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基本説明
様々な複雑なシステムのパフォーマンスを評価するための、最新の分析モデルとシュミレーション技術、コンピュータ・アルゴリズムについて実務上のケーススタディを交えながら解説を加える。
Full Description
For courses in Performance Analysis and Design of Communication Networks (PC) offered in departments of Electrical and Computer Engineering. Also appropriate for courses in Systems Engineering and Operations Research.Kobayashi and Mark present the most up-to-date analytical models, simulation techniques, and computational algorithms useful for performance evaluation of complex systems - including computer systems, communication networks, transportation systems, and manufacturing systems. Broader in scope than other texts, this book provides more in-depth coverage of topics such as computational algorithms and approximations. It appeals to students with a background or interest in a wide range of areas, including systems analysis or telecommunication networks.
Contents
1 Introduction 11.1 Role of Modeling and Analysis . . . . . . . . . . . . . . . . . . . . . 11.2 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Modeling Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 Examples of Performance Modeling . . . . . . . . . . . . . . . . . . . 161.5 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 38I Basic Queueing and Loss Models 392 Basic Queueing Models 402.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.2 Little's Formula and Its Generalization . . . . . . . . . . . . . . . . . 462.3 Birth-and-Death Processes . . . . . . . . . . . . . . . . . . . . . . . . 522.4 Birth-and-Death Queueing Models . . . . . . . . . . . . . . . . . . . 682.5 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 933 Basic Loss Models 953.1 Erlang Loss Model: M/M/m(0) or M/M/m/m . . . . . . . . . . . 953.2 Engset Loss Model: M(K)/M/m(0) or M/M/m/m/K . . . . . . . 1033.3 Insensitivity and Generalization of Loss Models . . . . . . . . . . . . 1113.4 Application Example: Blocking Analysis of Cellular CommunicationSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1123.5 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 1234 Non-Markovian Queues 1244.1 Renewal Process and Residual Life . . . . . . . . . . . . . . . . . . . 1244.2 Representations of General Distributions . . . . . . . . . . . . . . . . 1294.3 M/G/1 Queueing Model . . . . . . . . . . . . . . . . . . . . . . . . . 1394.4 G/M/1 Queueing Model . . . . . . . . . . . . . . . . . . . . . . . . . 1594.5 G/G/1 Queue and Waiting Time Distribution . . . . . . . . . . . . . 1694.6 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 1755 Quasi-Reversibility and Queues with Product-Form Solutions 1775.1 Markov Processes and Markov Chains . . . . . . . . . . . . . . . . . 1775.2 Departure Processes, Reversibility and Quasi-Reversibility . . . . . . 1885.3 M/G/1 Queueing Model . . . . . . . . . . . . . . . . . . . . . . . . 2085.4 M/G/1 with Processor Sharing . . . . . . . . . . . . . . . . . . . . . 2135.5 M/G/1 with LCFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2185.6 M/G/1 with LCFS-PR . . . . . . . . . . . . . . . . . . . . . . . . . . 2205.7 Multiple Customer Classes and Quasi-Reversible Stations . . . . . . 2215.8 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 233II Queueing and Loss Networks 2356 Queueing Networks 2366.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2366.2 Jackson Networks: Queueing Networks with Exponential Servers . . 2386.3 Networks with Quasi-Reversible Stations and Multiple Classes ofCustomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2766.4 Higher-Order Markov Routing . . . . . . . . . . . . . . . . . . . . . . 2876.5 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 2957 Loss Networks and Generalized Loss Models 2977.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2977.2 Generalized Loss Stations . . . . . . . . . . . . . . . . . . . . . . . . 2987.3 Loss Networks with Fixed Routing . . . . . . . . . . . . . . . . . . . 3107.4 Queueing-Loss Networks . . . . . . . . . . . . . . . . . . . . . . . . . 3347.5 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 3368 Computational Algorithms for Product-Form Networks 3388.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3388.2 Computational Algorithms for Queueing Networks . . . . . . . . . . 3388.3 Parametric Decomposition of a Queueing Network . . . . . . . . . . 3548.4 Computational Algorithms for Loss Networks . . . . . . . . . . . . . 3568.5 Reduced Load Approximation of a Loss Network . . . . . . . . . . . 3768.6 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 379III Advanced Queueing Models 3839 Conservation Laws, Priority Queues, and Polling Models 3849.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3849.2 Work-Conserving Queue Disciplines and Conservation Laws . . . . . 3849.3 M/G/1 Priority Queues . . . . . . . . . . . . . . . . . . . . . . . . . 3919.4 M/G/1 with Server Vacations and Polling Models . . . . . . . . . . 3979.5 Rate Conservation Law (RCL) . . . . . . . . . . . . . . . . . . . . . 4059.6 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 40910 Phase-Type Process and Matrix Geometric Method 41110.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41110.2 Phase-Type (PH) Distribution . . . . . . . . . . . . . . . . . . . . . 41210.3 Phase-Type (PH) Renewal Process . . . . . . . . . . . . . . . . . . . 41810.4 PH Renewal Service Process . . . . . . . . . . . . . . . . . . . . . . . 42610.5 PH/PH/1 Queue and Quasi-Birth-and-Death (QBD) Process . . . . 42810.6 Stationary Distribution of QBD and Performance Measures . . . . . 43210.7 Algorithms for the Rate Matrix R . . . . . . . . . . . . . . . . . . . 43710.8 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 43911 Discrete-Time Queues 44211.1 Geo/G/1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44211.2 Geo/Geo/1: Discrete-Time M/M/1 . . . . . . . . . . . . . . . . . . . 45011.3 Discrete-Time M/G/1 . . . . . . . . . . . . . . . . . . . . . . . . . 45411.4 Discrete-Time G/G/1 System . . . . . . . . . . . . . . . . . . . . . . 45511.5 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 45712 Traffic Modeling 45812.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45812.2 Second-order Properties of Arrival Processes . . . . . . . . . . . . . . 45912.3 Markovian Traffic Models . . . . . . . . . . . . . . . . . . . . . . . . 46712.4 Long-Range Dependent (LRD) Traffic Models . . . . . . . . . . . . . 48012.5 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 49213 Fluid Models 49413.1 Fluid Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 49413.2 Markov Fluid Model of Statistical Multiplexer . . . . . . . . . . . . . 49513.3 Two Limiting Cases: Buffer Overflows and Infinite Sources . . . . . 50913.4 Markov Fluid Model with Multiple Types of Sources . . . . . . . . . 51313.5 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 51714 Approximation and Bounding Techniques 51914.1 Inequalities and Bounds . . . . . . . . . . . . . . . . . . . . . . . . . 51914.2 Exponential Bounds on G/G/1 Waiting Time Distribution . . . . . . 52714.3 Bounds for Mean Waiting Time in G/G/1 . . . . . . . . . . . . . . . 54014.4 Bounds for Mean Waiting Time in G/G/m . . . . . . . . . . . . . . 54214.5 Heavy Traffic Approximation for G/G/1 Queue . . . . . . . . . . . . 54414.6 Diffusion Process Approximations for G/G/1 Queue . . . . . . . . . 54614.7 Diffusion Approximation of a Queueing Network . . . . . . . . . . . 56014.8 Bounds and Approximations for Bandwidth Allocation . . . . . . . . 56614.9 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 57715 Time-Dependent Solutions of Queues 57915.1 Time-Dependent Solution for M/G/1 . . . . . . . . . . . . . . . . . 57915.2 Time-Dependent Solution of a Markov Process Model . . . . . . . . 58115.3 Eigenvectors of the BD Process . . . . . . . . . . . . . . . . . . . . . 58715.4 Generating Function Method . . . . . . . . . . . . . . . . . . . . . . 59415.5 Uniformization of Continuous Time Markov Chain . . . . . . . . . . 61015.6 Time-Dependent Solution of a Fluid Flow Model . . . . . . . . . . . 61615.7 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 621IV Simulation Modeling and Analysis 62316 Formulation and Implementation of Simulation Models 62416.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62416.2 Self-Driven Simulation vs. Trace-Driven Simulation . . . . . . . . . . 62616.3 Formulation of Simulation Models . . . . . . . . . . . . . . . . . . . 62816.4 Implementation of Simulators . . . . . . . . . . . . . . . . . . . . . . 63416.5 Techniques for Generating Random Variables . . . . . . . . . . . . . 64116.6 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66316.7 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 68517 Simulation Experiments and Statistical Data Analysis 69017.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69017.2 Experiments and Statistical Inference . . . . . . . . . . . . . . . . . 69017.3 Analyzing a Simulation Run . . . . . . . . . . . . . . . . . . . . . . . 69517.4 Efficient Statistical Simulation . . . . . . . . . . . . . . . . . . . . . 70817.5 Fast Simulation of Rare Events . . . . . . . . . . . . . . . . . . . . . 71417.6 Discussion and Further Reading . . . . . . . . . . . . . . . . . . . . . 729A Number Theory 731Bibliography 737
