Page 481 - A First Course In Stochastic Models
P. 481
476 INDEX
Fluid flow model, 369 Laplace inversion, 460, 462
Laplace transform, 458
Law of total expectation, 431
Gamma distribution, 441
Gamma normalization, 448 Law of total probability, 431
Gauss-Seidel iteration, 109 Leaky bucket control, 138
Generalized Erlangian distribution, 444 Lindly equation, 376
Generating function, 449 Little’s formula, 50, 345
Geometric tail approach, 111, 157 Lognormal distribution, 443
Gibbs sampler, 118
GI/D/c queue, 406 Machine repair model, 224, 425
state probabilities, 406 MAP/G/1 queue, 230, 426
waiting-time probabilities, 407 Markov chains, 81–186
GI/D/∞ queue, 72, 313 continuous-time, 141–186
GI/G/1 queue, 371, 424 discrete-time, 81–139
approximations, 375, 424 Markov decision processes, 233–305
state probabilities, 398 discrete-time, 233–277
waiting-time probabilities, 371 linear programs, 252, 286
GI/G/c queue, 398 policy iteration, 247, 284
approximations, 399 probabilistic constraints, 255
GI/M/1 queue, 69, 86, 102 semi-Markov, 279–305
state probabilities, 69, 102 value iteration, 259, 285
waiting-time probabilities, 401
GI/M/c queue, 400 Markov modulated Poisson
process, 24
state probabilities, 400 Markovian property, 82, 142
waiting-time probabilities, 401
Matrix geometric method, 161
M/D/c queue, 378
H 2 distribution, see Hyperexponential state probabilities, 378, 380
distribution, waiting-time probabilities, 381
Hazard rate, 438 Mean recurrence time, 95
Heavy-tailed, 332 Mean-value algorithm, 224
Hyperexponential distribution, 446 Memoryless property, 2, 440
Metropolis-Hastings algorithm, 117
Incomplete gamma function, 442 M/G/1 queue, 58, 211, 327, 345
Independent increments, 5 bounded sojourn time, 213, 423
Infinitesimal transition rates, 144 busy period, 353
Insensitivity, 9, 196, 198, 202, 218, exceptional first service, 420, 422
226–228 finite buffer, 366
Insurance, 18, 104, 274, 326 impatient customers, 369
Inventory systems, 9, 13, 38, 195, 213, LCFS service, 356
275, 423 mean queue size, 58
Irreducible, 119 priorities, 76
processor sharing, 208
Jackson networks, 215, 219 server vacation, 421, 422
state probabilities, 60, 65, 346,
348
Kendall’s notation, 341 waiting-time probabilities, 63, 65,
Key renewal theorem, 315 212, 327, 349
Kolmogoroff’s forward differential work in system, 358
equations, 163 M/G/1/1 + N queue, 408
rejection probability, 410
Lack of memory, see Memoryless state probabilities, 408, 410
property waiting-time probabilities, 425
