Vacation Queueing Models: Theory and Applications Book

Introduction     1
Queueing Systems with Server Vacations     1
Vacation Policies     3
Stochastic Decomposition in Vacation Models     4
Bibliographic Notes     5
M/G/1 Type Vacation Models: Exhaustive Service     9
M/G/1 Queue with Multiple Adaptive Vacations     10
Classical M/G/1 Queue     10
Multiple Adaptive Vacation Model     12
Some Classical M/G/1 Vacation Models     19
Multiple Vacation Model     19
Single Vacation Model     21
Setup Time Model     24
M/G/1 Queue with Threshold Policy     27
N-Threshold Policy Model     27
Other Threshold Policy Models     32
Discrete-Time Geo/G/1 Queue with Vacations     35
Classical Geo/G/1 Queue     36
Geo/G/1 Queue with MAVs     37
Special Cases of the MAV Model     43
MAP/G/1 Vacation Models     46
General-Service Bulk Queue with Vacations     54
M[superscript X]/G/1 Queue with Vacations     54
M/G[superscript X]/1 Queue with Vacations     59
Finite-Buffer M/G/1 Queue with Vacations     69
Bibliographic Notes     73
M/G/1Type Vacation Models: Nonexhaustive Service     77
Regeneration Cycle Method     77
Nonexhaustive Service and Service Cycle     77
A Renewal-Reward Theorem     78
Gated Service M/G/1 Vacation Models     81
Gated Service Multiple Vacation Model     81
Gated Service Single Vacation Model     84
Binomial Gated Service Vacation Model     86
Limited Service M/G/1 Vacation Models     90
P-Limited Service Model     90
G-Limited Service Model     92
B-Limited Service Model     98
E-Limited Service Model     102
T-Limited Service Model     107
Bernoulli Scheduling Service Model     111
Decrementing Service M/G/1 Vacation Models     115
P-Decrementing Service Model     115
G-Decrementing Service Model     118
Binomial Decrementing Service Model     123
Bibliographic Notes     126
General-Input Single Server Vacation Models     129
GI/M/1 Type Structure Matrix     129
Classical GI/M/1 Queue     129
Matrix Geometric Solution     131
GI/M/1 Queue with Multiple Vacations     134
PH-Type Vacation Model      134
Stochastic Decomposition Property     140
Exponential Vacation Model     146
GI/M/1 Queue with Single Vacation     151
Embedded Markov Chain     151
Stationary Distribution     156
GI/M/1 Queue with N-Threshold Policies     162
General-Input Bulk Queue with Vacations     170
Finite-Buffer GI/M/1 Vacation Model     179
Discrete-Time GI/Geo/1 Queue with Vacations     183
Classical GI/Geo/1 Queue     183
GI/Geo/1 Queue with Multiple Vacations     184
Bibliographic Notes     191
Markovian Multiserver Vacation Models     193
Introduction to Multiserver Vacation Models     193
Quasi-Birth-and-Death Process Approach     196
QBD Process     196
Conditional Stochastic Decomposition     200
M/M/c Queue with Synchronous Vacations     203
Multiple Vacation Model     203
Single Vacation and Setup Time Models     214
M/M/c Queue with Asynchronous Vacations     220
Multiple Vacation Model     220
Single Vacation or Setup Time Model     230
M/M/c Queue with Synchronous Vacations of Some Servers     235
(SY, MV, d)-Policy Model      235
(SY, MV, e-d)-Policy Model     245
M/M/c Queue with Asynchronous Vacations of Some Servers     257
Bibliographic Notes     266
General-Input Multiserver Vacation Models     269
GI/M/c Queue with Exponential Vacations     269
GI/M/c Type Structure Matrix     269
Stationary Queue Length Distribution     272
Stationary Waiting Time Distribution     276
GI/M/c Queue with PH Vacations     280
Stationary Distributions of Queue Length and Waiting Time     285
Conditional Stochastic Decomposition Properties     292
Bibliographic Notes     295
Optimization in Vacation Models     297
M/G/1 Queue with Threshold Policies     297
Average Cost Function     298
The Exponential Vacations Case     302
The General Vacations Case     303
Determination of Optimal Threshold Values     307
The Convexity of the Average Cost function     315
Dynamic Control in M/G/1 System with Vacations of Multiple Types     318
The SMDP Model     321
Computation of the Optimal Policy     325
Numerical Examples     327
M/M/c Queue with Threshold Policies      330
The (d, N)-Policy Model     330
Model Formulation and Performance Measures     330
Searching for the Optimal Two-Threshold Policy: A Computational Example     339
Bibliographic Notes     341
Applications of Vacation Models     343
Modeling the Flexible Production System     343
Modeling the Stochastic Service System with Multitask Servers     345
Modeling SVCC-Based ATM Networks     350
Bibliographic Notes     358
References     359
Index     383