MAP/M/c and M/PH/c Queues with Constant Impatience Times
MAP/M/c and M/PH/c Queues with Constant Impatience Times
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具有恒定不耐烦时间的 MAP/M/c 和 M/PH/c 队列
DOI：
10.1007/s11134-015-9455-9
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发表时间：
2016
期刊：
影响因子：
1.2
通讯作者：
K. Kawanishi and T. Takine
中科院分区：
文献类型：
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作者：
M. Okumura;S. Takahashi;N. Tsuruta;M. Ohno;M. Torii;M. Okuno;Hisashi Kurata and Berdymurad Ovezmuradov;深田 秀実，中谷 未歩;奥村勝・高橋伸弥・鶴田直之;川村真也，深田秀実，橋本雄一;Hisashi Kurata;高橋伸弥，奥村勝，鶴田直之;深田 秀実;Hisashi Kurata;鶴田直之，奥村勝，高橋伸弥，奥野充，鳥井真之，稲倉寛仁;奥野祐介，橋本雄一;倉田久;Hisashi Kurata and Seong-Hyun Nam;K. Kawanishi and T. Takine
本文研究了具有常数不耐烦时间的平稳MAP/M/c和M/PH/c排队系统。在这些队列中，等待的客户离开系统，如果他们的等待时间超过预定义的确定性阈值，而不接受他们的服务。对于具有常数不耐烦时间的MAP/M/c排队，Choi等人（Math Oper Res 29：309-325，2004）推导出虚拟等待时间分布，由此得到丢失概率和实际等待时间分布。我们首先改进他们的结果的虚拟等待时间，然后推导出稳态队长分布。我们还讨论了感兴趣的性能指标的计算过程。其次，我们考虑具有常数不耐烦时间的平稳M/PH/c排队，并推导出损失概率、等待时间分布和队长分布。并给出了一些数值结果。
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.