An Upper Bound on Network Size in Mobile Ad-Hoc Networks

In this paper we propose a model to compute an upper bound for the maximum network size in mobile ad-hoc networks. Our model is based on the foundation that for a unicast route to be useful to initiate data transport, it is necessary that the time required to discover the route should be shorter than the time the route remains valid. From this model, we found that the node transmission range, mobility of nodes and number of contending nodes actually define the maximum feasible number of hops in a route, and therefore the maximum network size. Our model is derived from the combination of a route duration model, that we also derive in this paper, and a delay model for multi-hop routes extended from a single-hop delay model found in the literature. We evaluate our model numerically for different network conditions. To the best of our knowledge, this is the first time that a comparison between route discovery time and route duration is analyzed in order to establish the maximum network size in ad-hoc networks. We believe this is a fundamental scaling problem of ad-hoc networks that has not been looked at before from a mobility-delay perspective.