On the Random 1/2-Disk Routing Scheme in Wireless Ad Hoc Networks

TL;DR

This paper analyzes the random 1/2-disk routing scheme in wireless ad hoc networks, introducing a convergence concept and deriving conditions for finite-hop packet delivery with bounds on expected hops.

Contribution

It introduces a convergence notion for geometric routing and provides sufficient conditions and bounds for packet delivery in the random 1/2-disk routing scheme.

Findings

Convergence conditions ensure finite-hop delivery.

Modeling as a Markov process yields hop count bounds.

The scheme guarantees packet delivery under certain conditions.

Abstract

Random 1/2-disk routing in wireless ad-hoc networks is a localized geometric routing scheme in which each node chooses the next relay randomly among the nodes within its transmission range and in the general direction of the destination. We introduce a notion of convergence for geometric routing schemes that not only considers the feasibility of packet delivery through possibly multi-hop relaying, but also requires the packet delivery to occur in a finite number of hops. We derive sufficient conditions that ensure the asymptotic \emph{convergence} of the random 1/2-disk routing scheme based on this convergence notion, and by modeling the packet distance evolution to the destination as a Markov process, we derive bounds on the expected number of hops that each packet traverses to reach its destination.