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Stochastic Hybrid Systems: Application to Communication Networks

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Hybrid Systems: Computation and Control (HSCC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2993))

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Abstract

We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for Piecewise-Deterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finite-dimensional model.

This material is based upon work supported by the National Science Foundation under Grants No. CCR-0311084, ANI-0322476.

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Author information

Authors and Affiliations

  1. Dept. of Electrical and Computer Eng., Univ. of California, Santa Barbara, CA, 92106-9560, USA

    João P. Hespanha

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  1. João P. Hespanha
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Editor information

Editors and Affiliations

  1. University of Pennsylvania,  

    Rajeev Alur

  2. School of Engineering and Applied Science, University of Pennsylvania,  

    George J. Pappas

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© 2004 Springer-Verlag Berlin Heidelberg

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Hespanha, J.P. (2004). Stochastic Hybrid Systems: Application to Communication Networks. In: Alur, R., Pappas, G.J. (eds) Hybrid Systems: Computation and Control. HSCC 2004. Lecture Notes in Computer Science, vol 2993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24743-2_26

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  • DOI: https://doi.org/10.1007/978-3-540-24743-2_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21259-1

  • Online ISBN: 978-3-540-24743-2

  • eBook Packages: Springer Book Archive

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