Stochastic Modeling Analysis & Simulation,9780486425696

Stochastic Modeling Analysis & Simulation

by
ISBN13: 9780486425696
ISBN10: 048642569X
Format: Paperback
Pub. Date: 2003-02-04
Publisher(s): Dover Publications
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Summary

This introduction to techniques for modeling dynamic stochastic systems also provides a guide to the mathematical, numerical, and simulation tools used in systems analysis. The text explores Poisson and renewal processes, Markov chains in discrete and continuous time, semi-Markov processes, and queuing processes. Solution manual available upon request. 1995 edition.

Table of Contents

Preface xiii
1 Why Are We Here? 1(2)
2 Sample Paths 3(20)
2.1 The Case of the Copy Enlargement
3(1)
2.2 Notation and Review
4(2)
2.3 Sample-Path Decomposition
6(10)
2.3.1 Simulating the Self-Service System
11(3)
2.3.2 Simulating the Full-Service System
14(1)
2.3.3 Discussion
15(9)
2.4 Exercises
16(7)
3 Basics 23(38)
3.1 Probability
24(13)
3.1.1 Random Variables
24(4)
3.1.2 Joint Distributions
28(1)
3.1.3 Expected Value
29(3)
3.1.4 Conditional Probability
32(4)
3.1.5 Limit Distributions
36(57)
3.2 Statistics
37(6)
3.3 Random-Variate Generation
43(6)
3.4 The Case of the Copy Enlargement, Revisited
49(2)
3.5 Fine Points
51(1)
3.6 Exercises
51(10)
4 Simulation 61(22)
4.1 The Case of the Leaky Bit Bucket
61(1)
4.2 Notation and Review
62(1)
4.3 Stochastic Processes
62(2)
4.4 Simulating the Leaky Bit Bucket
64(6)
4.5 A Generic Stochastic-Process Model
70(3)
4.6 Simulating the Copy Enlargement
73(3)
4.7 Simulation Programming
76(4)
4.8 Fine Points
80(1)
4.9 Exercises
80(3)
5 Arrival-Counting Processes 83(44)
5.1 The Case of the Reckless Beehunter
83(2)
5.2 Notation and Review
85(1)
5.3 A Generic Arrival-Counting-Process Model
86(3)
5.4 Simulating the Reckless Beehunter
89(4)
5.5 The Poisson Arrival Process
93(5)
5.5.1 Probability Structure of the Sample Paths
93(5)
5.5.2 Parameterizing Poisson Processes
98(1)
5.6 More about Poisson Arrival Processes
98(9)
5.6.1 Decomposition of a Poisson Process
99(3)
5.6.2 Superposition of Poisson Processes
102(2)
5.6.3 Nonstationary Poisson Processes
104(5)
5.7 The Case of the Meandering Message
107(2)
5.8 Derivations
109(4)
5.8.1 Memoryless Property
109(1)
5.8.2 Independent-Increments and Stationary-Increments Properties
110(1)
5.8.3 Decomposition Property
111(1)
5.8.4 Superposition Property
111(1)
5.8.5 Nonstationary Poisson Process
112(1)
5.9 Results for the Renewal Arrival-Counting Process
113(4)
5.9.1 The Case of the Perpetual Payoff
114(2)
5.9.2 Derivations
116(1)
5.9.3 Other Arrival-Counting Processes
117(15)
5.10 Fine Points
117(1)
5.11 Exercises
118(9)
6 Discrete-Time Processes 127(42)
6.1 The Case of the Random Behavior
127(1)
6.2 Notation and Review
128(1)
6.3 Simulating the Random Behavior
129(3)
6.4 Markov Chains
132(7)
6.4.1 Probability Structure of the Sample Paths
132(5)
6.4.2 Parameterizing Markov Chains
137(1)
6.4.3 Transition Diagrams
138(2)
6.5 The Case of the Defective Detective
139(1)
6.6 Time-Dependent Performance Measures
140(7)
6.6.1 Examples
142(3)
6.6.2 Derivations
145(2)
6.7 Time-Independent (Long-Run) Performance Measures
147(7)
6.7.1 Classification of States
148(2)
6.7.2 Performance Measures
150(2)
6.7.3 Examples
152(1)
6.7.4 Derivations
153(17)
6.8 The Markov and Stationarity Properties Revisited
154(2)
6.9 Fine Points
156(2)
6.10 Exercises
158(11)
7 Continuous-Time Processes 169(52)
7.1 The Case of the Software Sellout
169(1)
7.2 Notation and Review
170(5)
7.2.1 Markov Chain Review
170(2)
7.2.2 Properties of the Exponential and Geometric Distributions
172(10)
7.3 Simulating the Software Sellout
175(3)
7.4 Sample Paths of the Software Sellout
178(4)
7.5 Markov Processes
182(6)
7.5.1 Probability Structure of a Markov Process
183(2)
7.5.2 Parameterizing Markov Processes
185(3)
7.6 Analysis of Markov Process Sample Paths
188(17)
7.6.1 Performance Measures
188(2)
7.6.2 Time-Dependent Performance Measures
190(3)
7.6.3 Time-Dependent Example
193(4)
7.6.4 Time-Independent (Long-Run) Performance Measures
197(2)
7.6.5 Time-Independent Example
199(2)
7.6.6 Derivations
201(21)
7.7 The Case of the Stressed-Out Student
205(3)
7.8 The Markov and Stationarity Properties Revisited
208(2)
7.9 Semi-Markov Processes
210(2)
7.10 Fine Points
212(1)
7.11 Exercises
213(8)
8 Queueing Processes 221(60)
8.1 The Case of the Last Parking Space on Earth
221(1)
8.2 Notation and Review
222(5)
8.2.1 Series and Recursions
222(2)
8.2.2 Markov Process Review
224(5)
8.3 A Queueing Model for the Last Parking Space on Earth
227(2)
8.4 Markovian Queueing Processes
229(6)
8.4.1 The Birth-Death Process
229(1)
8.4.2 Performance Measures
230(5)
8.5 Standard Formulations
235(4)
8.5.1 Arrival Rates
235(3)
8.5.2 Service Rates
238(2)
8.6 Parameterizing Queueing Processes
239(1)
8.7 Shorthand Notation and Examples
240(6)
8.7.1 The M/M/s Queue
241(3)
8.7.2 The M/M/s/n/k Queue with s = n
244(4)
8.8 The Case of the Tardy Ticket
246(2)
8.9 Networks of Markovian Queues
248(12)
8.9.1 The Case of the Incredible Shrinking Leviathan
249(5)
8.9.2 Markov Process Model of the Incredible Shrinking Leviathan
254(4)
8.9.3 Open Jackson Networks
258(2)
8.10 Non-Markovian Queues and Networks
260(8)
8.10.1 A GI/G/s Approximation
262(2)
8.10.2 A Queueing-Network Approximation
264(17)
8.11 Exercises
268(13)
9 Topics in Simulation of Stochastic Processes 281(26)
9.1 Statistical Issues in Simulation
281(16)
9.1.1 Initial-Condition Effects
282(6)
9.1.2 Measures of Error
288(4)
9.1.3 Random Number Assignment
292(5)
9.2 Rough-Cut Modeling
297(3)
9.3 Exercises
300(7)
A Simulation Programming Examples 307(8)
A.1 Fortran
308(4)
A.2 SLAM II
312(1)
A.3 SIMAN IV
313(1)
A.4 GPSS/H
313(2)
References 315(2)
Index 317

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