A Retrial BMAP/PH/N System

  • Authors:
  • Lothar Breuer;Alexander Dudin;Valentina Klimenok

  • Affiliations:
  • University of Trier, Department IV – Computer Science, 54286 Trier, Germany breuer@info04.uni-trier.de;Department of Applied Mathematics and Computer Science, Belarus State University, 4 F. Skorina Ave, 220050, Minsk, Belarus dudinby@bsu.by;Department of Applied Mathematics and Computer Science, Belarus State University, 4 F. Skorina Ave, 220050, Minsk, Belarus klimenokby@bsu.by

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2002

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Abstract

A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed. The continuous-time multi-dimensional Markov chain describing the behavior of the system is investigated by means of reducing it to the corresponding discrete-time multi-dimensional Markov chain. The latter belongs to the class of multi-dimensional quasi-Toeplitz Markov chains in the case of a constant retrial rate and to the class of multi-dimensional asymptotically quasi-Toeplitz Markov chains in the case of an infinitely increasing retrial rate. It allows to obtain the existence conditions for the stationary distribution and to elaborate the algorithms for calculating the stationary state probabilities.