The tail asymptotic behavior of the stationary distribution of a double M/G/1 process and their applications to a batch arrival Jackson network

  • Authors:

  • Masahiro Kobayashi;Masakiyo Miyazawa

  • Affiliations:

  • Tokyo University of Science;Tokyo University of Science

  • Venue:
  • Proceedings of the 4th International Conference on Queueing Theory and Network Applications
  • Year:
  • 2009

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Abstract

We consider a two dimensional reflected random walk on the nonnegative integer quadrant. This random walk is assumed to be skip free in the direction to the boundary, and referred to as a double M/G/1-type process. We are interested in tail asymptotic behavior of its stationary distribution, provided it exists. Assuming the arriving batch size distributions have light tails, we derive supremum for rough decay rates of the marginal stationary distributions in the coordinate directions. We then apply these results to a batch arrival Jackson network with two nodes. It is shown that the stochastic upper bound of Miyazawa and Taylor [4] is not tight except for a special case.