Analytical Study of the Expected Number of Hops in Wireless Ad Hoc Network

摘要

Due to the randomness and mobility of ad hoc networks, estimating the average number of hops becomes very essential in multi-hop ad hoc networks, which is used as a key metric for performance comparison between multi-hop routing protocols;however, most current research derives the average number of hops based on simulations and empirical results, lacking the theoretical analysis of this essential metric. This paper presents a theoretical study of the expected number of hops between any two random nodes using typical modeling assumptions -an N-node randomly Poisson distributed connected network (i.e. for any two random nodes, they are connected by at least one path). The proposed theoretical analysis studies the relationship between the average number of hop counts and other critical ad hoc network parameters such as transmission range (r_0), node density (p), and area (A). At last, simulation results will be given to verify the theoretical analysis.