End-to-End Throughput Analysis of Multi-Hop Wireless Networks Using Stochastic Geometry

This paper investigates the effect of relay randomness on the end-to-end throughput in multi-hop wireless networks using stochastic geometry. We model the nodes as Poisson Point Processes and calculate the spatial average of the throughput over all potential geometrical patterns of the nodes, with no constraints on the relay density or routing distance. More specifically, first, assuming nearest neighbor routing protocol, we derive the distribution of the longest hop distance in a multi-hop route for any given routing distance. Second, we analyze the average end-to-end throughput under the TDMA protocol. Our analysis indicates that compared with the relay-free case, even randomly distributed relays can significantly extend the communication distance. It is also observed that systems with equidistant relays generally achieve much higher throughput than those with random relays. Moreover, the optimal relay intensity varies with the routing distance, node density and interference levels. Our results are demonstrated through numerical examples.