Abstract
This paper evaluates the end-to-end delay in multi-hop wireless networks with random relays using stochastic geometry. We model the nodes as Poisson Point Processes and calculate the spatial average of the delay over all potential geometrical patterns of the nodes. More specifically, first, under a simple automatic repeat request (ARQ) retransmission protocol, we derive the average end-to-end delay and show that the average delay scales super exponentially with the increase of routing distance. Then we apply the maximal ratio combining (MRC) technique in ARQ, and derive an upper bound of the average end-to-end delay. We show that a linear scaling law of the delay with respect to the routing distance can be obtained with the help of MRC. Our analysis is demonstrated through simulation examples.
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