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Large deviations for a class of Markov processes modelling communication networks

Abstract : In this paper, we prove a sample path large deviation principle (LDP) for a rescaled process n^-1Q_nt, where Q_t is a multi-dimensional birth and death process describing the evolution of a communication network. In this setting, Q_t is the join number of documents on the set of routes at time t. Documents to be transferred arrive on route r as a Poisson process with rate _r and are transferred at rate _r_r(x) where x represents the state of the network, _r^-1 is the mean size of documents on route r and _r(x) is the bandwidth allocated to route r. We describe a set of assumptions over the allocation under which the LDP holds. Since we want the «classical» allocatio- ns to verify these assumptions, the difficulty is to deal with weak properties- . For example, _r(x) is assumed to be continuous on the set _r=x:x_r>0 but may be discontinuous elsewhere. Several examples are provided including the max-min-fairness allocation, a classical one in the context of data networks. Since the main object to work with is the local rate function, a great care has been devoted to its expression and its properties. It is expressed as the solution of a convex program from which many useful properties are derived. We believe that this kind of expression allows numerical computations.
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https://hal.inria.fr/inria-00072114
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Submitted on : Tuesday, May 23, 2006 - 7:49:29 PM
Last modification on : Friday, February 4, 2022 - 3:12:55 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:53:58 PM

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  • HAL Id : inria-00072114, version 1

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Franck Delcoigne, Arnaud de la Fortelle. Large deviations for a class of Markov processes modelling communication networks. [Research Report] RR-4474, INRIA. 2002. ⟨inria-00072114⟩

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