Network Stability of Cognitive Radio Networks in the Presence of Heavy Tailed Traffic

Abstract—The heavy tailed nature in dynamic spectrum networks challenges the applicability of conventional network stability criterions. To encounter this, a new stability criterion, namely moment stability, is introduced, which requires that the queue length of each secondary user has finite moments for every achievable order. Then, the necessary and sufficient conditions for the existence of a resource allocation policy to achieve moment stability are derived. Moreover, the network stability region yielded from these conditions is shown to be directly related to the statistics of secondary user traffics, primary user activities, the number of secondary users contending the spectrum, and the total number of primary user channels available to secondary users. In addition, a throughput-optimal policy, which stabilizes the network for any arrival rates in the stability region, is also introduced. In the end, the impact of the heavy tailed primary user traffic on the network stability is investigated, which shows that the tail heaviness of the primary user traffics determines what types of the network stability are achievable for a dynamic spectrum networks. I