Structure-Reversibility of a Two-Dimensional Reflecting Random Walk and Its Application to Queueing Network

Abstract

We consider a two-dimensional reflecting random walk on the non-negative integer quadrant. It is assumed that this reflecting random walk has skip-free transitions. We are concerned with its time-reversed process assuming that the stationary distribution exists. In general, the time-reversed process may not be a reflecting random walk. In this paper, we derive necessary and sufficient conditions for the time-reversed process also to be a reflecting random walk. These conditions are different from but closely related to the product form of the stationary distribution.

Simple error bounds for the QBD approximation of a special class of two dimensional reflecting random walks

“…On the other hand, for some special 2D-RRWs, the product-form solution [13], the mixedgeometric-form solution [4] and the partially geometric solution [12] of the stationary distribution are derived. Although these solutions are tractable and useful, they require restrictive conditions.…”