%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