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SCHEDULING IN A SINGLE-SERVER QUEUE WITH STATE-DEPENDENT SERVICE RATES

Published online by Cambridge University Press:  21 May 2019

Urtzi Ayesta ,
Balakrishna Prabhu  and
Rhonda Righter
Urtzi Ayesta
Affiliation:
CNRS, IRIT, 2 rue C. Camichel, 31071Toulouse, FranceLAAS-CNRS, Université de Toulouse, CNRS, INP, Toulouse, FranceIKERBASQUE - Basque Foundation for Science, 48011Bilbao, SpainUPV/EHU, Univ. of the Basque Country, 20018, Donostia, Spain E-mail: urtzi.ayesta@irit.fr
Balakrishna Prabhu
Affiliation:
LAAS-CNRS, Université de Toulouse, CNRS, INP, Toulouse, France
Rhonda Righter
Affiliation:
University of California, Berkeley, CA94720, United States
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Abstract

We consider single-server scheduling to minimize holding costs where the capacity, or rate of service, depends on the number of jobs in the system, and job sizes become known upon arrival. In general, this is a hard problem, and counter-intuitive behavior can occur. For example, even with linear holding costs the optimal policy may be something other than SRPT or LRPT, it may idle, and it may depend on the arrival rate. We first establish an equivalence between our problem of deciding which jobs to serve when completed jobs immediately leave, and a problem in which we have the option to hold on to completed jobs and can choose when to release them, and in which we always serve jobs according to SRPT. We thus reduce the problem to determining the release times of completed jobs. For the clearing, or transient system, where all jobs are present at time 0, we give a complete characterization of the optimal policy and show that it is fully determined by the cost-to-capacity ratio. With arrivals, the problem is much more complicated, and we can obtain only partial results.

Keywords

operations researchqueueing theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 4 , October 2020 , pp. 507 - 521
Copyright
Copyright © Cambridge University Press 2019

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