On the Origins of Heavy-Tailed Delay in Dynamic Spectrum Access Networks

Abstract

This paper provides an asymptotic analysis of the transmission delay experienced by SUs for dynamic spectrum access (DSA) networks. It is shown that DSA induces only light-tailed delay if both the busy time of PU channels and the message size of SUs are light tailed. On the contrary, if either the busy time or the message size is heavy tailed, then the SUs' transmission delay is heavy tailed. For this latter case, it is proven that if one of either the busy time or the message size is light tailed and the other is regularly varying with index \alpha, the transmission delay is regularly varying with the same index. As a consequence, the delay has an infinite mean provided \alpha < 1 and an infinite variance provided \alpha < 2. Furthermore, if both the busy time and the message size are regularly varying with different indices, then the delay tail distribution is as heavy as the one with the smaller index. Moreover, the impact of spectrum mobility and multiradio diversity on the delay performance of SUs is studied. It is shown that both spectrum mobility and multiradio diversity can greatly mitigate the heavy-tailed delay by increasing the orders of its finite moments.