Queueing TheoryThe series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students. |
Contents
| 1 | |
| 6 | |
| 10 | |
| 17 | |
| 29 | |
16 SemiMarkov linearwise and piecewiselinear processes | 43 |
17 Kronecker matrix product | 58 |
2 Defining parameters of queueing systems | 61 |
55 Use of renewal processes | 242 |
6 Other simple nonMarkov models | 253 |
62 GG system | 256 |
63 MDn system | 259 |
64 GMl system | 262 |
65 MGlr system | 268 |
66 MGn0 system | 272 |
7 MAPGlr system | 277 |
22 System structure | 68 |
23 Customer service times | 69 |
25 Performance indices of a queueing system | 70 |
27 Queueing networks | 72 |
3 Elementary Markov models | 85 |
32 MMnr system | 94 |
33 MMl system with impatient customers | 100 |
34 System with a finite number of sources | 106 |
35 MXMl system with batch arrivals | 110 |
36 MEml system | 116 |
37 MMl0 system with retrial queue | 124 |
algorithmic methods of analysis | 133 |
41 MHmlr and HlMlr systems | 134 |
42 M2Mnr system with nonpreemptive priority | 145 |
43 MPHlr and PHMlr systems | 152 |
44 MPHlr system with server vacations and flow dependent on the queue state | 163 |
45 PHPHlr system | 172 |
46 Markov systems described by generalised birthanddeath process | 189 |
investigation methods | 205 |
52 Virtual waiting time | 220 |
53 Residual service time | 226 |
54 Elapsed waiting time | 234 |
FCFS discipline | 278 |
FCFS discipline | 295 |
73 LCFS discipline | 306 |
74 Matrix exponential moments | 316 |
8 MAPGl system | 323 |
82 Virtual waiting time | 337 |
FCFS discipline | 342 |
84 LCFS discipline | 345 |
generalisation | 351 |
91 BMAPSMlr system | 352 |
92 MAPG2lr system with preemptive priority | 367 |
93 MAPG2lr system with nonpreemptive priority | 381 |
94 MAPGlr retrial system | 388 |
95 MAPGl system withforegroundbackground processor sharing discipline | 397 |
96 MAPGlr system with LCFS discipline and bounded total volume of customers | 403 |
97 GMSPlr system | 409 |
10 Queueing networks | 423 |
102 Open exponential networks | 427 |
103 Closed exponential networks | 432 |
| 439 | |
| 445 | |
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Common terms and phrases
assume buffer busy period calculate characteristics completion of service compute customer arrives customer generation process customer sojourn dB(x defined denote derived differential equations discrete component embedded Markov chain empty system equality equilibrium equations ergodic Erlang Erlang distribution exist exponentially distributed expression finite follows Hence idle period initial instant input flow interval irreducible Laplace transform Laplace-Stieltjes transform LCFS discipline Lemma linearwise Markov chain vn mean number mean sojourn method node non-priority customers normalisation condition number of customers obtain parameter PH-representation phase-type distribution Pi(t pỗ po(t Poisson flow priority customers probability flow process n(t queueing system queueing theory random variables recurrence relations renewal process retrial customers satisfy Section semi-Markov semi-Markov process served server service process solution solve stationary distribution stationary mean stationary probabilities stationary state probabilities steady system is empty theorem time-stationary vector virtual waiting virtue zero