2007/09/19 by Pascal Moyal, Moyal, Pascal
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.0709.3012
This paper has been withdrawn by the author. This paper has been published in a newer version, arXiv:0802.2495
arxiv created 2010/09/07 · arxiv updated 2010/09/08
In this paper, we study the stability of queues with impatient customers. Under general stationary ergodic assumptions, we first provide some conditions for such a queue to be regenerative (i.e. to empty a.s. an infinite number of times). In the particular case of a single server operating in First in, First out, we prove the existence (in some cases, on an enlarged probability space) of a stationary workload. This is done by studying a non-monotonic stochastic recursion under the Palm settings, and by stochastic comparison of stochastic recursions.