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Hop Count Distributions of the Furthest and Nearest Distance Routing Protocols in Mobile Ad Hoc Networks

Antunes, Nelson; Jacinto, G.; Pacheco, António

SIAM Journal on Applied Mathematics, 75(2) (2015), 335–349

In this paper, we derive the probability distribution of the number of hops required for a source node to reach a destination node in a two-dimensional mobile ad hoc network when a fixed number of nodes are uniformly distributed in a finite region under the nearest- and furthest-distance routing protocols. To achieve efficient progress towards the destination, a new dynamic propagation model is proposed. The analysis is based on the Poisson randomization technique which also allows us to obtain the hop count distribution when nodes are scattered according to a Poisson process. Numerical results are obtained to illustrate the shape of the hop count distribution for both protocols.