Coupling in the queue with impatience: case of several servers

Abstract

We present the explicit construction of a stable queue with several servers and impatient customers, under stationary ergodic assumptions. Using a stochastic comparison of the (multivariate) workload sequence with two monotonic stochastic recursions, we propose a sufficient condition of existence of a unique stationary state of the system using Renovation theory. Whenever this condition is relaxed we use extension techniques to prove the existence of a stationary state in some cases.