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

Amber L. Puha · Ruth J. Williams

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

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.

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References

1998State space collapse with application to heavy traffic limits for multiclass queueing networks 1998Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse 1998Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models 1996Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks 1996Convergence to equilibria for fluid models of FIFO queueing networks 2002The fluid limit of a heavily loaded processor sharing queue 2004Diffusion approximation for a processor sharing queue in heavy traffic 2004Diffusion approximation for a processor sharing queue in heavy traffic

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2024Routing and Staffing in Customer Service Chat Systems with Generally Distributed Service and Patience Times 2012The fluid limit of the multiclass processor sharing queue

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