| We define an Aloha type access control mechanism for large mobile, multihop, wireless networks. This mechanism is based on a new representation of the interferences and hence of the collisions adapted to the context of large networks with random mobility. The mechanism is designed for the multihop context, where it is important to find a compromise between the spatial density of communications and the range of each transmission. More precisely, it is possible to optimize the product of the number of simultaneously successful transmissions per unit of space (spatial reuse) by the average range of each transmission. The optimization is obtained via an averaging over all Poisson configurations for the location of interfering mobiles. The main mathematical tools stem from stochastic geometry and are spatial versions of the so called additive and max shot noise processes. The resulting MAC protocol can be implemented in a decentralized way provided some local geographic informations are available to the mobiles. Its transport capacity is proportional to the square root of the density of mobiles; under certain mobility and stability conditions discussed in the paper, the delay for transporting information from one mobile to any another is proportional to the distance between them and to the square root of the density of mobiles. |
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