Competitive time and traffic analysis of position-based routing using a cell structure

We present a strategy for organizing the communication in wireless ad hoc networks based on a cell structure. We use the unit disk graph model and assume positioning capabilities for all nodes. The cell structure is an abstract view on the network and represents regions where nodes reside (node cells), regions that can be used for the communication flow (link cells) and regions that cannot be bridged due to the restricted transmission range (barrier cells). The cell structure helps to determine local minima for greedy forwarding and improves recovery from such minima, because for recovery all edges can be used in contrast to other topology-based rules that work only on a planar subgraph. For the analysis of position-based routing algorithms the measures time and traffic are based on the cell structure. The difficulty of exploring the network is expressed by the size of the barriers (number of cells in the perimeters). Exploration can be done in parallel, but with increasing traffic. We propose a comparative measure to assess both time and traffic, the combined comparative ratio, which is the maximum of the ratio of routing time and optimal time and the ratio of the traffic and the minimum exploration costs. While flooding and common single-path strategies have a linear ratio, we present a simple algorithm that has a sub-linear combined comparative ratio of O(√h), where h is the minimal hop distance between source and target.