Scheduling servers in a two-stage queue with abandonments and costs
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Published:2022-07-20
Issue:
Volume:
Page:1-19
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ISSN:0269-9648
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Container-title:Probability in the Engineering and Informational Sciences
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language:en
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Short-container-title:Prob. Eng. Inf. Sci.
Author:
Zayas-Cabán GabrielORCID,
Cochran Amy L.
Abstract
Abstract
We consider the assignment of servers to two phases of service in a two-stage tandem queueing system when customers can abandon from each stage of service. New jobs arrive at both stations. Jobs arriving at station 1 may go through both phases of service and jobs arriving at station 2 may go through only one phase of service. Stage-dependent holding and lump-sum abandonment costs are incurred. Continuous-time Markov decision process formulations are developed that minimize discounted expected and long-run average costs. Because uniformization is not possible, we use the continuous-time framework and sample path arguments to analyze control policies. Our main results are conditions under which priority rules are optimal for the single-server model. We then propose and evaluate threshold policies for allocating one or more servers between the two stages in a numerical study. These policies prioritize a phase of service before “switching” to the other phase when total congestion exceeds a certain number. Results provide insight into how to adjust the switching rule to significantly reduce costs for specific input parameters as well as more general multi-server situations when neither preemption or abandonments are allowed during service and service and abandonment times are not exponential.
Funder
National Center for Advancing Translational Sciences
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
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