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1 results

  • Tail Asymptotics of the Stationary Distribution of a Two-Dimensional Reflecting Random Walk with Unbounded Upward Jumps

  • Part of
  • Masahiro Kobayashi, Masakiyo Miyazawa
  • Journal:
    Advances in Applied Probability / Volume 46 / Issue 2 / June 2014
    Published online by Cambridge University Press:
    22 February 2016, pp. 365-399
    Print publication:
    June 2014
    • Article
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  • We consider a two-dimensional reflecting random walk on the nonnegative integer quadrant. This random walk is assumed to be skip free in the direction to the boundary of the quadrant, but may have unbounded jumps in the opposite direction, which are referred to as upward jumps. We are interested in the tail asymptotic behavior of its stationary distribution, provided it exists. Assuming that the upward jump size distributions have light tails, we find the rough tail asymptotics of the marginal stationary distributions in all directions. This generalizes the corresponding results for the skip-free reflecting random walk in Miyazawa (2009). We exemplify these results for a two-node queueing network with exogenous batch arrivals.