Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics
Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics
复制标题
DOI：
10.1287/moor.2017.0887
复制
发表时间：
2015-02
期刊：
影响因子：
--
通讯作者：
Patrick C Eschenfeldt;D. Gamarnik
中科院分区：
文献类型：
--
作者：
Patrick C Eschenfeldt;D. Gamarnik
我们考虑在Halfin-Whitt重交通状态下，在加入最短队列（JSQ）策略下，具有n个并行队列的排队系统。我们使用鞅方法证明了一个规模化的过程计数的空闲服务器和队列的长度正好是两个弱收敛到一个二维的反映Ornstein-Uhlenbeck过程，而过程计数较长的队列收敛到一个确定性的系统衰减到零的常数时间。该限制系统与传统的Halfin-Whitt模型相当，但JSQ模型的排队行为存在关键差异。特别是，只有一小部分客户将不得不等待，但那些谁承担一个恒定的订单等待时间。
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.