Preface |
|
ix | |
|
|
1 | (52) |
|
1.1. Description of the Queueing Problem |
|
|
1 | (2) |
|
1.2. Characteristics of Queueing Processes |
|
|
3 | (4) |
|
|
7 | (2) |
|
1.4. Measuring System Performance |
|
|
9 | (1) |
|
1.5. Some General Results |
|
|
10 | (3) |
|
1.6. Simple Data Bookkeeping for Queues |
|
|
13 | (3) |
|
1.7. Poisson Process and the Exponential Distribution |
|
|
16 | (6) |
|
1.8. Markovian Property of the Exponential Distribution |
|
|
22 | (4) |
|
1.9. Stochastic Processes and Markov Chains |
|
|
26 | (19) |
|
1.10. Steady-State Birth-Death Processes |
|
|
45 | (2) |
|
|
47 | (6) |
|
2. Simple Markovian Birth-Death Queueing Models |
|
|
53 | (63) |
|
2.1. Steady-State Solution for the M/M/1 Model |
|
|
53 | (3) |
|
2.2. Methods of Solving Steady-State Difference Equations |
|
|
56 | (13) |
|
2.3. Queues with Parallel Channels (M/M/c) |
|
|
69 | (5) |
|
2.4. Queues with Parallel Channels and Truncation (M/M/c/K) |
|
|
74 | (6) |
|
2.5. Erlang's Formula (M/M/c/c) |
|
|
80 | (1) |
|
2.6. Queues with Unlimited Service (M/M/XXX) |
|
|
81 | (1) |
|
2.7. Finite Source Queues |
|
|
82 | (7) |
|
2.8. State-Dependent Service |
|
|
89 | (4) |
|
2.9. Queues with Impatience |
|
|
93 | (2) |
|
|
95 | (7) |
|
2.11. Busy-Period Analyses for M/M/1 and M/M/c |
|
|
102 | (2) |
|
|
104 | (12) |
|
3. Advanced Markovian Queueing Models |
|
|
116 | (49) |
|
3.1. Bulk Input (M[x]/M/1) |
|
|
116 | (6) |
|
3.2. Bulk Service (M/M[Y]/1) |
|
|
122 | (5) |
|
3.3. Erlangian Models (M/E(k)/1, E(k)/M/1, E(j)/E(k)/1) |
|
|
127 | (14) |
|
3.4. Priority Queue Disciplines |
|
|
141 | (18) |
|
|
159 | (6) |
|
4. Networks, Series, and Cyclic Queues |
|
|
165 | (44) |
|
|
167 | (7) |
|
4.2. Open Jackson Networks |
|
|
174 | (9) |
|
4.3. Closed Jackson Networks |
|
|
183 | (16) |
|
|
199 | (1) |
|
4.5. Extensions of Jackson Networks |
|
|
200 | (2) |
|
4.6. Non-Jackson Networks |
|
|
202 | (2) |
|
|
204 | (5) |
|
5. Models with General Arrival or Service Patterns |
|
|
209 | (57) |
|
5.1. Single-Server Queues with Poisson Input and General Service (M/G/1) |
|
|
209 | (33) |
|
5.2. Multiserver Queues with Poisson Input and General Service |
|
|
242 | (6) |
|
5.3. General Input and Exponential Service |
|
|
248 | (12) |
|
|
260 | (6) |
|
6. More General Models and Theoretical Topics |
|
|
266 | (60) |
|
6.1. G/E(k)/1, G[k]/M/1, and G/PH(k)/1 |
|
|
266 | (8) |
|
6.2. General Input, General Service (G/G/1) |
|
|
274 | (12) |
|
6.3. Multichannel Queues with Poisson Input and Constant Service (M/D/c) |
|
|
286 | (2) |
|
6.4. Semi-Markov and Markov Renewal Processes in Queueing |
|
|
288 | (6) |
|
6.5. Other Queue Disciplines |
|
|
294 | (6) |
|
6.6. Design and Control of Queues |
|
|
300 | (12) |
|
6.7. Statistical Inference in Queueing |
|
|
312 | (9) |
|
|
321 | (5) |
|
7. Bounds, Approximations, Numerical Techniques, and Simulation |
|
|
326 | (76) |
|
7.1. Bounds and Inequalities |
|
|
326 | (14) |
|
|
340 | (12) |
|
7.3. Numerical Techniques |
|
|
352 | (18) |
|
7.4. Discrete-Event Stochastic Simulation |
|
|
370 | (26) |
|
|
396 | (6) |
References |
|
402 | (13) |
|
Appendix 1. Symbols and Abbreviations |
|
|
415 | (8) |
Appendix 2. Summary of Models Treated and Types of Results |
|
423 | (4) |
Appendix 3. QTS Software |
|
427 | (6) |
Index |
|
433 | |