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Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics;

机译:加入具有多个服务器的最短队列。重交通渐近;

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摘要

We consider queueing systems with n parallel queues under a Join the Shortest Queue (JSQ) policy in the Halfin-Whitt heavy-traffic regime. We use the martingale method to prove that a scaled process counting the number of idle servers and queues of length exactly two weakly converges to a two-dimensional reflected Ornstein-Uhlenbeck process, while processes counting longer queues converge to a deterministic system decaying to zero in constant time. This limiting system is comparable to that of the traditional Halfin-Whitt model, but there are key differences in the queueing behavior of the JSQ model. In particular, only a vanishing fraction of customers will have to wait, but those who do incur a constant order waiting time. Keywords: queueing theory; parallel queues; diffusion models;

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  • 年(卷),期 2019(),
  • 年度 2019
  • 页码
  • 总页数 25
  • 原文格式 PDF
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  • 网站名称 数字空间系统
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