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Dynamic routing and jockeying controls in a two-station queueing system

Published online by Cambridge University Press:  01 July 2016

Susan H. Xu
Affiliation:
Pennsylvania State University
Y. Quennel Zhao
Affiliation:
University of Winnipeg

Abstract

This paper studies optimal routing and jockeying policies in a two-station parallel queueing system. It is assumed that jobs arrive to the system in a Poisson stream with rate λand are routed to one of two parallel stations. Each station has a single server and a buffer of infinite capacity. The service times are exponential with server-dependent rates, μ 1 and μ 2. Jockeying between stations is permitted. The jockeying cost is cij when a job in station i jockeys to station j, ij. There is no cost when a new job joins either station. The holding cost in station j is hj, h 1h 2, per job per unit time. We characterize the structure of the dynamic routing and jockeying policies that minimize the expected total (holding plus jockeying) cost, for both discounted and long-run average cost criteria. We show that the optimal routing and jockeying controls are described by three monotonically non-decreasing functions. We study the properties of these control functions, their relationships, and their asymptotic behavior. We show that some well-known queueing control models, such as optimal routing to symmetric and asymmetric queues, preemptive or non-preemptive scheduling on homogeneous or heterogeneous servers, are special cases of our system.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 1996 

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