Heavy traffic approximation for the stationary distribution of stochastic fluid networks |
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Authors: | Jean-Paul Haddad Ravi R Mazumdar |
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Institution: | 1.Department of Electrical and Computer Engineering,University of Waterloo,Waterloo,Canada |
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Abstract: | It has recently been shown that in the heavy traffic limit, the stationary distribution of the scaled queue length process
of a Generalized Jackson Network converges to the stationary distribution of its corresponding Reflected Brownian Motion limit.
In this paper, we show that this “interchange of limits” is valid for Stochastic Fluid Networks with Lévy inputs. Furthermore,
under additional assumptions, we extend the result to show that the interchange is valid for moments of the stationary distribution
and for state-dependent routing. The results are obtained using monotonicity and sample-path arguments. |
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Keywords: | |
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