Asymptotic Queuing Analysis for Dynamic Spectrum Access Networks in the Presence of Heavy Tails

The heavy tailed nature exhibited in both primary and secondary users' traffic fundamentally challenges the performance limit of dynamic spectrum access (DSA) networks under the conventional light tailed assumptions. This paper provides an asymptotic analysis of the steady-state queue length distribution of secondary users (SUs) under the heavy tailed network environment. Specifically, two network scenarios are investigated. In the first scenario where each SU has its exclusive access to a primary user (PU) channel, it is shown that the heavy tailed nature of either the PU traffic or the SU traffic can make SUs experience heavy tailed queue length with unbounded moments. In the second scenario where multiple SUs share a single PU channel, the queuing performance under throughput optimal scheduling policies is studied. It is proven that if the PU traffic has a heavier tail than any SU traffic, the queue length of each SU is at least one order heavier than the PU traffic under any scheduling policy. Otherwise, if the traffic from at least one of the SUs has a heavier tail than the PU traffic, it is proven that the celebrated throughput-optimal maximum weight scheduling leads to the worst possible asymptotic queuing performance for SUs by letting each SU queue have the heaviest possible tail. On the contrary, it is shown that there always exists a feasible set of β parameters such that the maximum weight-β scheduling yields the best asymptotic performance for the SU queues by letting each queue have the lightest possible tail.