MAP/M/c and M/PH/c queues with constant impatience times
| Autor: | Ken'ichi Kawanishi, Tetsuya Takine |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Mathematical optimization 021103 operations research M/G/k queue 0211 other engineering and technologies M/M/1 queue M/D/c queue G/G/1 queue 02 engineering and technology Management Science and Operations Research 01 natural sciences M/M/∞ queue Computer Science Applications Computer Science::Performance 010104 statistics & probability Computational Theory and Mathematics Burke's theorem M/G/1 queue M/M/c queue 0101 mathematics Mathematics |
| Zdroj: | Queueing Systems. 82:381-420 |
| ISSN: | 1572-9443 0257-0130 |
| DOI: | 10.1007/s11134-015-9455-9 |
| Popis: | This paper considers stationary MAP/M/c and M/PH/c queues with constant impatience times. In those queues, waiting customers leave the system without receiving their services if their elapsed waiting times exceed a predefined deterministic threshold. For the MAP/M/c queue with constant impatience times, Choi et al. (Math Oper Res 29:309---325, 2004) derive the virtual waiting time distribution, from which the loss probability and the actual waiting time distribution are obtained. We first refine their result for the virtual waiting time and then derive the stationary queue length distribution. We also discuss the computational procedure for performance measures of interest. Next we consider the stationary M/PH/c queue with constant impatience times and derive the loss probability, the waiting time distribution, and the queue length distribution. Some numerical results are also provided. |
| Databáze: | OpenAIRE |
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