Masahiro Kobayashi
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.
- A. A. Borovkov and A. A. Mogul'skii (2001) Large deviations for Markov chains in the positive quadrant, Russian Math. Surveys 56, 803--916.Google Scholar
Cross Ref
- W. L. Feller (1971) An Introduction to Probability Theory and Its Applications, 2nd edition, John Wiley&Sons, New York.Google Scholar
- M. Miyazawa (2009) Tail decay rates in double QBD processes and related reflected random walks, to appear in Mathematics of Operations Research. Google ScholarDigital Library
- M. Miyazawa and P. G. Taylor (1997) A geometric product-form distribution for a queueing network with non-standard batch arrivals and batch transfers. Adv. Appl. Prob. 29, 523--544Google ScholarCross Ref
- The tail asymptotic behavior of the stationary distribution of a double M/G/1 process and their applications to a batch arrival Jackson network
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