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Heavy traffic approximation for the stationary distribution of stochastic fluid networks

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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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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Canada

    Jean-Paul Haddad & Ravi R. Mazumdar

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  1. Jean-Paul Haddad
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  2. Ravi R. Mazumdar
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Correspondence to Jean-Paul Haddad.

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Haddad, JP., Mazumdar, R.R. Heavy traffic approximation for the stationary distribution of stochastic fluid networks. Queueing Syst 70, 3–21 (2012). https://doi.org/10.1007/s11134-011-9256-8

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  • DOI: https://doi.org/10.1007/s11134-011-9256-8

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