Measure-valued stochastic recurrences and the stability of queues
Probability
2010-09-08 v2
Abstract
In this paper we present a stability criterion for finite measure-valued stochastic recursions, generalizing Loynes's Theorem to spaces of measures. This result provides conditions for the reach of a "total stationary state" for the queue with an infinity of servers and the single-server SRPT queue. Indeed, we give in both cases a condition of existence of a stationary measure-valued recursive sequence characterizing the queueing system exhaustively.
Keywords
Cite
@article{arxiv.0706.0817,
title = {Measure-valued stochastic recurrences and the stability of queues},
author = {Pascal Moyal},
journal= {arXiv preprint arXiv:0706.0817},
year = {2010}
}
Comments
This paper has been withdrawn by the author. This paper has been published in a newer version, arXiv:0803.2459