Page 482 - A First Course In Stochastic Models
P. 482
INDEX 477
M/G/c queue, 384, 424 Phase-type distribution, 209, 342
delay probability, 388 Poisson process, 1–18
mean queue size, 389 compound, 18
state probabilities, 385 Markov modulated, 24
waiting-time probabilities, 391, 424 nonstationary, 22, 32
M/G/c/c + N queue, 224, 408 switched, 27
rejection probability, 410 Policy-improvement step, 240
state probabilities, 408, 410 Policy-iteration algorithm, 247, 284
waiting-time probabilities, 425 Pollaczek-Khintchine formula, 58, 68,
M/G/∞ queue, 9, 32, 72 352
M/M/1 queue, 188 Positive recurrent, 95
state probabilities, 189 Preemptive-resume discipline, 209,
waiting-time probabilities, 190 219
M/M/c queue, 190, 198 Priority queues, 76
state probabilities, 191 Probabilistic constraints, 255
waiting-time probabilities, 192 Processor sharing, 208
M/M/c/c + N queue, 224, 408 Product-form solution, 216
Modified value iteration, 264
X
M /D/c queue, 395 Randomized policy, 256
state probabilities, 395 Rare event, 48, 437
waiting-time probabilities, 396 Recurrent state, 94
X
M /G/1 queue, 360 Recurrent subclass, 120, 124
state probabilities, 361 Regenerative approach, 345
waiting-time probabilities, 363 Regenerative process, 40
X
M /G/c queue, 392, 397 Relative value, 240, 246
X
M /G/c/c + N queue, 413 Reliability models, 47, 49, 184, 323,
complete rejection, 415, 427 337, 437
partial rejection, 414 Renewal equation, 308, 310
X
M /G/∞ queue, 30, 32 Renewal function, 35, 308, 461
group service, 30, 228 asymptotic expansion, 36, 315, 334
individual service, 30 computation, 36, 310, 334
X
M /M/c queue, 392 Renewal process, 34, 308
state probabilities, 393 central limit theorem, 46
waiting-time probabilities, 394 Renewal-reward process, 41
central limit theorem, 46
Renewal-reward theorem, 41
N-policy, 66
Network of queues, 214–224 Residual life, 37, 71, 308, 317
Non-arithmetic, 314 Retrial queue, 77, 421
Nonstationary queues, 32, 169 Reversibility, 116, 194, 226
Null-recurrent, 95 Root-finding methods, 470
Numerical Laplace inversion, 462 Ruin probability, 326
(S − 1, S) inventory model, 9, 195
Offered load, 343
On-off sources, 162, 369, 425 backordering, 9
lost sales, 195
Open networks of queues, 215 (s, S) policy, 85, 275
Optimization of queues, 290
Semi-Markov decision process, 279–305
Server utilization, 189, 343
Panjer’s algorithm, 20 Shortest-queue, 161, 295
Parrando’s paradox, 135 Spectral expansion method, 161
PASTA property, 57 Square-root formula, 12, 200
Phase method, 36, 209 State classification, 119
