Invariant states and rates of convergence for a critical fluid model of a processor sharing queue

Ruth J. Williams, Amber L. Puha
2004 The Annals of Applied Probability  
This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid models as time approaches \infty. The main theorems of the paper provide sufficient conditions for a fluid model solution to converge to an invariant state and, under slightly more restrictive assumptions, provide a rate of convergence. These results are used in a related work by Gromoll for establishing a heavy traffic
more » ... ffusion approximation for a processor sharing queue.
doi:10.1214/105051604000000017 fatcat:ewui6padbre55pfilaemxijq24