Index. A age process, 21, 24, 25, 28, 30, 31, 33 arrival theorem, 147, 148, 159 ASTA, 59, 60, 103, 147, 148

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3 Index A age process, 21, 24, 25, 28, 30, 31, 33 arrival theorem, 147, 148, 159 ASTA, 59, 60, 103, 147, 148 B balance equations, 43 45, 83, 84, 100, 101, , 123, 128, 129, 131, , 143, 182, 186, , 215 beta distribution, 12 birth-and-death process, 108, 109, 111, , 168, 170, 181, 182, 201, 202 bottleneck, 157 C closed network, 116, 151, 154, , 178 continuous time Markov chains, 107, 108, 116, 124, 151, 152, 154, 174, 202 convolution algorithm, 155 cut balancing, 124, 125, 129, 132, 208 D decreasing hazard rate (DHR), 4, 18, 19, 35, 78 detailed balance, 45, 131, 134, 135, 143 discriminatory processor sharing (DPS), 116 E egalitarian processor sharing (EPS), 116, 166 embedding, 81, 92, 94, 105 ergodic theorem, 43, 44, 84, 101, 119, 152 Erlang, 1, 8 10, 16, 18, 22, 23, 27, 28, 34, 103, 111, 120, 167, 168, 171, 173, 178, 182 Erlang loss, 136 exponential distribution, 1 11, 13, 14, 16, 17, 22, 27 29, 31, 34, 61, 67, 73, 85 87, 92, 95, 99, 103, 105, , 111, 112, 116, 117, 120, 124, , 139, 142, 148, 149, 151, 162, 167, 168, 170, 178, 183, 185, 193, 210, 215 externalities, 65 F first-come first-served, 53, 56 58, 71, 72, 74, 75, 78, 79, 81, 86 88, 90, 91, 99, 112, 139, 145, 146, 149, 161, 162, 165, 166, 173 foreground-background (FB), 78 G gamma distribution, 8, 35 generator matrix, 123, 124, 184, 187, 205 H hazard, 1, 3, 4, 31, 33, 89 hyperexponantial, 34 hyperexponential, 1, 9, 18, 23 I increasing hazard rate (IHR), 4, 18, 19, 78 insensitivity, 97, 167, 173, 175 inspection paradox, 24, 26 K Khintchine Pollaczek, 51, 59, 88 M. Haviv, Queues: A Course in Queueing Theory, International Series in Operations Research & Management Science 191, DOI / , Springer Science+Business Media New York

4 220 Index L last-come first-served, 53, 56, 58, 71, 72, 79, 95, 165, 166, 173, 177 length process, 21 level, 181 limit probabilities, 31, 42 45, 49, 50, 54, 83, 100, 103, 105, , , 128, 129, 131, , 139, 140, 142, 143, , , 171, , 186, 197, 201, 202, 207 Lindley s equation, 67, 81, 87 Little s law, 51, 54 56, 58, 69, 72 75, 79, 90, 93, 95, 103, 104, 137, 147, 156, 161, 165, 167, 168, 171 M Markov chain, 92 Markov processes, 37, 39, 40, 45, 48, 94, 107, 112, 116, 119, 123, 124, 128, 129, 131, 132, 134, 135, 139, 143, 149, 152, 153, 159, 167, 170, 173, 174, 181, 183, 193, 202, 215 Mean Value Analysis (MVA), 161 Mean value analysis (MVA), 160, 162 memoryless, 1, 4, 5, 10, 11, 29, 34, 61, 63, 92, 99, 104, 107, 109, 112, 115, 116, 120, 124, , 181 mixture of Erlang, 1, 9, 10, 18, 23, 28, 34, 103, 120, 167, 168, 171, 173, 178 multiclass, 112, 115, 181 N nonpreemptive, 54, 72, 73, 75, 76, 78, 79, 81, 89, 90, 96, 165 null recurrent, 43 preemptive shortest job first (PSJF), 77 priority, 72, 73, 76 79, 116 product form, 123, 130, 142, 155, 162, 165, 167, 168, 173, 175, 177 Q quasi-birth-and-death processes, , 186, 215 R random order, 71, 72, 79, 80 relative priority, 116 renewal process, 21, 23, 31, 43, 56, 99, 151, 210 residual process, 21, 25, 27 S short-circuit, 48, 49, 158, 159 shortest job first (SJF), 75 stability, 55, 66, 67, 102, 123, 170, 202, 203, 205, 206, 215 stand-by customer, 64, 76 stationary distribution, 43, 94, 100, 119, 123, stationary process, 43, 45 steady-state, 55, 144 stochastic matrix, 40, 44, 45, 48, 105, 108, 124, 202 stochastic process, 37, 38, 59 super-positioning, 1, 13, 14, 146 symmetric queues, 165, 167, , 173, 174 symmetric shortest queue, 186 O one-chance queues, 165, 172, 173, 175, 178 open network, 112, 115, 139, , 154, 159, 178 order statistics, 12 P Pareto distribution, 19 partial balancedness, 143, 154 PASTA, 60, 89, 95, 120, 147, 159 phase, 181, 184, 186, 189, 191, 193, 215 Poisson process, 132 positive recurrent, 43, 45, 83, 84, 102, 131 preemption, 53, 58, 76, 77, 95, 165, 166, 173 T thinning, 1, 13, 146 time-reversed, 39, 45, , , , 169, 171, time-reversible, 45, 131, 132, 134, 135, 143, 149 traffic intensity, 54, 71, 73 transient matrix, 47, 48, 139, 202 transient state, 41 43, 48, 183 transition rate, , 111, 112, 115, , , 134, 140, 152, 153, 167, , , 181, 183, 186, 188, 191, 193, 194, 207, 211, 215 tree shape, 132

5 Index 221 U uniformization, 124, 138, 202 utilization, 51, 54 56, 66, 147, , 161, 174, 175, 209 W Weibull distribution, 19 V vacation, 65, 66, 81, 94, 215 virtual waiting time, 51, 57 59, 63, 64, 76 Z z-transform, 14 16, 84, 86, 91, 93