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DYNAMIC CONTROL OF A SINGLE-SERVER SYSTEM WHEN JOBS CHANGE STATUS

Published online by Cambridge University Press:  07 June 2017

Gabriel Zayas-Cabán and
Hyun-Soo Ahn
Gabriel Zayas-Cabán
Affiliation:
Center for Healthcare Engineering and Patient Safety, University of Michigan, Ann Arbor, MI, USA. E-mail: gzayasca@umich.edu
Hyun-Soo Ahn
Affiliation:
Ross School of Business, University of Michigan, Ann Arbor, MI, USA. E-mail: hsahn@umich.edu
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Abstract

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From health care to maintenance shops, many systems must contend with allocating resources to customers or jobs whose initial service requirements or costs change when they wait too long. We present a new queueing model for this scenario and use a Markov decision process formulation to analyze assignment policies that minimize holding costs. We show that the classic cμ rule is generally not optimal when service or cost requirements can change. Even for a two-class customer model where a class 1 task becomes a class 2 task upon waiting, we show that additional orderings of the service rates are needed to ensure the optimality of simple priority rules. We then show that seemingly-intuitive switching curve structures are also not optimal in general. We study these scenarios and provide conditions under which they do hold. Lastly, we show that results from the two-class model do not extend to when there are n≥3 customer classes. More broadly, we find that simple priority rules are not optimal. We provide sufficient conditions under which a simple priority rule holds. In short, allowing service and/or cost requirements to change fundamentally changes the structure of the optimal policy for resource allocation in queueing systems.

Keywords

operations researchqueuesstochastic dynamic programmingstochastic modeling

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 3 , July 2018, pp. 353 - 395
Copyright
Copyright © Cambridge University Press 2017 

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