Delay Characterization of Multihop Transmission in a Poisson Field of Interference

We evaluate the end-to-end delay of a multihop transmission scheme that includes a source, a number of relays, and a destination, in the presence of interferers located according to a Poisson point process. The medium access control (MAC) protocol considered is a combination of TDMA and ALOHA, according to which nodes located a certain number of hops apart are allowed to transmit with a certain probability. Based on an independent transmissions assumption, which decouples the queue evolutions, our analysis provides explicit expressions for the mean end-to-end delay and throughput, as well as scaling laws when the interferer density grows to infinity. If the source always has packets to transmit, we find that full spatial reuse, i.e., ALOHA, is asymptotically delay-optimal, but requires more hops than a TDMA-ALOHA protocol. The results of our analysis have applications in delay-minimizing joint MAC/routing algorithms for networks with randomly located nodes. We simulate a network where sources and relays form a Poisson point process, and each source assembles a route to its destination by selecting the relays closest to the optimal locations. We assess both theoretically and via simulation the sensitivity of the end-to-end delay with respect to imperfect relay placements and route crossings.