Approximation of the Mean Queue Length of an M/G/c Queueing System
Approximation of the Mean Queue Length of an M/G/c Queueing System
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DOI：
10.1287/opre.43.1.158
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发表时间：
1995-02
期刊：
影响因子：
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通讯作者：
B.N.W. Ma;J. Mark
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文献类型：
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作者：
B.N.W. Ma;J. Mark
提出了一种相对鲁棒的M/G/c排队系统平均队列长度近似分析方法。该近似方法是基于以下假设而开发的：一台繁忙服务器的剩余服务时间独立于其他繁忙服务器的剩余服务时间，并且所有服务器都繁忙的系统被以与单服务器系统相同的方式处理，其c倍于其中一台服务器的服务率。这两个假设的应用通过引入参数 np 来耦合。如果系统中的客户数量大于np，则采用假设2；否则使用假设 1。我们发现 np 的某些属性允许通过对较小的 M/G/c 排队系统的平均队列长度进行近似分析来估计大型 M/G/c 排队系统的平均队列长度。数值结果表明，即使系统的服务时间和通道数的变异系数分别大到20和200时，该近似也是准确的。
A relatively robust method for the approximate analysis of the mean queue length of an M/G/c queueing system is proposed. The approximation method is developed based on the following assumptions: the residual service time of one busy server is independent of those of the other busy servers, and the system in which all the servers are busy is treated in the same way as a single-server system with c times the service rate of one of the servers. The application of these two assumptions is coupled through the introduction of a parameter np. If the number of customers in the system is larger than np, assumption 2 is used; otherwise assumption 1 is used. We found that certain properties of np allow an estimation of the mean queue length of a large M/G/c queueing system through the approximate analysis of the mean queue length of a much smaller M/G/c queueing system. Numerical results show that the approximation is accurate even when the coefficient of variation of the service time and the number of channels of the system are as large as 20 and 200, respectively.