Optimum number of hops of linear multi-hop networks with equidistant relays

The optimum number of hops that can minimize the end-to-end delay of linear multi-hop networks with equidistant relays is studied in this paper. In the network, a source delivers message to its destination by using other nodes as relays. Each hop employs decode-and-forward (DF) with automatic repeat request (ARQ). Two scenarios are considered: one is a noise-limited environment, and the other is an interference-limited environment. The average end-to-end delays of both operation environment are derived as closed-form expressions of a number of parameters, such as the source-destination distance, the number of hops, the transmission and noise power, etc. With the analytical results, the optimum numbers of hops that can minimize the end-to-end delays of both scenarios are identified.