Decay rate for a PH/M/2 queue with shortest queue discipline

  • Authors:

  • Yutaka Sakuma;Masakiyo Miyazawa;Yiqiang Q. Zhao

  • Affiliations:

  • Department of Information Sciences, Tokyo University of Science, Tokyo;Department of Information Sciences, Tokyo University of Science, Tokyo;School of Mathematics and Statistics, Carleton University, Ottawa

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2006

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Abstract

In this paper, we consider a PH/M/2 queue in which each server has its own queue and arriving customers join the shortest queue. For this model, it has been conjectured that the decay rate of the tail probabilities for the shortest queue length in the steady state is equal to the square of the decay rate for the queue length in the corresponding PH/M/2 model with a single queue. We prove this fact in the sense that the tail probabilities are asymptotically geometric when the difference of the queue sizes and the arrival phase are fixed. Our proof is based on the matrix analytic approach pioneered by Neuts and recent results on the decay rates.