To Queue or Not to Queue: Equilibrium Behavior in Queueing SystemsSpringer Science & Business Media, 2003 - 191 pages 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. |
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 |
189 | |
Autres éditions - Tout afficher
To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems Refael Hassin,Moshe Haviv Aucun aperçu disponible - 2012 |
Expressions et termes fréquents
admission fee arg max arrival process arrival rate arriving customer assumed assumption Balachandran balking behavior best response Braess paradox buy priority choose computed considered customer who joins customer who observes customer's customers join decision decreasing demand equilibrium arrival rate equilibrium strategy expected full price expected number expected queueing expected waiting exponential exponentially distributed externalities FCFS follows function given Hassin and Haviv Hence Heterogeneous service values i-customer identical imposes incentive compatible induce jockeying join the queue LCFS-PR M/M/1 queue mixed strategies monotone increasing Naor's model number of customers Operations Research parameter payment prescribes probability profit maximizer purchase priority pure strategy queue length queueing models queueing system queueing theory random reneging result server service rate service requirement social welfare socially optimal Suppose symmetric equilibrium tagged customer THEOREM threshold strategy tomers unique equilibrium unobservable model unobservable queues value of service waiting costs