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We consider a two dimensional reflecting random walk on the nonnegativeinteger quadrant. It is assumed that this reflecting random walk has skip freetransitions. We are concerned with its time reversed process assuming that thestationary distribution exists. In general, the time reversed process may notbe a reflecting random walk. In this paper, we derive necessary and sufficientconditions for the time reversed process also to be a reflecting random walk.These conditions are different from but closely related to the product form ofthe stationary distribution.

Structure-reversibility of a two dimensional reflecting random walk and its application to queueing network