On the scaling of non-asymptotic capacity in multi-access networks with bursty traffic

The practicality of available (throughput) capacity results in multi-access networks, which dispense with coding schemes, is often questioned for several reasons including 1) the underlying asymptotic regimes, and 2) the assumption of saturated traffic sources. This paper jointly addresses these limitations by providing capacity results in non-asymptotic regimes, i.e., holding at all time scales and network sizes, for the very broad class of exponentially bounded burstiness (EBB) traffic sources. Both upper and lower bounds on capacity are derived in terms of probability distributions, which immediately yield all the moments. The explicit and closed-form nature of the results enable the investigation of the impact of burstiness on non-asymptotic network capacity. In particular, the results show that for the EBB class the non-asymptotic end-to-end capacity rate decays linearly in the number of hops.