Estimating Hop Counts in Position Based Routing Schemes for Ad Hoc Networks ∗

Abstract. The recent availability of small, inexpensive low power GPS receivers and techniques for finding relative coordinates based on signal strengths, and the need for the design of power efficient and scalable networks, provided justification for applying position based routing methods in ad hoc networks. A number of such algorithms were developed recently. They are all based on three greedy schemes, applied when the forwarding node is able to advance the message toward destination. In this paper we show that the hop count, that is the number of transmissions needed to route a message from a source node to a destination node can be estimated reasonably accurately (in random unit graphs with uniform traffic), with less than 10%, 5 % and 7 % error for directional (compass), distance (greedy) and progress (MFR) based schemes, respectively, for 100 nodes with average degrees between 5 and 14, without experiments. Our results are derived from statistical observations regarding expected position of forwarding neighbor