Asymptotic analysis of flooding in CSMA-based large scale ad-hoc wireless networks

In this article, we study the asymptotic behavior of flooding in large scale wireless networks. Specifically, we derive an upper bound on the coverage of flooding when the number of nodes n in the network goes to infinity. We consider two different regimes of transmission radii: first, the case of constant transmission radius r where the percentage of covered nodes scales as O(nr2e−KSnr) for a constant KS > 0. In this case, as an important result, we observe that the percentage of covered nodes is upper bounded by a decreasing function, vanishing as the network size grows. Second, the case of vanishing rn (i.e., r decreases as n increases) is considered where it is shown in the literature that the minimum value of rn which maintains connectivity is √ log n/πn. In this case, a coverage percentage of at most O(n−K ′ S log n) is expected for a constant value of K ′ S > 0, leading to an infinite number of covered nodes. In such case, the rate at which the network coverage is decreased can be controlled and be considerably reduced by a proper choice of network parameters (K ′ S). Consequently, this result shows that flooding is a suitable strategy even for large networks.