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Vacation queuing models: theory and applications

Author: Tian, Naishuo ; Zhang, Zhe George Series: International series in operations research and management science Publisher: Springer, 2006.Language: EnglishDescription: 385 p. ; 24 cm.ISBN: 0387337210Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print T57.9 .T53 2006
(Browse shelf)
001225741
Available 001225741
Total holds: 0

Includes bibliographical references and index

Digitized

Vacation Queueing Models Theory and Applications Contents 1. INTRODUCTION 1.1 Queueing Systems with Server Vacations 1.2 Vacation Policies 1.3 Stochastic Decomposition in Vacation Models 1.4 Bibliographic Notes 2. M/G/1 TYPE VACATION MODELS: EXHAUSTIVE SERVICE 2.1 M/G/1 Queue with Multiple Adaptive Vacations 2.1.1 Classical M/G/1 Queue 2.1.2 Multiple Adaptive Vacation Model 2.2 Some Classical M/G/1 Vacation Models 2.2.1 Multiple Vacation Model 2.2.2 Single Vacation Model 2.2.3 Setup Time Model 2.3 M/G/1 Queue with Threshold Policy 2.3.1 N-Threshold Policy Model 2.3.2 Other Threshold Policy Models 2.4 Discrete-Time Geo/G/1 Queue with Vacations 2.4.1 Classical Geo/G/1 Queue 2.4.2 Geo/G/1 Queue with MAVs 2.4.3 Special Cases of the MAV Model 2.5 MAP/G/1 Vacation Models 2.6 General-Service Bulk Queue with Vacations 2.6.1 Mx IG/1 Queue with Vacations 2.6.2 MIGx 11 Queue with Vacations 1 1 3 4 5 9 10 10 12 19 19 21 24 27 27 32 35 36 37 43 46 54 54 59 vi 2.7 Finite-Buffer M/G/1 Queue with Vacations 2.8 Bibliographic Notes 3. M/G/1 TYPE VACATION MODELS: NONEXHAUSTIVE SERVICE 3.1 Regeneration Cycle Method 3.1.1 Nonexhaustive Service and Service Cycle 3.1.2 A Renewal-Reward Theorem 3.2 Gated Service M/G/1 Vacation Models 3.2.1 Gated Service Multiple Vacation Model 3.2.2 Gated Service Single Vacation Model 3.2.3 Binomial Gated Service Vacation Model 3.3 Limited Service M/G/1 Vacation Models 3.3.1 P-Limited Service Model 3.3.2 G-Limited Service Model 3.3.3 B-Limited Service Model 3.3.4 E-Limited Service Model 3.3.5 T-Limited Service Model 3.3.6 Bernoulli Scheduling Service Model 3.4 Decrementing Service M/G/1 Vacation Models 3.4.1 P-Decrementing Service Model 3.4.2 G-Decrementing Service Model 3.4.3 Binomial Decrementing Service Model 3.5 Bibliographic Notes 4. GENERAL-INPUT SINGLE SERVER VACATION MODELS 4.1 GI/M/1 Type Structure Matrix 4.1.1 Classical GI/M/1 Queue 4.1.2 Matrix Geometric Solution 4.2 GI/M/1 Queue with Multiple Vacations 4.2.1 PH-Type Vacation Model 4.2.2 Stochastic Decomposition Property 4.2.3 Exponential Vacation Model 4.3 GI/M/1 Queue with Single Vacation 4.3.1 Embedded Markov Chain 4.3.2 Stationary Distribution 4.4 GI/M/1 Queue with N-Threshold Policies 4.5 General-Input Bulk Queue with Vacations 69 73 77 77 77 78 81 81 84 86 90 90 92 98 102 107 111 115 115 118 123 126 129 129 129 131 134 134 140 146 151 151 156 162 170 Contents vii 179 183 183 184 191 193 193 196 196 200 203 203 214 220 220 230 235 235 245 257 266 269 269 269 272 276 280 285 292 295 4.6 Finite-Buffer GI/M/1 Vacation Model 4.7 Discrete-Time GI/Geo/1 Queue with Vacations 4.7.1 Classical GI/Geo/1 Queue 4.7.2 GI/Geo/1 Queue with Multiple Vacations 4.8 Bibliographic Notes 5. MARKOVIAN MULTISERVER VACATION MODELS 5.1 Introduction to Multiserver Vacation Models 5.2 Quasi-Birth-and-Death Process Approach 5.2.1 QBD Process 5.2.2 Conditional Stochastic Decomposition 5.3 M/M/c Queue with Synchronous Vacations 5.3.1 Multiple Vacation Model 5.3.2 Single Vacation and Setup Time Models 5.4 M/M/c Queue with Asynchronous Vacations 5.4.1 Multiple Vacation Model 5.4.2 Single Vacation or Setup Time Model 5.5 M/M/c Queue with Synchronous Vacations of Some Servers 5.5.1 (SY, MV, d)-Policy Model 5.5.2 (SY, MV, e-d)-Policy Model 5.6 M/M/c Queue with Asynchronous Vacations of Some Servers 5.7 Bibliographic Notes 6. GENERAL-INPUT MULTISERVER VACATION MODELS 6.1 GI/M/c Queue with Exponential Vacations 6.1.1 GI/M/c Type Structure Matrix 6.1.2 Stationary Queue Length Distribution 6.1.3 Stationary Waiting Time Distribution 6.2 GI/M/c Queue with PH Vacations 6.2.1 Stationary Distributions of Queue Length and Waiting Time 6.2.2 Conditional Stochastic Decomposition Properties 6.3 Bibliographic Notes viii 7. OPTIMIZATION IN VACATION MODELS 7.1 M/G/1 Queue with Threshold Policies 7.1.1 Average Cost Function 7.1.2 The Exponential Vacations Case 7.1.3 The General Vacations Case 7.1.4 Determination of Optimal Threshold Values 7.1.5 The Convexity of the Average Cost function 7.2 Dynamic Control in M/G/1 System with Vacations of Multiple Types 7.2.1 The SMDP Model 7.2.2 Computation of the Optimal Policy 7.2.3 Numerical Examples 7.3 M/M/c Queue with Threshold Policies 7.3.1 The (d, N)-Policy Model 7.3.2 Model Formulation and Performance Measures 7.3.3 Searching for the Optimal Two-Threshold Policy: A Computational Example 7.4 Bibliographic Notes 8. APPLICATIONS OF VACATION MODELS 8.1 Modeling the Flexible Production System 8.2 Modeling the Stochastic Service System with Multitask Servers 8.3 Modeling SVCC-Based ATM Networks 8.4 Bibliographic Notes 9. REFERENCES Index 297 297 298 302 303 307 315 318 321 325 327 330 330 330 339 341 343 343 345 350 358 359 383

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