you, sir," said Lieutenant-
Colonel Greyhouse, "was the affair of my missing officers. In the first
instance they went off in a boat belonging to one of my lieutenants.
I cannot conceive how they came to be on board the lighter. True,
she was to be transferred to the R.A.F., but she left here under an
R.N.V.R officer and crew."
"Sub-lieutenant John McIntosh, sir, who reported from Donnikirk,"
announced the secretary, in response to his superior's inquiry —
mutely expressed by the raising of his bushy eyebrows.
"Exactly," agreed the Commander-in-Chief. "The situation required
further information, and I have wired instructions to Mr. McIntosh to
report immediately upon his return to-day."
"Then there is the question raised by the presence of Captain
Fennelburt——"
"That," interrupted the naval officer, "is a matter that concerns the
Air Force. I have no jurisdiction in the case."
"But," persisted Colonel Greyhouse, "that officer visited Auldhaig
Dockyard."
"He called upon the Staff Captain, sir," reported the secretary, who
appeared to have a knowledge of the movements of every stranger
within the gates of Auldhaig Dockyard at his fingers' ends.

"And yet the Air Ministry and Sheerness Air Station deny all
knowledge of him," continued Colonel Greyhouse. "I was away on
duty at the time he reported at my station, but curiously enough
Captain Cumberleigh, one of the missing officers, entertained a
suspicion of him. He communicated his doubts to my second-in-
command, Major Sparrowhawk, who this morning reported to me on
the matter. It is now his belief, although he scouted the idea at the
time, that this Captain Fennelburt is a spy, or at least an impostor,
masquerading as an R.A.F. officer, with certain shady motives behind
him. That is why I came, in order to find out his alleged motives for
visiting Auldhaig Dockyard."
"That's the worst of these new-fangled shows," declared the
Commander-in-Chief vehemently. He was a sailor of the Old School
who did not take kindly to innovations. "When the R.N.A.S. was in
existence we had good men who could fly. Now with this
amalgamation it seems to me that for every effective pilot the Air
Ministry grants a dozen commissions to men who never will 'go up'
and who apparently have nothing better to do than to knock about
in uniform doing work badly that a civilian clerk could do well, and
trying to bluff people that they are the salt of the earth. Apparently
Captain Fennelburt is one of this crowd, only the Air Ministry has
forgotten his existence. I rather feel inclined to pooh-pooh the spy
theory."
The colonel suffered the Commander-in-Chief's strictures in silence.
Although his career in the Service had been limited to a period of
four years, his promotion had been rapid. He had a real pride in the
R.A.F., but at the same time he knew that there was considerable
truth in the naval man's assertions. Also he realised that it was both
inadvisable and contrary to discipline to argue with an officer of
superior rank.
"Your best course," continued the Commander-in-Chief, "would be
to send some one over to Abercuish Cottage Hospital to interview

Mr. Pyecrust—I mean, Pyecroft. That is, naturally, if he is in a fit
state to give information."
Colonel Greyhouse inclined his head in assent. It was, moreover,
exactly what he had already given instructions to be done. The
colonel took his leave, and just as he stepped ashore at the Air
Station a motor car dashed into the parade-ground. From it alighted
Major Sparrowhawk.
"I've seen young Pyecroft, sir," he reported with a salute. "He's
going on well in the circumstances. The doctor informed me that he
will be fit to be removed to-morrow."
"That's good," commented the colonel. Together they walked a few
paces out of hearing of the transport driver and the coxwain of the
motor boat.
"Well?" inquired Colonel Greyhouse laconically.
"Dashed queer business, sir," replied the major. "Pyecroft is
perfectly fit mentally, which, considering what he has gone through,
is rather to be wondered at. It appears our fellows boarded a
derelict lighter and while on board were surprised by a Hun
submarine. Pyecroft got away, had a sticky time on a water-logged
boat, and finally drifted ashore more than half dead with cold and
exposure. The others, it seems, were taken prisoners by the Huns.
And now comes the extraordinary part of the story. We had an
officer here on inspection duties. Fennelburt—Captain George
Fennelburt—he announced himself on reporting."
Colonel Greyhouse nodded.
"Yes," he observed. "I know that much."
"Well, sir," explained Sparrowhawk, "he came ashore from the
German submarine at night, while Pyecroft was lying helpless on the
beach. Four men brought him ashore in a collapsible boat, and he

vanished inland, still rigged out in R.A.F. uniform. Pyecroft can swear
definitely on that point."
"And Sheerness Air Station has disclaimed all knowledge of him,"
remarked the C.O. "Why the deuce the Air Ministry cannot be more
particular in posting the movements of officers passes my
understanding! Can you give a fairly accurate description of Captain
—er—Fennelburt?"
"I think so, sir; he was at the mess to lunch, and I saw a good deal
of him."
"Good," ejaculated Colonel Greyhouse. "Send a report to 'Area,'
and at the same time to Scotland Yard. The police will then take the
matter up. You might also inform the Naval and Military Authorities.
If we don't lay the fellow by the heels within the next twelve hours
I'll eat my hat."
A vow that, taking into consideration the copious gold leaves that
adorned the peak, was an exceedingly rash one, unless Greyhouse
had the digestion of an ostrich.
CHAPTER XVI
COVERING HIS TRACKS
For the second time within forty-eight hours Karl von Preussen
tramped the deserted road leading to Nedderburn Junction railway
station. On the previous occasion he called himself Captain George
Fennelburt; on the second he had assumed the name of Ronald
Broadstone.

He travelled light, but in place of his khaki, leather-reinforced
haversack he carried a small portmanteau, which, owing to
unforeseen circumstances, was practically empty. He decided that at
the first favourable opportunity he would replenish a portion of his
kit and replace that lying at the Auldhaig Hotel. But in the
portmanteau was an automatic pistol of British manufacture. Its
possession showed economy and discrimination in small details.
Since it had been acquired from a battlefield, it had cost von
Preussen nothing; and being of British make it was in keeping with
the spy's rôle as an officer of the Royal Air Force.
He walked quickly and unhesitatingly along the bleak,
unfrequented road. Delay meant the great possibility of missing the
night train and a consequent detention at Nedderburn, which was
too close to Auldhaig to be pleasant. He had good reasons for
steering clear of Auldhaig "for the rest of the duration." The place
had been a "wash-out," and since von Preussen was of a
superstitious nature he always avoided scenes of previous failures.
Beyond meeting a belated shepherd, who greeted the spy in an
unknown Highland dialect, von Preussen arrived at Nedderburn
without encountering anyone. The station had just been lit up, two
feeble paraffin lamps providing the necessary illumination for the
safety of passengers. Peeping through the high wooden palisade,
von Preussen took stock of the people on the up-platform.
There were half a dozen "Jocks" with full equipment, including "tin
hats" and rifles with the breech-mechanism bound in strips of oiled
cloth.
"Highlanders returning from leave to the Front, curse them!"
muttered von Preussen.
He had reason for his maledictory utterance. In the earlier days of
the war, when he was a lieutenant of Uhlans, he soon learnt to have
a wholesome respect for the stalwart, bare-kneed, kilted men from

"Caledonia stern and wild." He recalled an incident at a certain
village about twenty kilometres from Mons. His squadron had
overtaken twenty tired Highlanders tramping along the pavé.
Observation by means of binoculars showed that they were
bordering on utter fatigue. Most of them wore blood-stained
bandages. They had no officer with them. They looked to be an easy
prey to the lances of his Uhlans. Von Preussen never had a worse
shock. Instead of the kilted men taking to their heels at the sight of
the charging cavalry and thus falling easy victims to the steel-tipped
lances, they coolly threw themselves into a circle fringed by a ring of
glittering bayonets. Three volleys in quick succession were too much
for the Uhlans to stomach. They galloped off, amongst them von
Preussen groaning and cursing with a bullet wound through his left
shoulder.
In the present instance he decided that he had nothing to fear
from these men. A little further on were three greatcoated officers.
With a grunt of satisfaction von Preussen noted that their cap-bands
were not black with the badge of the crown, eagle and wings. He
had good cause to avoid Air Force officers and men just at present.
Beyond stood a sturdily-built man with a long black coat and soft
hat—evidently a clergyman. He was trying to decipher a poster in
the feeble glimmer of the station lamps.
The changing of the signal from red to green warned the spy that it
was time to enter the station. Outside the entrance stood an old and
somewhat decrepit porter who, after inquiry as to whether the new
arrival had any luggage and receiving a negative reply, hobbled off
to ring the bell. At the doorway stood a girl ticket-collector.
"Warrant, miss!" exclaimed von Preussen, holding out a buff paper.
The girl examined it perfunctorily.
"Carlisle—change at Edinburgh!" she announced.

The spy thanked the girl for the gratuitous and unnecessary
information. To change at Edinburgh was his intention. By so doing
he could withhold and destroy the faked railway warrant, which, had
it been retained by the ticket collector, would eventually be
presented to the Air Ministry for payment. Already von Preussen had
travelled thousands of miles over British railways without payment,
and never once had he surrendered the buff slip that would
otherwise have been a clue to his movements.
With much hissing of steam the night mail train drew up at the
platform. The handful of travellers hurried along, peering into the
dimly-lit compartments in the hope of finding vacant seats. Von
Preussen happened to secure one in the company of five naval
officers who were already "bored stiff" with their tedious journey
from a far northern base. The spy soon discovered that there was
precious little information to be picked up from them.
At Perth the spy changed compartments. He now found himself in
the company of four rather lively subalterns and the clergyman he
had noticed on Nedderburn Junction platform. The latter, deep in the
pages of the Church Times, took no notice of the new arrival.
"Tickets, please!"
A gigantic inspector examined the tickets and vouchers of the
occupants of the compartment.
"Change at Edinburgh," he remarked, as he clipped von Preussen's
warrant. "Through train to Carlisle at 7.5."
With the resumption of the journey, the clerical passenger offered
von Preussen a copy of an evening paper as a prelude to opening
conversation. He was, he informed the spy, travelling from
Nedderburn to Hawick, where he was about to take up an Army
chaplaincy at Stobs Camp. In return von Preussen told a fairy tale to
the effect that he was joining an R.A.F. balloon station near Carlisle
and gave some vivid and totally imaginary stories of his adventures

in the air. Yet in spite of several attempts to draw the subalterns into
the conversation, the hilarious representatives of the "One Star
Crush" limited their discourse to anecdotes calculated to bring
blushes to the cheeks of the padre.
It was nearly six in the morning when the train reached Edinburgh.
Without difficulty von Preussen passed the barrier and emerged into
Princes Street. For the rest of the day he remained in seclusion at a
small private hotel just behind Edinburgh's main thoroughfare.
He had a nasty shock that evening. The evening papers came out
with an announcement that there was a reward of one hundred
pounds for information leading to the detection of a certain
individual giving the name of George Fennelburt, aged about thirty;
height, five feet seven or eight; broadly built, fair featured with blue
eyes. Believed to be wearing the uniform of a captain in the Royal
Air Force, and last seen in the neighbourhood of Auldhaig.
Von Preussen broke into a gentle perspiration. Furtively he glanced
at his companions in the commercial room. They were, fortunately
for him, deep in a game of chess.
The spy had registered in the name of Captain Broadstone. That
was now, of itself, a decidedly risky proceeding, since, the hue and
cry being raised, there would most certainly be a stringent
examination of registration forms at all the hotels.
Even in his panic von Preussen was curious. He could form no
satisfactory theory on the matter. How was his presence known,
since it was reasonable to conjecture that the authorities knew he
had gone on the fishing expedition that had been so unpropitious to
his temporary companions? Obviously the notice offering a reward
for his apprehension had not been issued before his visit to
Auldhaig; and since he, with others, was missing and presumed to
be drowned, why go to the length of advertising for his arrest?
Perchance U 247 had been captured and the British prisoners

released. Even in that case none of those knew the true facts. When
they were sent below they were under the impression that he, von
Preussen, was also a prisoner of war. In the absence of detail the
newspaper notice was terrible in its gaunt wording.
"I will have to find a different disguise," he decided. "But how? To
purchase civilian clothing would be courting instant suspicion. I
cannot get it myself, nor can I trust anyone to obtain it for me. Yet
to persist in appearing in this Air Force uniform would be simple
madness. It is equally futile to dye my hair and eyebrows. The
people here would notice the difference instantly. And if I changed
my hotel I would run fresh and possibly greater risks. Himmel! What
can I do?"
He glanced suspiciously round the room. The players, deep in their
game, paid no attention to anyone or anything else.
"There's one blessing," he soliloquised. "I registered as Broadstone,
not Fennelburt. I think I'll go to bed. It's safer."
He went, placed his automatic pistol under his pillow, and found
himself looking at the empty portmanteau. Then, switching off the
light, he attempted to court slumber.
It was in vain. For hours he lay wide awake, racking his ready brain
for a solution to the apparently insurmountable difficulty. He heard
the occupant of the next room retiring, the click of the electric light
switch, and very soon after, the first of a series of loud snores.
"At all events," thought the spy, "the fellow is luckier than I: he can
sleep soundly."
The sleeper and the empty portmanteau: subconsciously von
Preussen connected the two. Why, he knew not, but gradually and
with increasing lucidity a plan matured. Why not steal the sleeper's
clothes, pack them into his portmanteau, and change in a remote
country spot?

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