Measure-valued stochastic recurrences and the stability of queues
Pascal Moyal

TL;DR
This paper extends Loynes's Theorem to measure-valued stochastic recursions, providing stability criteria for complex queueing systems with infinitely many servers or single-server SRPT queues, ensuring the existence of stationary states.
Contribution
It introduces a stability criterion for measure-valued recursions, generalizing classical results to more complex queueing models with infinite measure spaces.
Findings
Established conditions for the existence of stationary measure-valued recursive sequences.
Provided a stability criterion applicable to queues with infinitely many servers.
Characterized the stationary states for the studied queueing systems.
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.
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Taxonomy
TopicsAdvanced Queuing Theory Analysis · Probability and Risk Models · Simulation Techniques and Applications
