Séminaire des équipes de recherche

Asymptotic analysis of some coupled queues arising in telecommunication networks.

Séminaires organisés par l'équipe-projet RAP, entrée libre à 10h30.

  • Date : 4/02/2011
  • Lieu : Rocquencourt, bâtiment 9
  • Intervenants : Fabrice Guillemin, Orange Labs, Lannion, France
  • Organisateurs : Equipe de recherche RAP

Coupled servers frequently arise in models for telecommunication networks. The most well known example is certainly the generalized processor sharing queue introduced by Kleinrock in the 70's and studied by Fayolle and his collaborators in the 80's. When considering two classes of customers, the analysis of such models amounts to studying the characteristics of an associated random walk in the quarter plane, for instance its stationary probability distribution;
the study of the transient behaviour can be included in the analysis of the stationary regime. In practice, this reduces to a Riemann-Hilbert formulation on a contour. The resolution of such a problem reveals very difficult, notably because closed formulas are known only for the unit circle. Hence, in general, a conformal mapping has to be exhibited for explicit numerical computations. In this keynote, we present an alternative approach to this problem by using
the Riemann surfaces associated with the algebraic curves arising in the resolution of some quadratic equations. The closed formulas obtained via this approach are then used to obtain asymptotic results for the number of customers in the system. The method is illustrated in the case the GPS queue and for some other models arising in the study of ad-hoc networks and cable TV networks.

Mots-clés : Paris - Rocquencourt Séminaire RAP

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