A simple upper bound on random access transport capacity

We attempt to quantify end-to-end throughput in multihop wireless networks using a metric that measures the maximum density of source-destination pairs that can successfully communicate over a specified distance at certain data rate. We term this metric the random access transport capacity, since it is similar to transport capacity but the interference model presumes uncoordinated transmissions. A simple upper bound on this quantity is derived in closed-form in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops - which is small and finite - and optimal per hop success probability for integer path loss exponents. We show that our result follows the well-known square root scaling law while providing exact expressions for the preconstants as well.