A multiclass Station with Markovian Feedback in Heavy Traffic

Jim G. Dai · Thomas G. Kurtz

30 citations0/0 files storedMathematics of Operations Research

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

Abstract

This paper proves a heavy traffic limit theorem for a multiclass service station with Markovian feedback. This result generalizes the one proved by Reiman (Reiman, M. I. 1988. A multiclass feedback queue in heavy traffic. Adv. Appl. Probab. 20 179–207.). Our approach also significantly simplifies Reiman's original proof. Numerical examples are presented to illustrate the effectiveness of the QNET method which is rooted in the theorem.

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References

1987Brownian Motion and Stochastic Flow Systems.1995On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models 1984Open Queueing Networks in Heavy Traffic 1970Multiple channel queues in heavy traffic. I 1970Multiple channel queues in heavy traffic. II: sequences, networks, and batches 1994Instability of FIFO Queueing Networks 1993Brownian models of multiclass queueing networks: Current status and open problems 1993Nonexistence of Brownian models for certain multiclass queueing networks

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2011Performance Analysis of Queueing Networks via Robust Optimization 2016Stochastic Processing Networks 1994On the Convergence of Multiclass Queueing Networks in Heavy Traffic 2000A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines 1996Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline

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