Deadlock Resolution in Computer Integrated Systems 1st Edition Mengchu Zhou (Editor)
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- 5. Deadlock Resolution in Computer Integrated Systems 1st Edition Mengchu Zhou (Editor) Digital Instant Download Author(s): MengChu Zhou (Editor); Maria Pia Fanti (Editor) ISBN(s): 9781482276534, 1315214660 Edition: 1 File Details: PDF, 46.18 MB Year: 2004 Language: english
- 9. Deadlock Resolution in Computer-Integrated S uste edited by MengChu Zhou NW Jersey Institute of Technology Newark, N w Jersey, U.S.A. Maria Pia Fanti Politecnico di Bari Bari, Italy Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business
- 10. First published 2005 by Marcel Dekker/CRC Press Published 2018 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2005 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works ISBN 13: 978-0-8247-5368-9 (hbk) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any foture reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MAO1923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system ofpayment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Library of Congress Cataloging-in-Publication Data Deadlock resolution in computer-integrated systems/ edited by MengChu Zhou. Maria Pia fanti. p. cm. Includes bibliographical references and index. ISBN 0-8247-5368-2 (alk. paper) I. Production enginee1ing 2. Computer integrated manufacturing systems. 3. Discrete-time systems. 4. System design. I. Fanti. Maria Pia. II. Title. TS I76.Z53 2004 670'.285--dc22 Library of Congress Card Number 2004059349 2004059349
- 11. Table of Contents List of Contributors vii Preface xi 1. Introduction to Deadlock Research in Computer-Integrated Systems by M. P. Fanti and M. C. Zhou .........................................................1 2. Deadlock Avoidance in Automated Manufacturing Systems Using Finite Automata and State Space Search by, A. Yalcin, T. Tai, and T. O. Boucher ... 35 3. Synthesis of Deadlock-Free Supervisory Controllers Using Automata by A. Ramirez-Serrano and B. Benhabib .........................................................57 4. Deadlock Avoidance and Dynamic Routing Flexibility in Automated Manu facturing Systems by M. Lawley I ll 5. Digraph-Based Techniques for Deadlock Resolution in Automated Manufac turing Systems by M. P. Fanti, B. Maione, G. Maione, and B. Turchiano........131 6. Deadlock-Free Supervisory Control for Assembly and Disassembly Systems by E. Roszkowska 155 7. Deadlock Avoidance Algorithms and Implementation: AMatrix Based Approach by J. Mireles Jr., F. Lewis, A. Giirel, and S. Bogdan................................................ 183 8. Deadlock Detection and Prevention ofAutomated Manufacturing Systems Using Petri Nets and Siphons by M. D. Jeng, and X. Xie ........................................ 233 9. Siphon-Based Characterization of Liveness and Liveness-Enforcing Supervision for Sequential Resource Allocation Systems by S. Reveliotis ............................283 10. Elementary Siphons of Petri Nets for Efficient Deadlock Control by Z. Li and M. C. Zhou .....................................................309 v
- 12. Contents vi 11. Resource-Oriented Petri Nets in Deadlock Prevention and Avoidance by N. Wu and M. C. Zhou .....................................................349 12. The Effect ofModeling and Control Techniques on the Management ofDead locks in FMS by L. Ferrarmi and L. Piroddi .................................................... 407 13. Deadlock Characterization and Resolution in Interconnection Networks by T. M. Pinkston .........................................................445 14. Deadlock Models for a Multi-Service Medium Access Protocol Employing a Slotted Aloha or Q-ary Tree Based Signaling Channel by M. V. Ivanovich ................................................... 493 15. Deadlock-Free TCP Over High-Speed Internet by Rocky K. C. Chang, H. Y. Chan and A. W. Yeung ........................................ 531 16. Deadlock Resolution in Large-Scale Internet Computing by J. Park .........................................................555 17. Models Used in Static Analysis for Deadlocks ofAda Tasking Programs by M. Tiusanen and T. Murata .........................................................585 18. Deadlock Handling in Database Systems by M. Weske ....................................635 Index .659
- 13. List of Contributors B. Benhabib (Chapter 3), benhabib@mie.utoronto.ca Department of Mechanical and Industrial Engineering, University of To- ronto, 5 King’s College Road, Toronto, Ontario, M5S 3G8, Canada Stjepan Bogdan (Chapter 7), stjepan.bogdan@fer.hr Department of Control and Computer Engineering in Automation, Faculty of Electrical Engineering and Computing (FER), University of Zagreb, Unska 3, HR-10000 Zagreb, Croatia Thomas O. Boucher (Chapter 2), tboucher@rci.rutgers.edu Department of Industrial and Systems Engineering, Rutgers University, P. O. Box 909, Piscataway, NJ 08854, USA Ho Y. Chan (Chapter 15), ckevin@computer.org Department of Computer Science, University of Southern California Los Angeles, CA 90089, USA Rocky K. C. Chang (Chapter 15), csrchang@comp.polyu.edu.hk Department of Computing, The Hong Kong Polytechnic University, Hung Horn, Kowloon, Hong Kong M. P. Fanti (Chapters 1 and 5), fanti@poliba.it Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Bari, Italy Luca Ferrarini (Chapter 12), ferrarin@elet.polimi.it Politecnico di Milano, Dipartimento di Elettronica e Informazione, Piazza L. da Vinci 32 - 20133 Milano, Italy Ayla Gürel (Chapter 7), ayla.gurel@emu.edu.tr Electrical and Electronic Engineering Department, Eastern Mediterranean University, Famagusta, via Mersin 10, Turkey vii
- 14. viii List of Contributors MuDer Jeng (Chapter 8), jeng@mail.ntou.edu.tw Department of Electrical Engineering, National Taiwan Ocean University, Keelung 202, Taiwan, ROC Mark Lawley (Chapter 4), malawley@ecn.purdue.edu School of Industrial Engineering, Purdue University, 1287 Grissom Hall, West Lafayette, IN 47905, USA Frank L. Lewis (Chapter 7), flewis@controls.uta.edu Automation & Robotics Research Institute, The University of Texas at Ar- lington, 7300 Jack Newell Blvd. S., Fort Worth, Texas 76118, USA Zhiwu Li (Chapter 10), zhwli@xidian.edu.cn School of Electro-Mechanical Engineering, Xidian University, Xi’an, China B. Maione (Chapter 5), maione@poliba.it Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Bari, Italy G. Maione (Chapter 5), gmaione@deemail.poliba.it Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Bari, Italy José Mireles, Jr. (Chapter 7), jmireles@arri.uta.edu Universidad Autònoma de Ciudad Juárez, Ave. Del Charro 450 Nte., Cd. Juarez Chihuahua, Mexico, CP 32310 Tadao Murata (Chapter 17), murata@cs.uic.edu Department of Computer Science, University of Illinois at Chicago, 851 S. Morgan St., Chicago, IL 60607-7053, USA Jonghun Park (Chapter 16), j.park@kaist.ac.kr Department of Industrial Engineering, Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul, 151-744, Korea Timothy M. Pinkston (Chapter 13), tpink@charity.usc.edu Department of Electrical Engineering, University of Southern California, 3740 McClintock Ave., Los Angeles, CA 90089-2562, USA Luigi Piroddi (Chapter 12), Piroddi@Elet.PoliMi.IT Politecnico di Milano, Dipartimento di Elettronica e Informazione Piazza L. da Vinci 32 - 20133 Milano, Italy
- 15. List of Contributors IX A. Ramirez-Serrano (Chapter 3), aramirez@enme.ucalgary.ca Department of Mechanical & Manufacturing Engineering University of Calgary, 2500 University Drive, Calgary, Alberta T2N 1N4, Canada Elzbieta Roszkowska (Chapter 6), ekr@pwr.wroc.pl Institute of Engineering Cybernetics, Wroclaw University of Technology, ul. Janiszewskiego 11/17, 50-372 Wroclaw, Poland Spyros Reveliotis (Chapter 9), spyros@isye.gatech.edu School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332, USA Tsuta Tai (Chapter 2), ttai@pfs.com State Street Corp., 600 College Road East, Princeton, NJ 08540, USA Mikko Tiusanen (Chapter 17), mikko.tiusanen@tut.fi Tampere University of Technology, P.O.Box 553, FIN-33101 Tampere, Finland B. Turchiano (Chapter 5), turchiano@poliba.it Dipartimento di Elettrotecnica ed Elettronica, Polytechnic of Bari, Bari, Italy Milosh Vladimir Ivanovich (Chapter 14), ivanovic@sub.net.au Telstra Research Laboratories, Melbourne, Australia Mathias Weske (Chapter 18), weske@hpi.uni-potsdam.de Hasso Plattner Institute for Software Systems Engineering at Potsdam University, Prof.-Dr.-Helmertstr. 2,14482 Potsdam, Germany Naiqi Wu (Chapter 11), nqwu@gdut.edu.cn Department of Mechatronics Engineering, Guangdong University of Technology, Guangzhou 510090, P. R. China Xiaolan Xie (Chapter 8), xie@loria.fr INRIA/Macsi Project and LGIPM, ISGMP-Bat. A, Ile Du Saulcy, 57045 Metz, France Ali Yalcin (Chapter 2), ayalcin@eng.usf.edu Industrial and Management Systems Engineering, University of South Florida, 4202 E. Fowler Avenue, ENB118, Tampa, FL 33620, USA
- 16. X List of Contributors Adam W. Yeung (Chapter 15), wkyeung@cisco.com Cisco Systems Inc., 170 West Tasman Drive, San Jose, CA 95134-1700, USA MengChu Zhou (Chapters 1,10 and 11), zhou@njit.edu and mengchu @ieee.org Department of Electrical and Computer Engineering, New Jersey Institute of Technology, 323 MLK Blvd., Newark, NJ 07102, USA and Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, P.O. Box 2728, Beijing 100080, P. R. China
- 17. Preface The Aims This book is edited and written to deal with the research and implementation issues in designing complex computer-integrated systems. These systems include auto mated production systems, transportation systems, computer operating systems, concurrent software systems, computer networks, distributed database systems, and other automated systems. As technological systems become more complex, auto mated, distributed, and computing-intensive, deadlock issues facing the researchers and engineers for complex system development become of major significance in both research and practice. Since the 1970s, there have been many studies to model, detect, resolve, and recover from deadlocks and practical applications in the men tioned areas. However, there is no single title that summarizes this important area of research efforts. Deadlock-related issues have been dealt with in some edited volumes and books but were never treated in a systematic and comprehensive manner as in this edited volume. Thus we view this volume as a timely publication to serve well this segment of research and development community that is growing in number and interest. The Contents Deadlock is a situation in which there is no system throughput due to inappropriate allocation of resources to concurrent executing processes. More precisely, a dead lock occurs when each element from a set of processes waits for resources held by other elements of the same set. Such phenomena can be observed in computer op erating systems, concurrent software systems, automated manufacturing systems, and transportation systems. Their modeling, detection, avoidance, and recovery are very important in improving a system’s performance. This book contains 18 chap ters that are contributed by prominent researchers in this area. They address one or more of the following research and development subjects: A. Deadlock prevention approaches including synthesis of deadlock-free mod els and deadlock-free scheduling; B. Deadlock detection and recovery methods that allow deadlock to occur with recovery options; xi
- 18. xii Preface C. Deadlock avoidance that formulates the dynamic control policies that depend upon the system states or at least upon the model structures. In this category, such mathematical and graphical modeling tools as digraphs, Petri nets, and automata are discussed; and D. Comparison and industrial benchmark studies that compare different ap proaches. All these contributions can be classified based on the deadlock modeling approaches they present, the solution types they propose, and applications they seek, as shown in the below table. Models Chapter Solutions Chapter Applications Chapter Automata 1-4,17 Prevention 1,3,8-10, 13,16,18 Manufacturing /Transportation 1-12 Digraphs 1,5,13, 17 Detection/ recovery I, 3,4,5,8- II, 13,17,18 Communication Network 13, 14 Petri nets 1,6-11, 17 Avoidance 1,2,4,5,7, 11-15,18 Internet 15, 16 Other methods 12,14- 18 Comparison 1,5,12-16, 18 Concurrent Pro- gram/Database 17, 18 The editors’ introductory chapter "Introduction to Deadlock Research in Computer-Integrated Systems” presents fundamental deadlock-research related materials and an up-to-date summary of the present deadlock resolution studies. A typical example from automated manufacturing is offered to illustrate the three primary modeling methods and the related solution approaches: digraphs, automata, and Petri nets. Their advantages and disadvantages are highlighted. The second chapter "Deadlock Avoidance in Automated Manufacturing Systems Using Finite Automata and State Space Search” by Thomas O. Boucher, Tsuta Tai, and Ali Yalcin of Rutgers University, USA, presents an ap proach to deadlock avoidance based on finite automata. This approach begins from the framework introduced by Ramadge and Wonham (R&W) for modeling and control of discrete event systems (DES) based on formal languages generated by finite automata. They apply this framework to the problem of dynamic scheduling and control of automated manufacturing systems. A typical automated manufac turing system is composed of multiple machines and workstations that perform various operations on a part, and a material handling system that interconnects these machines and workstations. Parts are processed to completion by routing them through various machines and workstations according to their individual process plans. Their presented approach to avoiding deadlock features 1) a simple and natural way of formulating the "requirements model” of the R&W framework from the part routing plans, 2) an ability to handle parts with multiple routing plans within the framework, 3) a solution that guarantees that the resulting controller is both deadlock-free and maximally permissive, and 4) an ability to dynamically
- 19. Preface X III reevaluate the controller logic as the active part mix in the manufacturing system changes. The direct application of the R&W framework can involve a large search space as problem size grows. Extensions of their approach have addressed the problems of scalability, state space search, and execution time. They have been accomplished through distributed control and the use of autonomous agents, as well as the introduction of more effective state space search algorithms. These exten sions and the relative efficiency of algorithms are also discussed and demonstrated in this chapter. The third chapter “Synthesis of Deadlock-free Supervisory Controllers Using Automata" by A. Ramirez-Serrano, University of Calgary, Canada, and B. Benhabib, University of Toronto, Canada, discusses the automata-based DES-controller synthesis methodologies capable of obtaining deadlock-free su pervisors by construction. Namely, the resultant controllers do not require the use of an on-line deadlock detection and recovery mechanism. This chapter reviews R&W control theory and describes its deadlock-free controller yielding charac teristics together with other significant properties that can be used for the speci fication, verification, analysis and synthesis of “correct" DES controllers. Then, the authors review another automata theory, Extended Moore Automata (EMA), which extends the capabilities of R&W theory in controlling more complex sys tems, e.g., multi-workcell systems producing parts with several alternate proc essing routes. The probability of encountering deadlocks in such multi-workcell Flexible Manufacturing Systems (FMS) is higher compared with single-workcell systems due to the existing “competition for resources" between the parts that can be processed in several different ways. Even if one is able to identify and detect a deadlock state in an on-line manner, there may be no easy way to resolve it. Thus, when dealing with the control of FMS, it would be beneficial to analyze the controller at hand for possible deadlock states and/or conflicting conditions, identify such states and eliminate them prior to their implementation. As pre sented in this chapter, the use of individual and independent supervisors for each workcell would reduce the computational complexity when synthesizing the (smaller size) supervisor set and allow for their a priori deadlock analysis. Such a deadlock identification method is presented herein based on the use of EMA theory. Naturally, however, an identified deadlock state can only be eliminated by changing the control specifications and constraints imposed by the user of the DES at hand and resynthesis of the supervisor. As an additional practical tool, the authors also present a method to minimize the state-space of the obtained super visors with respect to the control actions generated at each state of the controller. This minimization methodology can be used for the size reduction of controllers, while preserving their deadlock-free characteristics and the behaviors they en force. The fourth chapter “Deadlock Avoidance and Dynamic Routing Flexibility in Automated Manufacturing Systems" by Mark Lawley, Purdue University, USA, addresses the deadlock avoidance issues in automated manufacturing systems
- 20. xiv Preface (AMS) with dynamic routing flexibility. Dynamic routing arises from three types of system flexibility: machine flexibility, sequence flexibility, and central buffering. Machine flexibility occurs when an operation can be performed on more than one machine. Even though the sequence of operations might be fixed, machine flexi bility can generate a large number of potential routes for a part to follow. Sequence flexibility occurs when the set of operations specified by a part’s process plan is not completely ordered. Sequence flexibility can also spawn a large number of potential routes for a part to follow. Finally, automated manufacturing systems sometimes use central buffers to alleviate the blocking that occurs when parts finished on one machine await allocation of buffer space on the next. Under central buffering, such parts typically have the option of moving to and awaiting their next allocation at a centrally located buffer, if the buffer is not full. In each of these three cases, the supervisory controller is faced with the task of allocating resources among com peting parts when each part has allocation alternatives. These additional degrees of allocation freedom can affect the safety characteristics of the system and must be taken into account when developing deadlock avoidance logic. This chapter sum marizes the author’s deadlock avoidance research for systems with these types of flexibilities. It discusses the interaction between allocation flexibility and the com plexity of safety, presents sub-optimal deadlock avoidance policies for these highly flexible systems, and discusses cases where optimal deadlock avoidance is com putationally tractable. The fifth chapter “Digraph-Based Techniques for Deadlock Resolution in Automated Manufacturing Systems” by M. P. Fanti, В. Maione, G. Maione, and B. Turchiano, Politecnico di Bari, Bari, Italy, describes digraph-based methods to face deadlock in AMS. Compared with another popular method, Petri nets, digraphs lend themselves to represent the interactions between jobs and resources (resources allocated to and required by jobs) in an easy and immediate way. Digraphs, indeed, allow a formal characterization of deadlock conditions useful to derive several solving methodologies. The chapter considers different approaches to facing deadlock, consisting of detection/recovery methods and avoidance techniques. Detection/recovery methods require a low computation burden in the detection phase and a dedicated buffer to activate the recovery phase. On the contrary, avoidance techniques need no dedicated hardware and carry out a feedback event-control of the system. The proposed approaches differ in com plexity, in the degree of restriction they impose on the free assignment of the system resources to jobs and, consequently, in the production performances they allow. Finally, the proposed framework can be used to deal with the situations in which the deadlock avoidance approaches can be applied in decentralized form, i.e., by partitioning an AMS into subsystems, each controlled by a local controller independently of the other ones. This is particularly useful in cellular manufac turing systems to establish the cells that can be locally controlled and the ones requiring a centralized approach to deadlock avoidance. The sixth chapter “Deadlock-Free Supervisory Control for Assembly and Disassembly Systems” by Elzbieta Roszkowska, Wroclaw University of Tech
- 21. Preface XV nology, Poland deals with a class of processes modeling streams of materials that can join and split, such as in assembly/disassembly systems, at group transport and then individual part processing, or in processes that require temporary meeting of independently routed components. As each such process can be viewed as a set of interacting sequential processes, the processes considered here are called compound processes. By modeling the system dynamics with Petri nets, this chapter investigates the supervisor design problem for ensuring deadlock-free process flow. The required concurrency and use of the same resources by com ponent sequential processes may lead to a compound process that is not realizable. Therefore this chapter presents a model that allows more valuable resources, such as machines, to be released directly after an operation is completed. This is due to the fact that the buffer space required for the products of an operation is allocated together with the machine. Thus, from the viewpoint of deadlock-free process control, we can neglect the problem of machine allocation and only focus on the flow of materials among the buffers. The supervision problem is solved through a joint approach to establishing for each buffer a minimal sufficient capacity and constraining the system dynamics. The resultant supervisor is given in the form of a function that states whether a particular enabled transition or event can take place at a particular state. The underlying idea is that a buffer reserve changes dynamically to ensure that component sequential processes that need to be syn chronized can await each other without inducing a deadlock. The seventh chapter “Deadlock Avoidance Algorithms and Implementa tion: A Matrix-Based Approach” by Jose Mireles, Jr., Universidad Autonoma de Ciudad Juárez, Juarez Chihuahua, Mexico, Frank Lewis, University of Texas at Arlington, Ft. Worth, TX, USA, Ayla Giirel, Eastern Mediterranean University, Famagusta, Turkey, and Stjepan Bogdan, University of Zagreb, Zagreb, Croatia, presents the development of a matrix-based deadlock avoidance supervisory controller for Discrete Event (DE) Systems. The DE controller uses a rule-based matrix dispatching formulation. This matrix formulation makes it direct to write down the DE controller from standard manufacturing tools such as the Bill of Materials or the assembly tree. It is shown that the DE controller’s matrix form equations plus its Petri Net marking transition equation together provide a com plete dynamical description of DES. This provides a new method for Computer Simulation of DES. On-line deadlock-free firing rules are implemented by the DE matrix controller by performing circular wait analysis for possible deadlock situations, i.e., analyzing the so-called critical siphons and critical subsystems and presence of bottleneck resources. The chapter introduces a matrix-formulated analysis method to identify bottleneck and key resources shared among circular resource loops that lead to deadlock situations. The resultant matrix algorithms are implemented on a robotic Intelligent Material Handling (IMH) cell and its technical information includes the development of the deadlock-free controller in LabVIEW-a graphical programming language developed by National Instru ments.
- 22. xvi Preface The eighth chapter “Deadlock Detection and Prevention of Automated Manufacturing Systems Using Petri Nets and Siphons” by MuDer Jeng, Na tional Taiwan Ocean University, Taiwan, ROC, and Xiaolan Xie, INRIA, Metz, France, discusses Petri net siphon-based approaches for detecting and preventing deadlocks in AMS. Siphons, also named deadlock in some literature, are an im portant concept in characterizing the deadlock in Petri nets. First, the chapter pre sents the siphon-based deadlock analysis of AMS modelled by Petri nets. It gener alizes the well-known Commoner condition and exploits the notion of potential deadlocks, which are siphons that eventually become unmarked. The chapter then presents a linear programming-based sufficient condition under which a siphon is not a potential deadlock. Using the new sufficient condition, a mathematical pro gramming approach and a mixed-integer programming approach are proposed for checking Petri nets and structurally bounded Petri nets without explicitly generating siphons. The chapter presents stronger results that can be obtained for certain Petri net classes of AMS. These classes of Petri nets include the classical one, asym metric-choice nets, and some recently proposed classes, e.g., augmented marked graphs, S3PR, RCN merged nets, ERCN merged nets, and PNR. The chapter finally presents an iterative deadlock prevention approach for S3PR and discusses some ideas for future research concerning deadlock prevention of other net classes. The ninth chapter “Siphon-Based Characterization of Liveness and Live- ness-Enforcing Supervision for Sequential Resource Allocation Systems” by Spyros Reveliotis, School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA, deals with one of the most interesting develop ments from, both, a theoretical and a practical perspective, in the emerging theory of resource allocation systems (RAS), i.e., the characterization of the non-liveness of many RAS classes through the Petri net (PN)-based structural object of empty, or more generally, deadly marked siphon. The work presented in this chapter seeks to develop a general theory that provides a unifying framework for all the relevant existing results, and reveals the key structures and mechanisms that connect the RAS non-liveness to the concept of deadly marked and in certain cases, empty si phon. In this capacity, the presented results allow also the extension of the si phon-based characterization of non-liveness to broader RAS classes, and provide a clear and intuitive explanation for the limitations of the approach. The last part of the work discusses how the derived structural characterization of RAS non-liveness can be combined with some algorithms for detecting empty or deadly marked si phons in a given PN marking, in order to develop analytical liveness sufficiency tests and systematic procedures for the design of liveness-enforcing supervisors (LES). The related computational cost issues are discussed. The tenth chapter “Elementary Siphons of Petri Nets for Efficient Dead lock Control” by Zhiwu Li, Xidian University, Xi’an, China, and MengChu Zhou, New Jersey Institute of Technology, Newark, NJ, USA, prevents a recently pro posed novel siphon idea, i.e., elementary and redundant siphons. The latter is line arly dependent upon the former. This provides a new avenue to achieve their non-emptiness control by controlling only the elementary siphons, thus obtaining
- 23. Preface xv u the desired liveness property of Petri nets. The chapter proves that the number of elementary siphons is bounded by the number of the transitions in a Petri net. It further establishes the results on the siphon control by adding monitors and related arcs to only elementary siphons. The proposed elementary siphon theory is then used to construct two novel deadlock prevention policies that are applied to the S3PR of two FMS. The chapter illustrates their significant advantages over the previous methods that have to deal with an exponentially growing number of minimal siphons when they add monitors and arcs for the same type of Petri nets. The eleventh chapter “Resource-Oriented Petri Nets in Deadlock Preven tion and Avoidance” by Naiqi Wu, Guangdong University of Technology, Guangzhou, China, and MengChu Zhou, New Jersey Institute of Technology, Newark, NJ, USA, develops a finite capacity Petri net called Colored Re source-Oriented Petri Net (CROPN) for the problem of deadlock avoidance in AMS. This model is very concise and relates deadlock to a full circuit in the model. By using the model for AMS in which each machine has an input (output) buffer, this chapter presents necessary and sufficient conditions for deadlock-free and deadlock avoidance policy. This policy is a maximal permission policy. A maximal permission policy in deadlock avoidance may allow blocking to occur in the rule-based scheduling environment. Based on the CROPN, this chapter relaxes the maximal permission policy and presents a new control policy called L-policy by using a sufficient condition so as to reduce blocking. Their applications to a me dium size automated manufacturing system are presented. The simulation results illustrate the significant gain in system performance by using the L-policy over a maximally permissive policy under the rule-based scheduling environment. Finally, the concept of CROPN is applied to and the related theory is developed for AGV systems that allow both uni- and bi-directional lanes for deadlock avoidance. One-step look-ahead control policies are presented for such systems. The twelfth chapter “The Effect of Modeling and Control Techniques on the Management of Deadlocks in FMS” by Luca Ferrarmi and Luigi Piroddi, Politecnico di Milano, Milano, Italy addresses several deadlock control policies and their performance when the time is considered. To avoid deadlock in FMS, it is necessary to adopt suitable control policies which limit the resource allocation in the system, thus affecting the overall system performance. In spite of the in teresting results obtained in the research world, traditionally relegated to untimed models, the problem of deadlock is still conceived by practitioners as a real-time problem, or as a problem due to a bad structured system layout and global or ganization. However, it is definitely a control problem that can be solved pre cisely and elegantly from a control system theory perspective, keeping per formance optimality in mind also. In the present paper, the authors try to combine the two perspectives, considering both the deadlock avoidance control problem and a more pragmatic, performance-oriented point of view. In particular, the problem addressed here is that of evaluating and comparing the performance of deadlock avoidance control policies applied to FMS, taking into account some of the most common in the literature. This is done considering, first, timed and un-
- 24. xviii Preface timed models, and, second, models of uncontrolled systems, models of systems controlled with imperfect deadlock avoidance algorithms, and deadlock-free controlled systems. Through the definition of suitable indices and reference models, and of suitable analysis and simulation approaches, it is shown how it is possible to design appropriate control schemes tailored to specific purposes. Two different application examples are analyzed in detail, with the help of a com mercial simulation package (Arena). Finally, an adaptive algorithm that can learn from system evolution to avoid deadlock is illustrated. The thirteenth chapter “Deadlock Characterization and Resolution in In terconnection Networks” by Timothy Mark Pinkston, University of Southern California, Los Angeles, CA, USA, presents the deadlock modeling and resolution methods for high-performance interconnection networks. Such networks comprise the communication backbone in digital systems at several system levels. For ex ample, at the higher system levels, local-area networks are used in clusters of PCs, networks of workstations and other distributed processing systems which serve as cost/performance-effective alternatives to tightly coupled massively parallel proc essing systems. At lower levels, networks-on-chip are used to overcome many of the performance limitations of bus-based systems at the chip level. Parallel com puting and communication systems require high-performance communication ser vices with high reliability, availability and dependability. The performance of the interconnection network is measured, in part, by packet delivery time from source to destination (i.e., latency) and by the number of packets delivered per unit time (i.e., throughput). In essence, a high-performance network allows the maximum number of packets to make forward progress to their destinations in minimal time. Likewise, the reliability, availability and dependability of a network equally impact the overall “goodness” quality of a system. These attributes are measured, in part, by the network’s ability to remain up and running at near normal levels even when unexpected events occur. This chapter presents how various network parameters influence the formation of message blocking and deadlocks in interconnection networks. A model of resource allocations and dependencies is described which allows various types of message blocking to be described precisely, including deadlock. Ways in which a network’s susceptibility to deadlock can be reduced are given, and guidelines for designing networks which maximize routing flexibility and resource utilization are also provided. The fourteenth chapter “Deadlock Models for a Multi-Service Medium Access Protocol Employing a Slotted Aloha or Q-ary Tree Based Signaling Channel” by Milosh Vladimir Ivanovich, Telstra Research Laboratories, Mel bourne, Australia, presents the deadlock issues in Medium Access Control (MAC) protocols. Such protocols are used for cable modem hybrid fibre/coaxial (HFC) networks, as well as wireless ATM networks. They often utilize a collision-based capacity request signaling channel. This signaling channel typically relies on either the Slotted Aloha or Q-ary Tree multiaccess principles. This chapter studies in de tail the performance of a p-persistence Slotted Aloha contention resolution algo rithm (CRA), subject to extreme inter-station correlation, by means of a dis
- 25. Preface x ıx crete-time Markov chain analysis. It examines, by simulation, the performance of a Q-ary Tree CRA called msSTART (Multi-slot Stack Random Access Algorithm), which was proposed for use in the IEEE 802.14 HFC standard. The performance of the two types of CRA is discussed and contrasted, under what the IEEE 802.14 working group has termed the “disaster scenario”, where the entire station popula tion simultaneously requests capacity after a neighborhood-wide power failure, for example. The conditions leading to a deadlock are examined in detail-deadlock being a situation where the time to collision resolution becomes unacceptably high and the system is practically unstable. This chapter analyses several disaster sce nario deadlock models and studies the effect of channel error probability, signaling traffic load, and the contention resolution algorithm used. Key factors of the CRAs are identified, with the finding that it is the collision rate but not channel errors, which more strongly governs throughput performance. Further, it is demonstrated that the introduction of an effective priority scheme does not have a significant impact on the stability of the Q-ary Tree based CRA. Three signaling channel schemes introduced in this chapter provide insight into the stability of the MAC after the implementation of priority for different traffic classes. This chapter finds that of the three schemes evaluated, the full Contention Mini-Slot (CMS) sharing scheme employing multiple CMSs per data region extends a MAC protocol’s us able load region the furthest. The fifteenth chapter “Deadlock-Free TCP Over High-Speed Internet” by Rocky K. C. Chang, The Hong Kong Polytechnic University, Kowloon, Hong Kong, Ho Y. Chan, University of Southern California, Los Angeles, CA, USA, and Adam W. Yeung, Cisco Systems Inc., San Jose, CA, USA, explores the deadlock phenomena in Transport Control Protocol (TCP) that dominates Internet traffic and presents several algorithms to handle them. A throughout deadlock is reported when TCP is operated on high-speed networks. This deadlock occurs when the Silly Window Syndrome Avoidance Algorithms (SWSAAs) are turned on in both sender and receiver, and the send-receive socket buffer sizes fall in a certain region. The main factor contributing to this problem is that the connec tion’s Maximum Segment Size (MSS), which is used by the SWSAAs, is no longer small when compared with the send-receive socket buffer sizes. Conse quently, a TCP sender may not able to compose a MSS segment if its send buffer size is not large enough; similarly, a TCP receiver may not be able to acknowl edge since the amount of data received is not large enough when compared with MSS. The result is a deadlock, which can be resolved only by a receiver’s 200-ms delayed acknowledgment timer. This chapter proposes a new Adaptive Ac knowledgment Algorithm (AAA) to eliminate throughput deadlock while avoiding SWS. Unlike the current delayed acknowledgment strategy, AAA does not rely on the exact value of MSS and the receive buffer size to determine the acknowledgment threshold. This chapter shows that AAA is able to eliminate all throughput deadlocks in a non-congested network. Moreover, to further enhance AAA, it introduces a slow-start-like mechanism in the receiver to account for network congestion, leading to an algorithm called Congestion-Sensitive AAA
- 26. Other documents randomly have different content
- 27. “No, but he won’t learn much, because when I tell Payson he will shut down on any new stuff. It’s too bad, though, because we need to try out those plays.” At that moment the Yardley team came on and the Yardley cheerers started into action. “We’d better find some seats or there won’t be any,” suggested Harry. “Wait a minute,” said Gerald. Davis had hurried away and was speaking to the coach. When he turned back Gerald hailed him. “What did Payson say, Perky?” “Asked me if I was certain, and I said I was. Then he nodded and called Charlie and Bert. I guess they’re making over the programme.” At a little distance Payson, Merriwell and Simms were in consultation. The rest of the team had taken the field and the footballs were already flying through the air. “Someone ought to kick him out,” said Harry, fixing the Broadwood youth with hostile regard. “We might kidnap him,” suggested The Duke dreamily. “Anyone got a gunny-sack handy? We could tie him up in it and drop him into the Bosphorus—I mean the Wissining.” “What we should have done,” said Davis, “is to have sent someone to watch Broadwood play Nordham to-day. If it’s fair for them it’s fair for us.” “It’s extremely low-bridge,” replied The Duke disapprovingly. “Quite reprehensible, whatever that may be. Also, fellows, if anything should happen to him he’d have only himself to thank.” “What’s going to happen to him?” asked Gerald, eyeing The Duke with suspicion. The Duke only smiled carelessly. “Why ask me? I don’t say anything is going to happen. I only say if anything should happen——”
- 28. “Oh,” murmured Davis disappointedly, “I thought perhaps you had a plan to get rid of him.” The Duke viewed him reprovingly. “Perky, if you want anyone put out of the way you must do it yourself. I refuse to stain my hands with the life blood of even a Broadwood fellow. I’m that particular!” “Well, I hope he enjoys himself,” muttered the manager. “He won’t learn much, anyway.” He nodded and hurried off, drawing his note- book and pencil into sight. The Duke quietly beckoned Gerald and Harry toward the entrance. Outside the three stood for several minutes with their heads together. When they ambled carelessly back their countenances were as innocent of guile as the faces of three babies. Only there was a suspicious twinkle in The Duke’s eyes. The grand stand being filled, the three found a space on the grass near the rope and watched the two teams take their positions. It was a clear, nippy Fall day, with a brisk northwest breeze quartering across the field and streamers of white clouds scudding by overhead. Forest Hill had won the toss and chosen the north goal. The whistle blew and Fales kicked off.
- 29. Y CHAPTER XI BROADWOOD IS FOILED ardley’s first chance to score came within three minutes of the kick-off, after Forest Hill’s quarter had fumbled on the second play and Stark had fallen on the ball near the twenty-yard line. But although the Blue worked down to within twelve yards of the goal, the attack weakened and the pigskin changed hands. Forest Hill kicked on first down and the play went to the middle of the field. And about the middle of the field, with small advantage to either side, it stayed for the rest of the twelve-minute period, with neither team being able to gain much ground. A minute or two before the whistle sounded The Duke carelessly arose, yawned, stretched and wandered away down the line. Now and then he paused to look back at the play or to speak to an acquaintance, but presently, having left the grand stand far behind, he doubled back and hurried around between the stand and the tennis courts, reappearing at the entrance just as the two teams, donning blankets, paused for the two-minute intermission. The Duke pushed his way through the throng with an important air and faced the sloping tiers. “Mr. Gibson wanted at the telephone!” announced The Duke loudly. “Is Mr. Gibson here?” Without appearing to look in his direction The Duke saw the Broadwood fellow start in his seat, look indecisively down and settle back again. “Mr. Gibson wanted at the ’phone!” he continued, passing along in front of the stand. “Mr. Gibson wanted at the ’phone immediately. Is Mr. Gibson here?”
- 30. The fellows took up the cry. “Is Mr. Gibson here? O you Mr. Gibson! Show yourself, Gib! There he goes! Here he is! Who wants Gibson? I don’t! O you Mr. Gibson!” At the first aisle a tall, broad-shouldered youth in a derby hat was picking his way down as unostentatiously as possible. The Duke turned back and met him as he reached the ground. “Is your name Gibson?” he asked. The other nodded. “You’re wanted at the ’phone. I’ll show you where it is.” Followed by the youth in the derby, The Duke pushed his way through the crowd about the entrance. Back of him a whistle shrilled and the teams lined up once more. “Do you know who wants me?” asked Gibson as they started up the path. “I couldn’t say,” replied The Duke. “Nice day for the game, isn’t it? You’re a Forest Hill fellow, aren’t you?” “Hm,” responded the other noncommittally. “Where is this telephone?” “Oxford,” replied The Duke, leading the way around the front of the gymnasium and thereby lengthening the journey. “It’s right around the corner here.” A burst of cheering came from the field below them and Gibson looked regretfully over his shoulder. “Those are your fellows cheering,” said The Duke. “I shouldn’t wonder if you beat us to-day. How many of you came along?” “Er—quite a number; forty or fifty, I guess. This the building?” “Next,” said The Duke, conducting the visitor past Merle. “Here we are.” They went up the steps of Oxford and The Duke led the way down the dim and silent corridor to the telephone booth. Politely he opened the door and, Mr. Gibson once inside, politely and very carefully he closed it. The click of the lock was simultaneous with the lifting of the receiver from the hook. “Hello! Hello! This is Mr. Gibson.... What say?... Gibson!...”
- 31. “‘Hello! Hello! This is Mr. Gibson.... What say?’” The Duke, stealing softly down the corridor, heard no more. At the doorway he cast a fleeting glance back at the booth. Then he slipped from sight. Halfway back to the field he paused and did an erratic breakdown, with much snapping of fingers and many loud chuckles. Then, pulling his features back into their former innocence of expression, he went on. He reached the gridiron at an exciting moment and had seated himself between Gerald and Harry before his fellow-conspirators realized his return. Then, “All right?” whispered Gerald.
- 32. The Duke, supremely interested in the game, closed one eye slowly and portentously. Gerald grinned. Harry hugged a foot ecstatically. “Like a sheep to the slaughter,” whispered The Duke gloatingly. “Oh, what do you suppose he’s saying to Central?” “How long will he stay there?” asked Harry. “Until he gets out. There’s no one in the Office on Saturday afternoons. Anyway, they couldn’t hear him—unless he broke a window and yelled like sixty. Did you tell Perky?” “Yes, and they’ve worked a couple of the new plays already.” “Tried to, you mean,” corrected Harry gloomily. “They didn’t gain much.” “Anyone scored?” asked The Duke. “Not yet. No one’s had a chance. Kendall tried a placement from the forty-five yards and missed by a yard. Too bad. He had the wind with him, too.” “Pete made a rotten pass, though,” said Gerald. “Simms had to scramble for it. It’s a wonder they got the kick off at all. There’s the whistle. Half’s over.” As the players seized their blankets and trotted off the field Davis hurried up to the trio beside the rope. “What did you do with him?” he asked in a hoarse whisper. “Do with him? With who?” asked The Duke innocently. “Gibson.” “Perky, you jump to conclusions,” returned The Duke calmly. “If anything has been done to Mr. Gibson you shouldn’t lay it to me. I have nothing but the kindest, sweetest sentiments toward the gentleman.” “Oh, chop it! Is he—is he safe?” “Oh, I do hope so!” replied The Duke. “Don’t tell me that anything has happened to him, Perky!”
- 33. “Quit kidding,” begged Davis. “I want to know. Can we go ahead with the new plays, Duke? Will he be back?” “Blessed if I know. I know he isn’t here now, but there’s no telling how long he’s going to stay away. Tell you what, Perky. I’ll stand at the entrance and keep watch. If I see him coming back I’ll pass the word to you and you can tell Payson.” “All right. I’ll tell Payson that. Don’t miss him, though.” “Nary a miss, Perky!” The Duke, followed by Gerald and Harry, went to take up a position at the corner of the grand stand and Davis scurried off to the gymnasium in the wake of the team. The Duke, hands in pockets, wandered outside and viewed the path. But save for the players trotting up the steps of the gymnasium and Davis speeding to overtake them no one was in sight. “Look here,” said Gerald, who had been studying the situation in his mind, “what that fellow will do is to tell Central that he’s locked up in the booth. Then Central will telephone to Merle or Clarke and they’ll let him out. We didn’t think of that.” The Duke frowned. “That’s so,” he acknowledged. “And it’s dollars to doughnuts Central will get Collins on the ’phone and then there will be the dickens to pay!” “Thunder!” breathed Harry. “Just so,” agreed The Duke. “Well, I’m in for it now, so there’s no use worrying and getting a wrinkle. After all, it was a patriotic deed and my conscience is at peace. I done it for the good of my fellow critters.” “I don’t see how Collins will know it was you,” said Harry hopefully. The Duke viewed him with a pitying eye. “Merely because I paraded up and down in front of the grand stand yelling my little heart out for Mr. Gibson, Harry. Collins may be dense, but I think he will be able to follow that clue; what?”
- 34. “He will get you,” acknowledged Gerald sadly. “The question is ——” “The question is what will I get! Well, never mind. What’s done is did. And here comes the team again and Mr. Gibson is not in sight. What I should have done after getting him in there was cut the line!” He looked longingly up the hill. “Maybe it isn’t too late yet,” he added musingly. “Then you would get it!” said Gerald. “I guess you’ve done enough, Duke.” “Sure; too much is plenty! Anyway, if Mr. Gibson doesn’t get back before the game’s over I’ll be satisfied.” The Yardley team came piling through the entrance, Merriwell in the lead, Coach Payson and Davis following. As he passed Davis lifted his eyebrows questioningly and The Duke returned a reassuring shake of the head. Davis whispered to the coach and the latter smiled demurely as he passed on to the field. “You fellows,” said The Duke presently, “had better get away from here. If they see you sticking around with me they’re bound to think you had a hand in it.” “So we did,” replied Gerald. “So you didn’t! What did you do, I’d like to know. Move on now, move on! Don’t block the sidewalk!” “Oh, who cares?” asked Harry. “It’s only a joke, anyway. They can’t do anything to any of us.” “Besides, Gibson won’t make a fuss,” said Gerald. “He won’t want to confess that he came over to spy on the team.” “Well, suit yourselves,” replied The Duke with a shrug of his shoulders. “If you must have trouble, have it. They’re kicking off.” The three saw the game, or as much of it as they could, from their post, at the same time keeping a sharp watch for the reappearance of Mr. Gibson. The third period proved conclusively that Yardley still
- 35. had much to learn about offense. Her attack in the middle of the field was fairly strong and at times showed flashes of brilliancy, but once past the thirty-yard line her play slowed up and all the “punch” vanished. Forest Hill, although light, was remarkably quick and decidedly “scrappy.” She had many defeats to atone for and when the third period ended, like the previous ones, without a score against her it was evident that she had come to the conclusion that here was the opportunity to obtain vengeance. She started the fourth quarter with a dash and vim that startled the spectators and staggered the Blue team. Her back-field, working together beautifully, fooled Yardley time and again and made short and steady gains until the ball was well down in the Blue’s territory and Simms was imploring his men to “stop them!” It was only the Blue’s secondary defense that stood between Forest Hill and a score, for the Yardley line was too slow and played too high and the Forest Hill backs sliced through it almost at will. Payson made two changes when the ball was down on the Blue’s thirty-two yards, putting in Jackson for Fales and Jensen for Stark. And later, just before the end of the game, Best relieved Girard at center. The rest of the team, however, played the contest through, and that without gaining much credit. Yardley captured the ball on her twenty-five-yard line, worked a double pass for a slight advance and then punted out of danger. But Forest Hill came back desperately. Her quarter led a glorious attack and what had been on the point of happening for two periods finally happened. An on-side kick was recovered by a Forest Hill back, Metz and Crandall each missed a tackle and the runner after tearing off nearly twenty yards, was finally downed by Simms on the Blue’s seventeen yards. The ball was well over toward the side of the field when the two teams lined up again and a skin-tackle play gained two yards and brought the pigskin nearer the center of the field. The full-back trotted to the twenty-five-yard line and, although the angle was severe, it seemed that a drop-kick might put the ball over. But Forest Hill, smarting under many defeats, disdained a victory so simply bought. The ball went back to the outstretched arms, but the full-back didn’t kick. Instead he dashed off across the
- 36. field, with the two teams trailing after him, found a chance to turn in, eluded one player after another while the Forest Hill supporters on the stand shrieked their triumph, and, finally, dragging two Yardley players after him, staggered and crawled across the goal line! That touchdown spelled defeat for Yardley and even the staunchest supporter of the Blue realized it. Even though Forest Hill failed at the goal the lead was too big to overcome in the two or three minutes that remained. But Yardley went desperately to work again. It was agreed afterward that had she played during the first of the game as she played then there would have been a different tale to tell. Using every play he knew, Simms, when a lucky fumble gave Yardley the ball after the kick-off, hurled his backs and tackles against the weakening Forest Hill line. From their own forty yards to the enemy’s thirty-five they went, gaining their distance at times by only an inch or two, but always gaining it. And there, with the timekeeper proclaiming forty seconds left, Kendall was sent back to the forty-five-yard line, while the stand held its breath, took the ball breast-high from Best, dropped it lightly to earth and sent it spinning as straight as an arrow over the very center of the cross-bar! Let us be thankful for small favors. Five to three was better than five to naught, and Yardley cheered philosophically and rose up in the grand stand and called Kendall blessed. And at the entrance The Duke, casting one final glance up the hill, derived what satisfaction he might from a plot well carried out. Forest Hill, all smiles, hurried off with the captured football, and Yardley, rather glum and very tuckered, wrapped her blankets about her and trotted back to the gymnasium under the stigma of her first defeat. Gerald and Harry were inclined to dejection, although Kendall’s brilliant goal from the field was a mitigating ray in the surrounding gloom of failure. But The Duke, with the fine bravado of one on the way to the guillotine, refused to be downcast.
- 37. “Who cares?” he demanded. “What’s Forest Hill to us? She showed us we weren’t as good as we thought we were and that ought to help. It’s Broadwood’s scalp we want, fellows, and to-day’s little setback will do us a lot of good. Besides,” he chuckled, “our friend Gibson is returning empty-handed. Let us rejoice and make merry, O my comrades, for to-morrow we die! At least, I do!”
- 38. M CHAPTER XII COTTON MEETS A FRIEND r. William Gibson, of Broadwood Academy, really deserves no place in this narrative, yet I hardly see how we can keep him out inasmuch as his trip to Yardley that Saturday afternoon proved to be the first link in a chain of events involving many of the principal actors in our little drama. For if Gibson had not come to Yardley he would not have been ignominiously imprisoned in the telephone booth, and if he had not been shut up in the booth he would not have run across Charles Cotton, and—but I am getting ahead of the story. The practice of detailing players or coaches to attend games played by a rival school or college in order to gain information that may aid in defeating such rival is a questionable one, in spite of its prevalence, and I have no intention of defending it. At the same time I very much doubt if William Gibson—over at Broadwood they called him Billy—considered that he was doing anything out of the way. I am willing, even eager, to attribute the highest patriotic motives to Mr. Gibson, up to the time he met Charles Cotton. For what happened subsequently I offer no excuses. Even the most rabid patriotism will not explain it. Gibson had purposely attired himself to look as little like a student as possible. That is, he had donned a derby hat instead of the usual cap and a rather dressy light overcoat, hoping perhaps to give the impression of being a young gentleman of mercantile pursuits, say a youthful but promising bank clerk or a budding broker. Unfortunately, Billy’s countenance and figure, once seen, were nearly unforgettable. The countenance was heavy and pugnacious and the figure broad- shouldered and massive, massive even for his eighteen years. He
- 39. had never actually attained a first choice position on the Broadwood eleven, but he was a good player and an excellent substitute guard, and he had more than once opposed Yardley during his football career. He had taken pains to arrive early at the field and was in his seat before the teams came on the field, and it is probable that his presence would not have been discovered by the enemy had not Davis’s eyes gone roaming over the Forest Hill contingent in search of an acquaintance. Gibson saw that he was recognized; the hostile stares of the group below told him that; and he was disappointed. However, there was no help for it, and, as he was there, he might as well remain. Even if Yardley failed to show any new tricks it was still possible to get a line on her formations in attack and defense and get a general idea of her ability. When The Duke summoned him to the telephone Gibson had no suspicions. It was quite possible that the Broadwood coach had thought of some feature of Yardley’s playing that he wanted information on. He hesitated for a moment to show himself, thinking that perhaps his presence might be resented. Then, realizing that he had already been recognized and that to disregard the summons would look strange, he answered it. It was only when, cooped up in the telephone booth, he learned from the Greenburg operator that there was no record of any call for him that it began to dawn upon him that he had been made the victim of a hoax. Very angrily he slammed up the receiver and pushed at the door. A minute or so later his anger had visibly increased. It was too dark in the booth to examine the latch with any hope of discovering the trouble. There was nothing for it but to raise his voice in a demand for release, which he did. Unfortunately, however, it is very doubtful if there was a living soul from one end of Oxford Hall to the other. Eventually, perhaps ten minutes after he had unsuspectingly entered the booth, the plan of breaking open the door occurred to him. He tried it. The telephone company, however, had caused that booth to be constructed of exceedingly strong materials, and finally Gibson, very warm and breathless, gave up the attempt. Next he considered breaking the glass. There were several panes and he could take his
- 40. choice. But while he had not hesitated to try to force the lock or wreck a panel the idea of breaking glass struck him as peculiarly destructive and he paused to consider. And at about that time it occurred to him that a very simple way of escape confronted him. He snatched down the receiver and explained his predicament to a sympathetic Central. “I will call up the Office,” said the operator. But the Office was empty and no one answered her ring. So she tried Clarke Hall and was successful. The telephone in Clarke was in the study of Mr. Collins, the Assistant Principal. Ordinarily Mr. Collins would have been out at this hour of the afternoon, but it so happened that a slight cold had suggested to him the advisability of remaining indoors and taking a nap. The imperative ringing of the telephone bell put an end to the nap, and, some five minutes later, having discarded dressing-gown and slippers in favor of outer clothing and shoes, Mr. Collins, none too pleased with the necessity, strode down the corridor of Oxford and liberated a strange, perspiring youth from his cell. Gibson, failing in the dimness of the hall to recognize authority in the slight, medium-sized person before him, immediately gave vent to his wrath. “Say, what kind of a fool thing is that?” he demanded. “I’ve been suffocating in there for twenty minutes!” Mr. Collins viewed him gravely. “Wonder you wouldn’t have that latch fixed! It would have served you right if I’d bust the glass out of it!” “It pains me deeply to learn of your discomfort,” replied the Assistant Principal dryly. “Perhaps if you had telephoned to Central at once you’d have been released sooner. May I ask who you are and how you happen to have been using the booth?” Gibson, having now discovered that he was talking to neither a student nor the janitor, changed his tune. “My name is Gibson. I—I came to see the football game. A fellow sung out that I was wanted on the telephone and showed me up here. When I asked the
- 41. operator she said no one had called me. Then I tried to get out and couldn’t.” “Hm,” said Mr. Collins. “We have reported the matter to the company and they have agreed to send up and fix that latch. As a matter of fact, I presumed that they had done so. I am very sorry, Gibson. I don’t understand, however, why the messenger should have deceived you. Some mistake, doubtless.” “He—he did it on purpose,” blurted Gibson, still too angry to be discreet. Mr. Collins looked surprised. They had reached the steps and now the Assistant Principal viewed the boy thoughtfully. “Why?” he asked. “I—I don’t know,” muttered Gibson. “It doesn’t matter, though. I— I’ll be going. Thank you, sir.” “One moment, please. You live in Greenburg?” Gibson hesitated. Then, “No, sir, I—I’m at Broadwood. I just came over to see the game.” “Really?” Mr. Collins raised his brows. “Your Broadwood team doesn’t play to-day, then?” “Yes, sir, they play Nordham.” “At home?” “Yes, sir.” “You, however, preferred to see this game, eh? I see. Now this boy who brought you up here, Gibson; what was he like?” Gibson, rather uncomfortable under the other’s sarcastic gaze, thought a moment and at last gave a very excellent description of The Duke. Mr. Collins nodded again. Then he smiled. It was a fleeting smile, but Gibson saw it. “He knew I’d get locked up in there,” he declared aggrievedly. “He closed the door after me himself!”
- 42. “I find no difficulty in crediting that, Gibson,” replied Mr. Collins gravely. “I think I know the young gentleman and I’ll have something to say to him. Good-day, Gibson. I regret exceedingly that you have missed seeing so much of the game. Perhaps, however, it is not yet entirely over.” But whether it was or wasn’t Gibson had no idea of returning to the field. He remained on the steps a moment, watching Mr. Collins out of sight around the corner of the old stone building, and then, thrusting his hands into his pockets, set off with a frown down the drive. He had almost reached the entrance gate at the foot of The Prospect when he saw a boy walking rapidly toward him from the direction of the village. Gibson wasn’t at all interested in the other pedestrian and gave him no more than a thought. But when they drew abreast he glanced up casually. Recognition was mutual. “Hello, Cotton, what the dickens are you doing here?” “Hello, Gibson! What are you doing here?” “Me? Just came over to see the game. Say, you aren’t at school here, are you?” Cotton nodded. “Yes, I entered this Fall. I don’t like it, though.” Gibson grinned none too kindly. “You don’t like it anywhere very long, do you? I thought someone said you were at school somewhere down South.” “I was last year. But I’d rather be up North.” “Gee, did they fire you, too?” laughed Gibson. Cotton colored. “No,” he answered shortly, “I didn’t like it. So I didn’t go back.” “They didn’t like you, you mean! How you getting on here?” “All right,” replied Cotton, ignoring the statement in favor of the question. “It’s a punk school, though. Not half as good as Broadwood.”
- 43. “Wonder you didn’t behave yourself when you were with us, then,” said Gibson. “You’re a bit of a mutt, Cotton, I guess. Well, I must be getting on. How far is it to Greenburg?” “Oh, twenty minutes, maybe. Is the game over?” “No, judging by the sounds it isn’t. I’ve had enough of it, though. You’ve got a rotten team here this year, Cotton.” “You bet we have!” assented the other eagerly. “That’s what I tell them. You’ll lick the stuffing out of them, Gibson. Are you on the team this year?” “Me? Not exactly. I’m running Browne pretty hard, though. I may get on next week. Why aren’t you at the game?” “I had to get a letter off on the three o’clock mail and the only way to do it was to take it to Greenburg. They only have two collections a day up here. It’s a rotten place. I wanted to see the game, too. That’s why I was hurrying back.” “Well, don’t let me keep you.” “Oh, that’s all right. They’ll get licked, anyway.” Gibson, who had turned to go on, paused and observed Cotton attentively, speculatively. “You don’t seem to love your team, Cotton,” he suggested. “Oh, they’re a great bunch of snobs,” replied Cotton bitterly. “If you haven’t got some sort of a drag you can’t get any show. It’s that way with everything here. Now, at Broadwood——” “Your admiration for your dear old alma mater is touching,” sneered Gibson. “I suppose you tried for the team and got chucked, eh?” “I didn’t have any pull. They don’t care how well you play. If you don’t know the fellows——” “Hm,” said Gibson thoughtfully. “Well, say, if you aren’t crazy to see the end of the game, Cotton, why don’t you turn around and
- 44. walk back to Greenburg with me? I’ll treat to a soda, if you like, and we’ll have a chin.” “Sure! I don’t care about the game. It must be almost over now, anyway. But what were you doing over here, Gibson?” Cotton frowned his perplexity. “Me? Oh, just watching.” Gibson winked slowly and meaningly. “By Jove!” Cotton smiled delightedly. “That’s your game, eh? Did you get anything?” “Think I’d tell you if I did?” laughed Gibson, taking the other boy’s arm. “Oh, shucks!” said Cotton. “You can trust me, old man; you know that.” “Well, come along and I’ll tell you about it.”
- 45. T CHAPTER XIII THE DUKE STARTS SOMETHING he day after the Forest Hill defeat was warm and languid, more like a November day. Gerald had gone to Sound View the evening before, as was his custom when his father was at home, and Kendall, having attended church in the forenoon and eaten a dinner at the training table for which he had had little appetite, was at a loss how to spend his afternoon. There were fellows whom he might look up and who would doubtless be glad to see him, but somehow he didn’t feel very sociable. For one thing, he had been through forty-eight minutes of hard play the day before and felt lame and battered, although there were no scars to show. Perhaps, too, the weather induced a feeling of apathy; it was too warm. He wrote his Sunday letter, taking a good deal of time over it, and managing to fill six pages. But after that was sealed and addressed there seemed nothing left to do. Gerald had suggested that he might come up after dinner and take him to ride in the automobile, but evidently Gerald had changed his mind. The dormitory was quiet and probably pretty well deserted, for it was no sort of a day to stay indoors. Kendall finally reached that conclusion himself and, pulling a cap on to the back of his head, he sauntered along the hall and down the stairs and so out into the afternoon world, wincing now and then when his sore muscles protested and dimly oppressed with the emptiness of existence. Kendall’s condition of mind was, had he but known it, no uncommon one for the football player the day after a hard game and a defeat. One cares very little for bruises and weariness after a victory, but a defeat takes all the glory from them. There was a handful of fellows on the steps as he came out and he spoke to them, but had no wish to join them. There were other
- 46. groups in front of Whitson and Oxford, and several boys were lolling on the grass near the flag-pole on The Prospect. One or two had books, but it was a noticeable fact that none was reading. Even the effort of holding a book was too much on such a day. Kendall nodded now and then, refused an invitation to join the group on the grass and skirted Oxford with a dim idea of walking down to the river. But back of Merle he heard a hail and, turning, saw The Duke waving to him across the yard. The Duke was resplendent to-day. There was a suit of blue-gray flannel, a vividly pink shirt, dark blue socks, tan shoes and a green tie. And The Duke seemed in high feather. Kendall sat down on the step of Merle and waited for the gorgeous one to join him. He had not seen The Duke since shortly after the game the day before and now he wondered whether that youth had got into difficulties over the affair of Mr. Gibson. He certainly didn’t have the appearance of a fellow in trouble! One would have thought, seeing him coming along the path, hands in pockets, whistling cheerfully, that he hadn’t a care in the world. “Greetings, O doughty warrior!” saluted The Duke. “Hello,” replied Kendall apathetically. “Where’s the party?” “Party? Oh, you refer to my chaste get-up.” The Duke viewed his apparel approvingly. “Some togs, what?” He seated himself beside Kendall. “There’s no party, Sir Knight. I have merely dressed myself according to my mood. My mood to-day is one of triumph and joy. Where’s Gerald?” “Home,” replied Kendall moodily. “He’s a lucky chap to have a home around the corner. Be it never so humble there’s no place like home. What’s the matter with you to-day? Got the dumps?” “N-no.” “Meaning ye-es? Perk up! Observe the cerulean sky and the waving tree tops, the bright sun and the—the——” “It’s a beast of a day.”
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