To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems

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Springer Science & Business Media, 2003 - 191 pages
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The literature on equilibrium behavior of customers and servers in queuing systems is rich. However, there is no comprehensive survey of this field. Moreover, what has been published lacks continuity and leaves many issues uncovered. One of the main goals of this book is to review the existing literature under one cover. Other goals are to edit the known results in a unified manner, classify them and identify where and how they relate to each other, and fill in some gaps with new results. In some areas we explicitly mention open problems. We hope that this survey will motivate further research and enable researchers to identify important open problems. The models described in this book have numerous applications. Many examples can be found in the cited papers, but we have chosen not to include applications in the book. Many of the ideas described in this book are special cases of general principles in Economics and Game Theory. We often cite references that contain more general treatment of a subject, but we do not go into the details. we have highlighted the results For each topic covered in the book, that, in our opinion, are the most important. We also present a brief discussion of related results. The content of each chapter is briefly de scribed below. Chapter 1 is an introduction. It contains basic definitions, models and solution concepts which will be used frequently throughout the book.
 

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Table des matières

INTRODUCTION
1
1 Basic concepts
2
12 Steadystate
4
13 Subgame perfect equilibrium
5
16 Avoid the crowd or follow it?
6
2 Threshold strategies
7
3 Costs and objectives
9
4 Queueing theory preliminaries
11
43 Heterogeneous values of service
93
5 Bribes and auctions
96
51 Homogeneous customers
97
52 Heterogeneous customers
100
6 Class decision
104
7 Related literature
107
RENEGING AND JOCKEYING
109
2 Reneging in unobservable queues
113

5 A shuttle example
14
52 The observable model
17
53 Social optimality
18
6 Nonstochastic models
19
OBSERVABLE QUEUES
21
2 The LCFSPR model
24
3 Social optimization
27
4 Profit maximization
29
5 Heterogeneous customers
34
6 NonFCFS queues without reneging
36
61 LCFS
37
62 EPS and random queues
38
7 Discounting
39
8 State dependent pricing
40
9 Waiting for the right server
41
10 Nonexponential service requirements
42
11 Related literature
43
UNOBSERVABLE QUEUES
45
11 Equilibrium
46
12 Social optimization
47
13 Profit maximization
49
2 Observable vs unobservable queues
51
3 Heterogeneous service values
53
4 Heterogeneous service values and time costs
56
42 Social optimization
57
5 Customers know their demand
58
52 EPS
59
53 Shortest service first
60
7 Multiserver models
62
72 Heterogeneous service values
64
73 Class decision
67
8 Queueing networks
68
82 Heterogeneous service values
69
83 Serial networks with overtaking
70
PRIORITIES
73
12 Two priority classes
75
13 Profit maximization
82
2 Unobservable queues
83
3 Discriminatory processor sharing
85
31 Two relative priority parameters
86
32 A continuum of relative priority parameters
87
4 Incentive compatible prices
91
42 Pricing based on externalities
92
22 Convex waiting costs
114
23 Heterogeneous customers
115
3 Jockeying
117
31 Jockeying and the value of information
118
32 Expected waiting time
119
33 Steadystate probabilities
120
34 The value of information
121
4 Related literature
122
SCHEDULES AND RETRIALS
123
2 ?M1
124
3 Arrivals to scheduled batch service
127
4 Retrials
130
41 Steadystate probabilities
131
42 Social optimality
133
5 Related literature
137
COMPETITION AMONG SERVERS
139
1 Unobservable queues with heterogeneous time values
140
12 Two time values
141
2 Unobservable queues with heterogeneous values of service
142
21 Single class of customers
143
22 Multiple classes of customers
144
3 Observable queues
145
4 Price and priority competition
148
5 Search among competing servers
150
6 Information based competition
151
61 Existence of an equilibrium
152
62 Solution of the model
154
7 Related literature
155
SERVICE RATE DECISIONS
157
1 Heterogeneous service values
158
2 Service rate at a fixed price
160
3 Bribes and auctions
161
4 Asymmetric information
163
42 Heterogeneous time values
165
5 Observable vs unobservable queues
166
6 Coproduction
167
62 Multiclass extensions
169
7 Competition among servers
171
8 Capacity expansion
172
9 Related literature
173
Index
189
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