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Pathwise comparison results for stochastic fluid networks

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Abstract

We prove some new pathwise comparison results for single class stochastic fluid networks. Under fairly general conditions, monotonicity with respect to the (state- and time-dependent) routing matrices is shown. Under more restrictive assumptions, monotonicity with respect to the service rates is shown as well. We conclude by using the comparison results to establish a moment bound, a stability result for stochastic fluid networks with Lévy inputs, and a comparison result for multi-class GPS networks.

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Authors and Affiliations

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

    Jean-Paul Haddad & Ravi R. Mazumdar

  2. Electrical Engineering Department, University of Chile, Av. Tupper 2007, Santiago, Chile

    Francisco J. Piera

Authors
  1. Jean-Paul Haddad
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  2. Ravi R. Mazumdar
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  3. Francisco J. Piera
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Correspondence to Ravi R. Mazumdar.

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Haddad, JP., Mazumdar, R.R. & Piera, F.J. Pathwise comparison results for stochastic fluid networks. Queueing Syst 66, 155–168 (2010). https://doi.org/10.1007/s11134-010-9187-9

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  • DOI: https://doi.org/10.1007/s11134-010-9187-9

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