M/M/3/3 and M/M/4/4 retrial queues
M/M/3/3 and M/M/4/4 retrial queues
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DOI：
10.3934/jimo.2009.5.431
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发表时间：
2009-06
影响因子：
1.3
通讯作者：
Tuan Phung-Duc;H. Masuyama;S. Kasahara;Yutaka Takahashi
中科院分区：
文献类型：
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作者：
Tuan Phung-Duc;H. Masuyama;S. Kasahara;Yutaka Takahashi
本文研究了M/M/$c$/$c$重试排队系统，其中$c$服务台都是相同的。在重试队列中，如果到达的客户在到达时发现空闲的服务器，则立即为到达的客户提供服务，否则客户尝试独立于其他客户在指数分布的时间之后进入系统。众所周知，对于M/M/$c$/$c$重试排队系统，特别是当$c \ge 3$时，如何求出重试顾客数和忙碌服务器数的平稳联合分布是一个具有挑战性的问题。在某些技术假设下，给出了$c \ge 3$的一些解析解。本文在不作这些技术假设的情况下，导出了M/M/3/3和M/M/4/4重试排队的解析解.通过大量的数值算例，我们证明了导出的解析解可以用数值稳定的算法来计算。
This paper studies M/M/$c$/$c$ retrial queues, where $c$ servers are all identical. In the retrial queues, an arriving customer is served immediately if it finds an idle server upon arrival, otherwise the customer tries to enter the system after an exponentially distributed time independently of other customers. As is well known, it is a challenging problem to obtain an analytical solution for the stationary joint distribution of the numbers of retrial customers and busy servers in the M/M/$c$/$c$ retrial queue especially for $c \ge 3$. Under some technical assumptions, a few analytical solutions have been presented for $c \ge 3$. This paper derives analytical solutions for M/M/3/3 and M/M/4/4 retrial queues without such technical assumptions. Through many numerical examples, we show that the derived analytical solutions can be computed by a numerically stable algorithm.