Skip to Main content Skip to Navigation
Journal articles

Continuum equilibria and global optimization for routing in dense static ad hoc networks

Eitan Altman 1 Pierre Bernhard 2 Merouane Debbah 3 Alonso Silva 1, 3
1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
2 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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 origin to its destination so as to minimize its individual cost. Finally, 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 and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a method based on Green's 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.
Complete list of metadata

https://hal.inria.fr/hal-00847271
Contributor : Jean-Luc Gouzé <>
Submitted on : Tuesday, July 23, 2013 - 11:22:14 AM
Last modification on : Monday, December 14, 2020 - 2:36:02 PM

Links full text

Identifiers

Citation

Eitan Altman, Pierre Bernhard, Merouane Debbah, Alonso Silva. Continuum equilibria and global optimization for routing in dense static ad hoc networks. Computer Networks, Elsevier, 2010, 54 (6), pp.1005--1018. ⟨10.1016/j.comnet.2009.10.019⟩. ⟨hal-00847271⟩

Share

Metrics

Record views

504