Throughput and delay analysis of an opportunistic tree algorithm

Abstract

Tree algorithms are a well known class of random access algorithms with a provable maximum stable throughput under the infinite population model (as opposed to ALOHA or the binary exponential backoff algorithm). In this paper, we propose a tree algorithm for opportunistic spectrum usage in cognitive radio networks. A channel in such a network is shared among so-called primary and secondary users, where the secondary users are only allowed to use the channel if there is no primary user activity. The tree algorithm designed in this paper can be used by the secondary users to share the channel capacity left by the primary users.We analyze the maximum stable throughput and mean packet delay of the secondary users by developing a tree structured Quasi-Birth Death Markov chain under the assumption that the primary user activity can be modeled by means of a finite state Markov chain and that packets lengths follow a discrete phase-type distribution.Numerical experiments provide insight on the effect of various system parameters and indicate that the proposed algorithm is able to make good use of the bandwidth left by the primary users.