Acta Scientiarum Naturalium Universitatis Pekinensis

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A Queueing System GIX/M/1/N with Balking and Batch Arrivals

WANG Hao1, 2, LI Xiaoming1, YAN Wei1   

  • Received:2005-09-12 Online:2006-05-20 Published:2006-05-20



Abstract: A queueing system GIX/M/1/N with balking and batch arrivals was discussed. The interarrival and service times are arbitrarily and exponentially distributed, respectively. The distributions of the number of customers in the system at prearrival and arbitrary epochs are obtained. In addition, some performance metrics are given, such as the customer loss rate, the system utilization, the mean and variance of the queue length, the mean of the waiting time. Some application scenarios on computer communication network are discussed concerning this queueing system.

Key words: queueing system, balking, GIX/M/1/N, batch arrivals, computer communication network

摘要: 研究了一个顾客成批到达,到达间隔服从一般分布,服务时间服从指数分布,1个服务台,等待队列长度有限,且具有阻行机制的排队系统GIX/M/1/N;获得了该排队系统在稳态情况下,顾客到达前一瞬间系统中顾客数的概率分布和任意时刻系统中顾客数的概率分布;给出了该排队系统的顾客丢失率、系统利用率、队列长度的均值/方差、平均等待时间等性能指标的计算公式。最后,讨论了该排队系统在计算机网络中的应用。

关键词: 阻行, GIX/M/1/N, 成批到达, 计算机网络, 排队系统

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