Coupling in the queue with impatience: case of several servers

2017/11/08 by Moyal, Pascal
#37A25 #60G10 #60K25 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1711.02931

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.

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