%0 Journal Article
%T Measure-valued stochastic recurrences and the stability of queues
%A Pascal Moyal
%J Mathematics
%D 2007
%I arXiv
%X 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.
%U http://arxiv.org/abs/0706.0817v2