On the maximum throughput of a single chain wireless multi-hop path

In this paper, the maximum achievable throughput of a single chain wireless multi-hop path is investigated analytically. First, we prove that in an error free radio environment, a wireless multi-hop path (the number of hops k ges 3), in which all nodes are optimally placed and all links have an identical normalized capacity of 1, has a maximum achievable throughput of 1/3. Moreover, we show that this maximum throughput can only be achieved when all links of the path are separated into three maximal independent sets and each set of links become active alternatively for the same amount of time. Second, we extend our analysis to an erroneous radio environment, and prove that the maximum throughput of the k-hop path is determined by its bottleneck consecutive three-hop segment. That is, the maximum throughput of the k-hop path is the minimum of the maximum throughputs of all its consecutive three-hop segments. The findings in this paper lay guidelines for designing optimum scheduling algorithms.