Can dynamic spectrum access induce heavy tailed delay?

Abstract

Dynamic Spectrum Access (DSA) allows secondary users (SUs) to opportunistically transmit when the channels belonging to primary users (PUs) are idle. This paper provides an asymptotic analysis of the transmission delay experienced by SUs for DSA networks. It is shown that DSA induces only light-tailed delay as long as 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 α, then the transmission delay is regularly varying with the same index α. As a consequence, the delay has an infinite mean provided α <1 and an infinite variance provided α <2. Furthermore, if both the busy time and the message size are regularly varying with index α and α, respectively, then the tail distribution of the delay is as heavy as the one with the smaller index. Moreover, the impact of spectrum mobility and multi-radio diversity on the delay performance of SUs is studied. It is shown that the spectrum mobility can mitigate the heavy tailed delay of SUs, while the use of multiple radio interfaces may aggravate it.