Asymptotic Critical Transmission Radii for Greedy Forward Routing in Wireless Ad Hoc Networks

In wireless ad hoc networks, greedy forward routing is a localized geographic routing algorithm in which one node discards a packet if none of its neighbors is closer to the destination of the packet than itself, or otherwise forwards the packet to the neighbor closest to the destination. If all nodes have the same transmission radii, the critical transmission radius for greedy forward routing is the smallest transmission radius which ensures packets can be delivered by greedy forward routing through any source-destination pair. In this paper, we study asymptotic critical transmission radii of randomly deployed wireless ad hoc networks. Assume network nodes are represented by a Poisson point process of density n over a unit-area convex compact region whose boundary curvature is bounded. We show that the ratio of critical transmission radii to radic (lnn/pin) is asymptotically almost surely equal to radic (1/ (2/3 - radic(3)/2pi)) ap 1.6.