A Stochastic Two-Dimensional Fluid Model

Nigel Geoffrey Bean · Małgorzata M. O’Reilly

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

Abstract

We introduce a Stochastic Two-Dimensional Fluid Model that consists of two stochastic fluid flows driven by the same underlying Markov chain, where one of the fluids is unconstrained. We develop the theoretical and numerical framework for the transient analysis of the model. We derive the important generator matrix of a particular Laplace-Stieltjes transform of the model, which is the foundation of our analysis. We use it to develop expressions for the Laplace-Stieltjes transforms of various performance measures for the transient analysis of the model and construct powerful algorithms for their numerical evaluation. An example of an application in a queueing environment is given.

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References

1995Stationary distributions for fluid flow models with or without brownian noise 1999Matrix analytic methods for stochastic fluid flows 2003Fluid Flow Models and Queues—A Connection by Stochastic Coupling 2005Efficient algorithms for transient analysis of stochastic fluid flow models 2004Risk processes analyzed as fluid queues 2004Transient Analysis of Fluid Flow Models via Stochastic Coupling to a Queue 2007Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier 2007Performance measures of a multi-layer Markovian fluid model

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2014The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process, which is a stochastic fluid model itself

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