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Stochastic Computer Simulation 6 7 7 8 Shane G horm13 v.2006/04/25 Prn:2/05/2006; 15:24 F:horm13001.tex; VTEX/jovi p. 1 aid: 13001 pii: S0927-0507(06)13001-7 docsubty: REV S.G. Henderson and B.L. Nelson (Eds.), Handbook in OR & MS, Vol. 13 Copyright © 2006 Elsevier B.V. All rights reserved 1 DOI: 10.1016/S0927-0507(06)13001-7 1 2 2 3 3 4 Chapter 1 4 5 5 6 Stochastic Computer Simulation 6 7 7 8 Shane G. Henderson 8 9 School of Operations Research and Industrial Engineering, Cornell University, USA 9 10 E-mail: [email protected] 10 11 Barry L. Nelson 11 12 12 Department of Industrial Engineering and Management Sciences, Northwestern University, 13 USA 13 14 E-mail: [email protected] 14 15 15 16 16 17 17 18 Abstract 18 19 19 20 We introduce the topic of this book, explain what we mean by stochastic computer 20 21 simulation and provide examples of application areas. We motivate the remaining 21 22 chapters in the book through two in-depth examples. These examples also help clarify 22 23 several concepts and techniques that are pervasive in simulation theory and practice. 23 24 24 25 25 26 26 27 27 28 1 Scope of the Handbook 28 29 29 30 What is “stochastic computer simulation?” Perhaps the most common ex- 30 31 ample in everyday life is an electronic game, such as Solitaire or Yahtzee, that 31 32 depends on a source of randomness to imitate shuffling cards, rolling dice, 32 33 etc. The fidelity of the electronic game, which is a simulation of the physical 33 34 game, depends on a faithful imitation of the physical source of randomness. 34 35 The electronic game is useless (and no fun) otherwise. Of course, an electronic 35 36 game usually needs a game player. If you replace the player by an algorithm 36 37 that plays the game, and you compare different algorithms by playing many 37 38 sessions of the game, then you have a pretty good representation of what sto- 38 39 chastic computer simulation is and how it is used in operations research and 39 40 the management sciences. 40 41 This book is a collection of chapters on key issues in the design and analysis of 41 42 computer simulation experiments on models of stochastic systems. The chapters 42 43 are tightly focused and written by experts in each area. For the purposes of this 43 44 volume, “stochastic computer simulation” (henceforth just “stochastic simu- 44 45 lation”) refers to the analysis of stochastic processes through the generation 45 1 horm13 v.2006/04/25 Prn:2/05/2006; 15:24 F:horm13001.tex; VTEX/jovi p. 2 aid: 13001 pii: S0927-0507(06)13001-7 docsubty: REV 2 S.G. Henderson and B.L. Nelson 1 of sample paths (realizations) of the processes. We restrict attention to design 1 2 and analysis issues, and do not address the equally important problems of rep- 2 3 resentations (modeling) and execution (see, for instance, Fishwick, 1995). In 3 4 broad terms, the goal of this volume is to survey the concepts, principles, tools 4 5 and techniques that underlie the theory and practice of stochastic simulation 5 6 design and analysis, emphasizing ideas and methods that are likely to remain 6 7 an intrinsic part of the foundation of the field for the foreseeable future. The 7 8 chapters provide an up-to-date reference for both the simulation researcher 8 9 and the advanced simulation user, but they do not constitute an introductory 9 10 level “how to” guide. (See, instead, Banks (1998), Banks et al. (2004), Law 10 11 and Kelton (2000) or Fishman (2001). The latter book is at a slightly more 11 12 advanced level than the others.) 12 13 Computer scientists, financial analysts, industrial engineers, management 13 14 scientists, operations researchers and many other professionals use stochastic 14 15 simulation to design, understand and improve communications, financial, man- 15 16 ufacturing, logistics and service systems. A theme that runs throughout these 16 17 diverse applications is the need to evaluate system performance in the face 17 18 of uncertainty, including uncertainty in user load, interest rates, demand for 18 19 product, availability of goods, cost of transportation and equipment failures. 19 20 Much like the electronic game designer, stochastic simulation users develop 20 21 models that (they hope) faithfully represent the sources of uncertainty in the 21 22 systems that they simulate. Unlike the game designer, the simulation user also 22 23 needs to design the simulation experiment – decide what cases to simulate, and 23 24 how much simulation to do – and analyze the results. 24 25 Later in this chapter we provide two examples of the types of problems that 25 26 are solved by stochastic simulation. The examples motivate and provide con- 26 27 text for the remaining chapters in the book. We do not attempt – either in this 27 28 chapter or in the remainder of the book – to cover the wide range of applica- 28 29 tions of simulation. A few important application areas are listed below. 29 30 Financial engineering/quantitative finance: The classical problem in this area is 30 31 valuing a derivative, which is a financial instrument whose value depends 31 32 on an underlying asset such as a stock or bond. Uncertainty in the value 32 33 of the asset over time makes simulation a natural tool. Other problems in 33 34 this vein include estimating the value-at-risk of a portfolio and designing 34 35 hedging strategies to mitigate risk. See, for instance, Glasserman (2004). 35 36 Computer performance modeling: From the micro (chip) level to the macro 36 37 (network) level, computer systems are subject to unpredictable loads and 37 38 unexpected failures. Stochastic simulation is a key tool for designing and 38 39 tuning computer systems, including establishing expected response times 39 40 from a storage device, evaluating protocols for web servers, and testing the 40 41 execution of real-time control instructions. See, for instance, Jain (1991). 41 42 Service industries: Service industries include call/contact centers, an applica- 42 43 tion in which simulation has been used to design staffing and call-routing 43 44 policies. Service applications emphasize delivering a specified level of ser- 44 45 vice with a high probability; such issues arise in food delivery, financial 45 horm13 v.2006/04/25 Prn:2/05/2006; 15:24 F:horm13001.tex; VTEX/jovi p. 3 aid: 13001 pii: S0927-0507(06)13001-7 docsubty: REV Ch. 1. Stochastic Computer Simulation 3 1 services, telecommunications and order fulfillment, for instance, and sim- 1 2 ulation helps to ensure quality service in the face of uncertainty. 2 3 Manufacturing: Stochastic simulation has seen extensive use in manufacturing 3 4 applications. A few representative contributions include evaluation of pro- 4 5 duction scheduling algorithms; work-center design and layout; estimation 5 6 of cycle time-throughput curves; and evaluation of equipment replacement 6 7 and maintenance policies. 7 8 Military: Military applications include life-cycle management of defense sys- 8 9 tems; combat and munitions logistics; crisis communications evaluation; 9 10 and modeling network architectures for command and control. 10 11 Transportation and logistics: Simulation has been used to evaluate the effec- 11 12 tiveness of Internet and cell-phone-based traveler information services; to 12 13 perform benefits analyses for regional Intelligent Transportation Systems; 13 14 and to design public transportation systems for the elderly and disabled. 14 15 When the transportation system is part of a supply chain, simulation may 15 16 be used to determine replenishment policies for manufacturers, distribu- 16 17 tion centers and retailers, or to estimate the impact of demand uncertainty 17 18 on supplier inventories. 18 19 The Proceedings of the annual Winter Simulation Conference is an out- 19 20 standing source of applications and success stories from these and other 20 21 areas. The Proceedings from 1997 through the present can be found at 21 22 http://www.wintersim.org. 22 23 The focus of this volume is narrow, by necessity, because the label “com- 23 24 puter simulation” is attached to a number of activities that do not fall under 24 25 the umbrella of “generating sample paths of stochastic processes”. For in- 25 26 stance, there is a vast literature on, and countless applications of, simulation 26 27 of dynamic systems that are represented by differential and partial differential 27 28 equations. Such systems may be stochastic, but the approach is to numerically 28 29 integrate the system of equations through time to determine levels, probabili- 29 30 ties, moments etc., rather than generating sample paths and averaging across 30 31 repetitions as we do. Systems dynamics (see Sterman, 2000) is a popular ap- 31 32 proach for developing and analyzing differential equation models, and there 32 33 is a substantial intersection between applications of systems dynamics and ap- 33 34 plications of stochastic simulation in operations research and the management 34 35 sciences. 35 36 Although closely related, we do not consider issues that arise in person-in- 36 37 the-loop simulations that are used for, among other things, training of per- 37 38 sonnel and evaluation of supervisory systems prior to insertion in the field. 38 39 A key feature of stochastic simulation is that the source of randomness is un- 39 40 der the control of the experimenter, which is not the case when a person is 40 41 incorporated into the experiment.
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