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Optimal multi-threshold control by the BMAP/SM/1 retrial system

Author

Listed:
  • Che Kim
  • Valentina Klimenok
  • Alexander Birukov
  • Alexander Dudin

Abstract

A single server retrial system having several operation modes is considered. The modes are distinguished by the transition rate of the batch Markovian arrival process (BMAP), kernel of the semi-Markovian (SM) service process and the intensity of retrials. Stationary state distribution is calculated under the fixed value of the multi-threshold control strategy. Dependence of the cost criterion, which includes holding and operation cost, on the thresholds is derived. Numerical results illustrating the work of the computer procedure for calculation of the optimal values of thresholds are presented. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Che Kim & Valentina Klimenok & Alexander Birukov & Alexander Dudin, 2006. "Optimal multi-threshold control by the BMAP/SM/1 retrial system," Annals of Operations Research, Springer, vol. 141(1), pages 193-210, January.
    • Handle: RePEc:spr:annopr:v:141:y:2006:i:1:p:193-210:10.1007/s10479-006-5299-3
    DOI: 10.1007/s10479-006-5299-3
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    References listed on IDEAS

    as
    1. Alexander Dudin & Srinivas Chakravarthy, 2002. "Optimal Hysteretic Control for the BMAP/G/ 1 System with Single and Group Service Modes," Annals of Operations Research, Springer, vol. 112(1), pages 153-169, April.
    2. Alexander N. Dudin & Valentina I. Klimenok, 1999. "Multi-dimensional quasitoeplitz Markov chains," International Journal of Stochastic Analysis, Hindawi, vol. 12, pages 1-23, January.
    3. Choi, B. D. & Chung, Y. H. & Dudin, Alexander N., 2001. "The BMAP/SM/1 retrial queue with controllable operation modes," European Journal of Operational Research, Elsevier, vol. 131(1), pages 16-30, May.
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    Cited by:

    1. 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.
    2. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.

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