Annals of Operations Research

, Volume 141, Issue 1, pp 193–210 | Cite as

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

  • Che Soong 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.

Keywords

Batch Markovian arrival process Controlled operation modes Cost criterion Optimal control 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Che Soong Kim
    • 1
  • Valentina Klimenok
    • 2
  • Alexander Birukov
    • 2
  • Alexander Dudin
    • 2
  1. 1.Department of Industrial EngineeringSangji UniversityWonju, KangwonKorea
  2. 2.Department of Applied Mathematics and Computer ScienceBelarusian State UniversityMinsk

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