Heavy-Traffic Limits for Loss Proportions in Single-Server Queues

被引:1
作者
Ward Whitt
机构
[1] Columbia University,Department of Industrial Engineering and Operations Research
来源
Queueing Systems | 2004年 / 46卷
关键词
single-server queue; finite-capacity queue; finite dam; blocking probability; loss rate; overflows; heavy-traffic; local limit; diffusion approximation; heavy-tailed probability distribution; stable process;
D O I
暂无
中图分类号
学科分类号
摘要
We establish heavy-traffic stochastic-process limits for the queue-length and overflow stochastic processes in the standard single-server queue with finite waiting room (G/G/1/K). We show that, under regularity conditions, the content and overflow processes in related single-server models with finite waiting room, such as the finite dam, satisfy the same heavy-traffic stochastic-process limits. As a consequence, we obtain heavy-traffic limits for the proportion of customers or input lost over an initial interval. Except for an interchange of the order of two limits, we thus obtain heavy-traffic limits for the steady-state loss proportions. We justify the interchange of limits in M/GI/1/K and GI/M/1/K special cases of the standard GI/GI/1/K model by directly establishing local heavy-traffic limits for the steady-state blocking probabilities.
引用
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页码:507 / 536
页数:29
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