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Threshold policies for controlled retrial queues with heterogeneous servers

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  • Dimitri frosinin
  • L. Breuer

Abstract

Retrial queues are an important stochastic model for many telecommunication systems. In order to construct competitive networks it is necessary to investigate ways for optimal control. This paper considers K -server retrial systems with arrivals governed by Neut' Markovian arrival process, and heterogeneous service time distributions of general phase-type. We show that the optimal policy which minimizes the number of customers in the system is of a threshold type with threshold levels depending on the states of the arrival and service processes. An algorithm for the numerical evaluation of an optimal control is proposed on the basis of Howar's iteration algorithm. Finally, some numerical results will be given in order to illustrate the system dynamics. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:141:y:2006:i:1:p:139-162:10.1007/s10479-006-5297-5
    DOI: 10.1007/s10479-006-5297-5
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    References listed on IDEAS

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    1. Lothar Breuer, 2002. "An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure," Annals of Operations Research, Springer, vol. 112(1), pages 123-138, April.
    2. V. Rykov & M. Yu. Kitaev, 1995. "Controlled queueing systems," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-3, January.
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    Cited by:

    1. Ciro D’Apice & Maria Pia D’Arienzo & Alexander Dudin & Rosanna Manzo, 2023. "Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers," Mathematics, MDPI, vol. 11(21), pages 1-34, November.
    2. Velika I. Dragieva, 2016. "Steady state analysis of the M/G/1//N queue with orbit of blocked customers," Annals of Operations Research, Springer, vol. 247(1), pages 121-140, December.
    3. 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.
    4. 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.
    5. Srinivas R. Chakravarthy & Alexander N. Dudin & Sergey A. Dudin & Olga S. Dudina, 2023. "Queueing System with Potential for Recruiting Secondary Servers," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    6. E. Lerzan Örmeci & Evrim Didem Güneş & Derya Kunduzcu, 2016. "A Modeling Framework for Control of Preventive Services," Manufacturing & Service Operations Management, INFORMS, vol. 18(2), pages 227-244, May.

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