Construction of a stationary queue with impatient customers
Probability
2010-09-08 v2
Abstract
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.
Cite
@article{arxiv.0709.3012,
title = {Construction of a stationary queue with impatient customers},
author = {Pascal Moyal},
journal= {arXiv preprint arXiv:0709.3012},
year = {2010}
}
Comments
This paper has been withdrawn by the author. This paper has been published in a newer version, arXiv:0802.2495