Fluid Flow Models and Queues—A Connection by Stochastic Coupling

Soohan Ahn · V. Ramaswami

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Advanced Queuing Theory Analysis Probability and Statistical Research Stochastic processes and statistical mechanics

Abstract

We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from a quasi birth and death queue. This is accomplished through the construction of the processes on a common probability space and the demonstration of a distributional coupling relation between them. The results here provide an interpretation for the quasi-birth-and-death processes in the matrix-geometric approach of Ramaswami and subsequent results based on them obtained by Soares and Latouche.

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References

1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1982Stochastic Theory of a Data-Handling System with Multiple Sources 1982Poisson Arrivals See Time Averages 1993A logarithmic reduction algorithm for quasi-birth-death processes 1995Stationary distributions for fluid flow models with or without brownian noise 1980Stationary state probabilities at arrival instants for closed queueing networks with multiple types of customers 1999Matrix analytic methods for stochastic fluid flows 1990A duality theorem for the matrix paradigms in queueing theory

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