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Analysis of the MAP/PH/1/K queue with service control

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  • S. Chakravarthy

Abstract

We consider a finite capacity queue with Markovian arrivals, in which the service rates are controlled by two pre‐determined thresholds, M and N. The service rate is increased when the buffer size exceeds N and then brought back to normal service rate when the buffer size drops to M. The normal and fast service times are both assumed to be of phase type with representations (β, S), and β θS), respectively, where θ>1. For this queueing model, steady state analysis is performed. The server duration in normal as well as fast periods is shown to be of phase type. The departure process is modelled as a MAP and the parameter matrices of the MAP are identified. Efficient algorithms for computing system performance measures are presented. We also discuss an optimization problem and present an efficient algorithm for arriving at an optimal solution. Some numerical examples are discussed.

Suggested Citation

  • S. Chakravarthy, 1996. "Analysis of the MAP/PH/1/K queue with service control," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 12(3), pages 179-191, September.
    • Handle: RePEc:wly:apsmda:v:12:y:1996:i:3:p:179-191
    DOI: 10.1002/(SICI)1099-0747(199609)12:33.0.CO;2-U
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