Multi-channel queues in heavy traffic
Multi-channel queues in heavy traffic
复制标题
人流量大时多渠道排队
DOI：
10.2307/3212380
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发表时间：
1973
影响因子：
1
通讯作者：
R. Loulou
中科院分区：
文献类型：
--
作者：
R. Loulou
本文在一般的假设下，将重载排队的收敛定理推广到多通道系统。Whitt（1968），Iglehart和Whitt（1970）证明了单通道排队的队长过程和等待过程的弱收敛性。多服务器队列的扩展是为队列长度过程建立的，但只是部分地为等待过程建立的（仅ρ = 1）。本文给出了当ρ > 1时等待过程的收敛定理。我们的方法使用弱收敛理论，但与以前的方法不同之处在于我们使用虚拟延迟作为中间结果。所考虑的队列类比GI/G/m更一般。
In this paper, convergence theorems for heavy traffic queues are extended to multi-channel systems under general assumptions. Whitt (1968), and Iglehart and Whitt (1970) have proved weak convergence of the queue length process and the wait process for one-channel queues. Extensions to multi-server queues were established for the queue length process but only partly for the wait process (ρ = 1 only). We give here convergence theorems for the wait process when ρ > 1. Our approach uses weak convergence theory, but is different from previous ones in that we use the virtual delay as an intermediate result. The class of queues considered is more general than GI/G/m.