Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams
Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams
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DOI：
10.1081/stm-120023565
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发表时间：
2003-08
影响因子：
0.7
通讯作者：
H. Masuyama;T. Takine
中科院分区：
文献类型：
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作者：
H. Masuyama;T. Takine
本文研究了一个连续时间有限状态马尔可夫链控制的多批马尔可夫到达流的工作守恒FIFO单服务台排队系统。该队列的一个特殊特征是，对于不同的到达流，客户的服务时间分布可能是不同的。在简要讨论了各个到达流中顾客的实际等待时间分布后，我们导出了一个关于虚拟等待时间分布的时间平均联合队长分布的向量母函数公式。进一步假设离散相位型批量大小分布，我们开发了一个数值上可行的程序来计算联合队长分布。文中还提供了一些数值例子。
This paper considers a work-conserving FIFO single-server queue with multiple batch Markovian arrival streams governed by a continuous-time finite-state Markov chain. A particular feature of this queue is that service time distributions of customers may be different for different arrival streams. After briefly discussing the actual waiting time distributions of customers from respective arrival streams, we derive a formula for the vector generating function of the time-average joint queue length distribution in terms of the virtual waiting time distribution. Further assuming the discrete phase-type batch size distributions, we develop a numerically feasible procedure to compute the joint queue length distribution. Some numerical examples are provided also.