Fluid Model Driven by an Ornstein-Uhlenbeck Process

V. G. Kulkarni · Tomasz Rolski

45 citations0/0 files storedProbability in the Engineering and Informational Sciences

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

Abstract

In this paper we consider a fluid model of a single buffer in a random external environment modeled by an Ornstein-Uhlenbeck process. Such a model appears as the limiting case of the multiplexing model of Anick, Mitra, and Sondhi [2] in a heavy traffic environment. We use the change of measure technique to derive an exponential upper bound on the tail probabilities of the steady-state buffer content. We also establish an asymptotic upper and lower exponential bounds on the tail probabilities.

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References

1982Stochastic Theory of a Data-Handling System with Multiple Sources 1980MULTI-DIMENSIONAL DIFFUSION PROCESSES 1987Brownian Motion and Stochastic Flow Systems.1976Stochastic Processes in Queueing Theory 1986Asymptotic Methods in Queueing Theory.1965Limiting diffusion approximations for the many server queue and the repairman problem 1985Asymptotic methods in queueing theory 1991Heavy-Traffic Analysis of a Data-Handling System with Many Sources

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1998Markov-modulated and feedback fluid queues 1999On–off fluid models in heavy traffic environment 1995A Gaussian fluid model

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