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Modelling and Optimization of Stochastic Routing for Wireless Multi-Hop Networks

We introduce a novel approach to multi-hop routing in wireless networks. Instead of the usual graph description we characterize the network by the packet delivery ratio matrix whose entries represent the probability that a given node decodes the packet transmitted by any other node. The model lends itself naturally to the formulation of stochastic routing protocols in which packets are randomly routed to neighboring nodes; and routing algorithms search for a matrix of routing probabilities according to properly defined optimality criteria. The goal of the paper is to show that this novel framework offers a useful model to aid in the design of optimal routing algorithms. In particular, it is established that: (i) performance is improved with respect to graph descriptions; and (ii) optimal routes can be obtained as the solution of optimization problems, many of which turn out to be convex and can thus be solved in polynomial time using interior point methods.