Stability of a processor sharing queue with varying throughput

TL;DR

This paper establishes a stability criterion for processor sharing queues where throughput varies with the number of customers, modeled through a measure-valued stochastic recursion.

Contribution

It introduces a novel stability analysis for processor sharing queues with throughput depending on system state, using a measure-valued stochastic recursion framework.

Findings

Derived a stability criterion for variable throughput queues

Modeled the system with a measure-valued stochastic recursion

Provides insights into queue stability under interference effects

Abstract

In this paper, we present a stability criterion for Processor Sharing queues, in which the throughput may depend on the number of customers in the system (in such cases such as interferences between the users). Such a system is represented by a point measure-valued stochastic recursion keeping track of the remaining processing times of the customers.