THE INPUT-OUTPUT MAP OF A MONOTONE DISCRETE-TIME QUASI-REVERSIBLE NODE

A class of discrete-time quasireversible nodes called monotone, which includes discrete-time analogs of the ./M/infinity and ./M/1 nodes is considered. For stationary ergodic nonnegative integer valued arrival processes, the existence and uniqueness of stationary regimes are prov en when a natural rate condition is met. Coupling is used to prove the contractiveness of the input-output map relative to a natural distanc e on the space of stationary arrival processes that is analogous to Or nstein's dBAR distance. A consequence is that the only stationary ergo dic fixed points of the input-output map are the processes of independ ent and identically distributed Poisson random variables meeting the r ate condition.