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The authors consider a network where each route comprises a backlogged source, a number of relays and a destination at a finite distance. The locations of the sources and the relays are realizations of independent Poisson point processes. Given that the nodes observe a TDMA/ALOHA MAC protocol, their objective is to determine the number of relays and their placement such that the mean end-to-end delay in a typical route of the network is minimized. They first study an idealistic network model where all routes have the same number of hops, the same distance per hop and their own dedicated relays. Combining tools from queueing theory and stochastic geometry, they provide a precise characterization of the mean end-to-end delay.
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