Cost analysis of a finite M/M/R queueing system with balking, reneging, and server breakdowns
Cost analysis of a finite M/M/R queueing system with balking, reneging, and server breakdowns
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DOI：
10.1007/s001860200206
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发表时间：
2002-11
影响因子：
1.2
通讯作者：
Kuo-Hsiung Wang;Y. Chang
中科院分区：
文献类型：
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作者：
Kuo-Hsiung Wang;Y. Chang
研究了具有止步、中途退出和服务台故障的有限容量M/M/R排队系统。到达的顾客以概率(1−bn)止步(不进入)，并根据负指数分布退出(进入后离开队列)。即使系统中没有客户，服务器也可能随时出现故障。假设客户的到达时间和服务时间、服务器的故障时间和维修时间服从负指数分布。我们使用矩阵几何方法来推导稳态概率，利用该稳态概率可以获得各种系统性能指标。建立了一个成本模型来确定服务器的最佳数量。在最优运行条件下，给出了基于给定系统参数的假设数值来评估几种系统性能指标的数值结果。并对其进行了灵敏度分析。
We study an M/M/R queueing system with finite capacity plus balking, reneging, and server breakdowns. Arriving customers balk (do not enter) with a probability (1 −bn) and renege (leave the queue after entering) according to a negative exponential distribution. The server can break down at any time even if no customers are in the system. Arrival and service times of the customers, and breakdown times and repair times of the servers are assumed to follow a negative exponential distribution. We use a matrix geometric method to derive the steady-state probabilities, using which various system performance measures that can be obtained. A cost model is developed to determine the optimum number of servers. Under the optimal operating conditions, numerical results are presented in which several system performance measures are evaluated based on assumed numerical values given to the system parameters. Sensitivity analysis is also investigated.