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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.
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Submitted on : Tuesday, July 23, 2013 - 11:22:14 AM
Last modification on : Thursday, January 20, 2022 - 5:28:32 PM

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



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