A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment

Yunan Liu () and Ward Whitt ()
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Yunan Liu: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Ward Whitt: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027

Operations Research, 2011, vol. 59, issue 4, 835-846

Abstract: 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.

Keywords: queues; time-varying arrivals; queueing networks; many-server queues; deterministic fluid model; customer abandonment; non-Markovian queues (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (13)

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