Page 480 - A First Course In Stochastic Models

Index

Absorbing state, 89, 170 Defective renewal equation, 329
Accessible, 119 Detailed balance, 193
Adelson’s recursion, 20 D/G/1 queue, 374, 376, 424
Aloha system, 274 Directly Riemann integrable, 315
Alternating renewal process, 43, 321, Discrete-time queues, 114, 417, 426
334, 336 Doubly stochastic, 135
Analytic, 452
Aperiodic, 45, 121 E k distribution, see Erlang
Arrival theorem, 222 distribution,
Average cost optimal, 240, 282 Elementary renewal theorem, 313
Average cost optimality equation, 248 Embedded Markov chain, 86
Embedding technique, 291
Balanced means, 447 Engset model, 196, 227
BCMP-networks, 219 Equilibrium excess distribution, 318
Bounded convergence theorem, 439 Equilibrium distribution, 98, 155
Burke’s theorem, 193 Equilibrium equations, 99, 149
Busy period, 32, 66, 353 Equilibrium probabilities, 99, 149
Erlang delay model, 187
Erlang delay probability, 192, 388
Call centers, 198 Erlang distribution, 442, 461
C 2 distribution, see Coxian-2 Erlang loss formula, 196
distribution, Erlang loss model, 194, 226
Cesaro limit, 439 E r /D/∞ queue, 72
Chapman-Kolmogoroff equations, 87 Exceptional first services, 420
Closed networks of queues, 203, 219, Excess life, 37, 71, 308, 317
229 Exponential distribution, 440
Closed set, 98
Coefficient of variation, 437
Communicating states, 119 Failure rate, 438
Convolution formula, 434 Fast Fourier Transform method, 455
Coupon-collecting problem, 450 Fatou’s lemma, 439
Coxian-2 distribution, 447 FFT method, see Fast Fourier Transform
Customer-average probabilities, 69 method
Cycle, 40 Fictitious decision epochs, 287
Finite-capacity queues, 408–420
Finite-source queues, 224, 425
D-policy, 318 First passage time, 48, 92, 170
Data transformation, 263, 282 Flow rate equation method, 150

A First Course in Stochastic Models H.C. Tijms
c 2003 John Wiley & Sons, Ltd. ISBNs: 0-471-49880-7 (HB); 0-471-49881-5 (PB)