A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment
成果类型：
Article
署名作者：
Liu, Yunan; Whitt, Ward
署名单位：
Columbia University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1110.0942
发表日期：
2011
页码：
835-846
关键词：
摘要：
To describe the congestion in large-scale service systems, we introduce and analyze a non-Markovian open network of many-server fluid queues with customer abandonment, proportional routing, and time-varying model elements. Proportions of the fluid completing service from each queue are immediately routed to the other queues, with the fluid not routed to one of the queues being immediately routed out of the network. The fluid queue network serves as an approximation for the corresponding non-Markovian open network of many-server queues with Markovian routing, where all model elements may be time varying. We establish the existence of a unique vector of (net) arrival rate functions at each queue and the associated time-varying performance. In doing so, we provide the basis for an efficient algorithm, even for networks with many queues.