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Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

Part of: Computer system organization Operations research and management science Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

Hyun-Soo Ahn ,
Izak Duenyas  and
Rachel Q. Zhang
Hyun-Soo Ahn*
Affiliation:
University of Michigan
Izak Duenyas*
Affiliation:
University of Michigan
Rachel Q. Zhang*
Affiliation:
University of Michigan
*
∗ Postal address: Department of Industrial and Operations Engineering, The University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117, USA.
∗ Postal address: Department of Industrial and Operations Engineering, The University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117, USA.
∗ Postal address: Department of Industrial and Operations Engineering, The University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117, USA.
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Abstract

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

Keywords

Stochastic schedulingmultiserver queuestandem queues

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 90B22: Queues and service 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 4 , December 1999 , pp. 1095 - 1117
Copyright
Copyright © Applied Probability Trust 1999 

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