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

What is it about?

A two-dimensional reflecting random walk on the nonnegative integer quadrant has a wide application area including queueing theory. In particular, it stationary distribution is important, but analytically hard to get. So, we study its tail asymptotics. Assuming that the upward jump size distributions have light tails, we find the rough tail asymptotics of the marginal stationary distributions in all directions.

Featured Image

Why is it important?

This paper assume that upward jumps may be unbounded, which relaxes the skip-free assumption for a multidimensional reflecting random walk. It enables us to study a two-node queueing network with exogenous batch arrivals. Another important feature is to use geometric objects for answering the tail asymptotics. Thus, the results such as tail decay rates are visible, and easy to see how they are influenced by modeling primitives.