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Dynamic scheduling of a single-server two-class queue with constant retrial policy

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  • Anastasia Winkler

Abstract

We analyze the non-preemptive assignment of a single server to two infinite-capacity retrial queues. Customers arrive at both queues according to Poisson processes. They are served on first-come-first-served basis following a cost-optimal routing policy. The customer at the head of a queue generates a Poisson stream of repeated requests for service, that is, we have a constant retrial policy. All service times are exponential, with rates depending on the queues. The costs to be minimized consist of costs per unit time that a customer spends in the system. In case of a scheduling problem that arise when no new customers arrive an explicit condition for server allocation to the first or the second queue is given. The condition presented covers all possible parameter choices. For scheduling that also considers new arrivals, we present the conditions under which server assignment to either queue 1 or queue 2 is cost-optimal. Copyright Springer Science+Business Media, LLC 2013

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  • Anastasia Winkler, 2013. "Dynamic scheduling of a single-server two-class queue with constant retrial policy," Annals of Operations Research, Springer, vol. 202(1), pages 197-210, January.
    • Handle: RePEc:spr:annopr:v:202:y:2013:i:1:p:197-210:10.1007/s10479-011-0950-z
    DOI: 10.1007/s10479-011-0950-z
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    References listed on IDEAS

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    1. Josef Weichbold & Anastasia Winkler, 2010. "Optimal stochastic scheduling in a single server biclass retrial queueing system," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 405-431, December.
    2. A. Gómez-Corral, 2006. "A bibliographical guide to the analysis of retrial queues through matrix analytic techniques," Annals of Operations Research, Springer, vol. 141(1), pages 163-191, January.
    3. Dimitri frosinin & L. Breuer, 2006. "Threshold policies for controlled retrial queues with heterogeneous servers," Annals of Operations Research, Springer, vol. 141(1), pages 139-162, January.
    4. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
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    Cited by:

    1. Ioannis Dimitriou, 2016. "A queueing model with two classes of retrial customers and paired services," Annals of Operations Research, Springer, vol. 238(1), pages 123-143, March.
    2. Alexander Moiseev & Maria Shklennik & Evgeny Polin, 2023. "Infinite-server queueing tandem with Markovian arrival process and service depending on its state," Annals of Operations Research, Springer, vol. 326(1), pages 261-279, July.
    3. Ioannis Dimitriou, 2016. "A queueing model with two classes of retrial customers and paired services," Annals of Operations Research, Springer, vol. 238(1), pages 123-143, March.
    4. Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik, 2023. "Robustness of the cμ -Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates," Mathematics, MDPI, vol. 11(18), pages 1-14, September.

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