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We consider a two dimensional reflecting random walk on the nonnegativeinteger quadrant. This random walk is assumed to be skip free in the directionto the boundary of the quadrant, but may have unbounded jumps in the oppositedirection, which are referred to as upward jumps. We are interested in the tailasymptotic behavior of its stationary distribution, provided it exists.Assuming the upward jump size distributions have light tails, we completelyfind the rough tail asymptotics of the marginal stationary distributions in alldirections. This generalizes the corresponding results for the skip freereflecting random walk in Miyazawa (2009) [Mathematics of Operations Research34, 547-575]. We exemplify these results for a two node network with exogenousbatch arrivals.

Tail asymptotics of the stationary distribution of a two dimensional reflecting random walk with unbounded upward jumps