Alonson Silva, INRIA Sophia

Location :

SUPELEC
3 rue Joliot-Curie
91192 GIF SUR YVETTE CEDEX
France

Abstract :

Computing optimal routes in massively dense ad-hoc networks becomes intractable as the
number of nodes becomes very large. One recent approach to solve this problem is to use
a fluid type approximation in which the whole network is replaced by a continuum plain.
Various paradigms from physics have been used recently in order to solve the continuum model.

We consider massively dense ad-hoc networks and study their continuum limits as the node
density increases and as the graph providing the available routes becomes a continuous area
with location and congestion dependent costs. We study both the global optimal solution as
well as the non-cooperative routing problem among a large population of users where each
user seeks a path from its source to its destination so as to minimize its individual cost.
We seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive
meaningful cost models as a function of the scaling properties of the capacity of the network
as a function of the density of nodes. We present various solution methodologies for the
problem: (1) the viscosity solution of the Hamilton-Bellman-Jacobi equation, for the global
optimization problem, (2) a method based on Green Theorem for the least cost problem of
an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation
into an equivalent global optimization problem.

SHORT BIOGRAPHY: Alonso Silva was born in 
Santiago, Chile. He received his B.Sc of 
Engineering and his Mathematical Engineering 
degree from the Universidad de Chile, in 2004 and 
2006 respectively. Currently, he is pursuing his 
Ph.D. degree at Maestro Team at INRIA and 
Chaire Alcatel-Lucent at Supelec. His thesis 
advisor is prof. Eitan Altman and his thesis co-
advisor is prof. Merouane Debbah. His research 
interests include optimal transportation, game 
theory. markov decision processes, and random 
matrix theory. 

Host :

Merouane Debbah