Fundamentals of Queueing Theory, Solutions Manual

Donald Gross is the author of Solutions Manual to accompany Fundamentals of Queueing Theory, 4e, published by Wiley. John F. Shortle is the author of Solutions Manual to accompany Fundamentals of Queueing Theory, 4e, published by Wiley.

"Despite its title, the book is rather advanced, so it is appropriate for practitioners, those in academia, and upper-class students. However, any reader will benefit from the concise introductions to the problems, the detailed descriptions supported with step-by-step formulas, the solutions provided by the manual, and the QtsPlus software." (Computing Reviews, 1 December 2011)

• Dedication v Preface xiAcknowledgments xiiiIntroduction 1Description of the Queueing Problem 2Characteristics of Queueing Processes 3Notation 7Measuring System Performance 8Some General Results 9Simple Data Bookkeeping for Queues 12Poisson Process and the Exponential Distribution 16Markovian Property of the Exponential Distribution 20Stochastic Processes and Markov Chains 24Introduction to the QtsPlus Software 40Problems 41Simple Markovian Queueing Models 49Birth-Death Processes 49Single-Server Queues (M/M/1) 53Multiserver Queues (M/M/c) 66Choosing the Number of Servers 73Queues with Truncation (M/M/c/K) 76Erlang's Loss Formula (M/M/c/c) 81Queues with Unlimited Service (M/M/[infinity]) 84Finite-Source Queues 85State-Dependent Service 91Queues with Impatience 95Transient Behavior 97Busy-Period Analysis 102Problems 103Advanced Markovian Queueing Models 117Bulk Input (M[superscript X]/M/1) 117Bulk Service (M/M[superscript Y]/1) 123Erlangian Models 128Priority Queue Disciplines 141Retrial Queues 157Problems 171Networks, Series, and Cyclic Queues 179Series Queues 181Open Jackson Networks 187Closed Jackson Networks 195Cyclic Queues 209Extensions of Jackson Networks 210Non-Jackson Networks 212Problems 214General Arrival or Service Patterns 219General Service, Single Server (M/G/1) 219General Service, Multiserver (M/G/c/[infinity], M/G/[infinity]) 254General Input (G/M/1, G/M/c) 259Problems 270General Models and Theoretical Topics 277G/E[subscript k]/1, G[superscript k]/M/1, and G/PH[subscript k]/1 277General Input, General Service (G/G/1) 284Poisson Input, Constant Service, Multiserver (M/D/c) 294Semi-Markov and Markov Renewal Processes in Queueing  296Other Queue Disciplines 301Design and Control of Queues 306Statistical Inference in Queueing 317Problems 325Bounds and Approximations 329Bounds 330Approximations 343Network Approximations 356Problems 367Numerical Techniques and Simulation 369Numerical Techniques 369Numerical Inversion of Transforms 385Discrete-Event Stochastic Simulation 398Problems 421References 427Symbols and Abbreviations 439Tables 447Transforms and Generating Functions 455Laplace Transforms 455Generating Functions 462Differential and Difference Equations 467Ordinary Differential Equations 467Difference Equations 483QtsPlus Software 489Instructions for Downloading 493Index 495