On the asymmetric clocked buffered switch

A 2 x 2 clocked buffered switch is a device used in data-processing network s for routing messages from one node to another. The message handling proce ss of this switch can be modelled as a two-server, time slotted, queueing p rocess with state space the number of messages (x(n),y(n)) present at the s ervers at the end of a time slot. The (x(n),y(n))-process is a two-dimensio nal nearest-neighbour random walk. In the present study the bivariate gener ating function Phi(p, q) of the stationary distribution of this random walk is determined, assuming that this distribution exists. Phi(p,q) is known, whenever Phi(p,0) and Phi(0, q) are known. The essential points of the pres ent study are the construction of these two functions from the knowledge of their poles and zeros and the simple determination of these poles and zero s.