Hop Count Distribution of Multihop Paths in Wireless Networks With Arbitrary Node Density: Modeling and Its Applications

The significance of hop counts on the throughput and delay performance in multihop wireless networks has been well demonstrated in the literature. However, so far, there has been very little analytical work on determining the expected hop count for packet forwarding in multihop wireless networks. In this paper, we develop an analytical framework for the hop count distribution in a multihop wireless network with an arbitrary node density. We derive the average progress per hop and obtain the path connectivity probability in a network. Together with the derived per-hop progress and the path connectivity probability, we can express the probability distribution for the expected hop count in multihop wireless networks. We also demonstrate that, based on our analytical result, many network design guidelines can be provided. Specifically, the average packet delivery ratio in the network under a hop count limitation can be estimated accurately, and the tradeoff between the flooding cost and the search latency for target location discovery that is commonly used in many ad hoc routing protocols can also be evaluated.