I Basic Queueing Theory 9
1 Fundamental Concepts of Queueing Theory 11
1.1 PerformanceMeasuresofQueueingSystems . . . . . . . . . . . . . . . . 12 1.2
... [Show More] Kendall’sNotation .............................. 14 1.3 BasicRelationsforBirth-DeathProcesses . . . . . . . . . . . . . . . . . 15 1.4 QueueingSoftwares.............................. 16
2 Infinite-Source Queueing Systems 17
2.1 TheM/M/1Queue.............................. 17 2.2 TheM/M/1QueuewithBalkingCustomers................ 25 2.3 PriorityM/M/1Queues ........................... 30
2.4 The M/M/1/K Queue, Systems with Finite Capacity . . . . . . . . . . . 32 2.5 TheM/M/∞Queue ............................. 37 2.6 TheM/M/n/nQueue,Erlang-LossSystem ................ 38 2.7 TheM/M/nQueue.............................. 44 2.8 The M/M/c/K Queue - Multiserver, Finite-Capacity Systems . . . . . . 55 2.9 TheM/G/1Queue.............................. 57
3 Finite-Source Systems 69
3.1 TheM/M/r/r/nQueue,Engset-LossSystem . . . . . . . . . . . . . . . 69
3.2 TheM/M/1/n/nQueue........................... 73
3.3 HeterogeneousQueues ............................ 88
3.3.1 TheM⃗/M⃗/1/n/n/PSQueue .................... 89
3.4 TheM/M/r/n/nQueue ........................... 92
3.5 TheM/M/r/K/nQueue........................... 104
3.6 TheM/G/1/n/n/PSQueue......................... 106
3.7 TheG⃗/M/r/n/n/FIFOQueue ....................... 109
II Exercises
4 Infinite-Source Systems
117
119
5
5 Finite-Source Systems 137
III Queueing Theory Formulas 141
6 Relationships 143
7
6.1 NotationsandDefinitions .......................... 143 6.2 Relationshipsbetweenrandomvariables .................. 145
Basic Queueing Theory Formulas 147
7.1 M/M/1Formulas ............................... 147 7.2 M/M/1/KFormulas ............................. 149 7.3 M/M/cFormulas ............................... 150 7.4 M/M/2Formulas ............................... 152 7.5 M/M/c/cFormulas.............................. 154 7.6 M/M/c/KFormulas ............................. 155 7.7 M/M/∞Formulas .............................. 157 7.8 M/M/1/K/KFormulas............................ 158 7.9 M/G/1/K/KFormulas............................ 160 7.10M/M/c/K/KFormulas............................ 161 7.11D/D/c/K/KFormulas ............................ 163 7.12M/G/1Formulas ............................... 164 7.13GI/M/1Formulas............................... 173 7.14GI/M/cFormulas............................... 175 7.15M/G/1Priorityqueueingsystem ...................... 177 7.16M/G/cProcessorSharingsystem ...................... 185 7.17M/M/cPrioritysystem............................ 186 [Show Less]