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A complete solution for the optimal stochastic scheduling of a two-stage tandem queue with two flexible servers

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Klaus Schiefermayr  and
Josef Weichbold
Klaus Schiefermayr*
Affiliation:
Upper Austrian University of Applied Sciences, Wels
Josef Weichbold*
Affiliation:
Universität Linz
*
∗Postal address: Fachbereich Mathematik, Fachhochschule Wels, Stelzhamerstr. 23, Wels, A-4600, Austria. Email address: k.schiefermayr@fh-wels.at
∗∗Postal address: Institut für Stochastik, Universität Linz, Altenbergerstr. 69, Linz, A-4040, Austria. Email address: josef.weichbold@jku.at
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Abstract

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We consider a two-stage tandem queue with two parallel servers and two queues. We assume that initially all jobs are present and that no further arrivals take place at any time. The two servers are identical and can serve both types of job. The processing times are exponentially distributed. After being served, a job of queue 1 joins queue 2, whereas a job of queue 2 leaves the system. Holding costs per job and per unit time are incurred if there are jobs holding in the system. Our goal is to find the optimal strategy that minimizes the expected total holding costs until the system is cleared. We give a complete solution for the optimal control of all possible parameters (costs and service times), especially for those parameter regions in which the optimal control depends on how many jobs are present in the two queues.

Keywords

Optimal stochastic schedulingflexible servertandem queueclearing system

MSC classification

Secondary: 90B22: Queues and service 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 778 - 796
Copyright
© Applied Probability Trust 2005 

References

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