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

Puha, Amber L.; Williams, Ruth J.

Ann. Appl. Probab., Tome 14 (2004) no. 1, p. 517-554 / Harvested from Project Euclid

Résumé

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 ∞. 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 diffusion approximation for a processor sharing queue.

Publié le : 2004-05-14
Classification: Processor sharing queue, critical fluid model, measure-valued solution, invariant states, coupling renewal processes, renewal functions, renewal measures, 60K25, 68M20, 90B22

@article{1082737103,
     author = {Puha, Amber L. and Williams, Ruth J.},
     title = {Invariant states and rates of convergence for a critical fluid model of a processor sharing queue},
     journal = {Ann. Appl. Probab.},
     volume = {14},
     number = {1},
     year = {2004},
     pages = { 517-554},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082737103}
}

Puha, Amber L.; Williams, Ruth J. Invariant states and rates of convergence for a critical fluid model of a processor sharing queue. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp.  517-554. http://gdmltest.u-ga.fr/item/1082737103/