Pricing Policy for a Dynamic Spectrum Allocation Scheme with Batch Requests and Impatient Packets in Cognitive Radio Networks

In cognitive radio networks (CRNs), multiple secondary users may send out requests simultaneously and one secondary user may send out multiple requests at one time, i.e., request arrivals usually show an aggregate manner. Moreover, a secondary user packet waiting in the buffer may leave the system due to impatience before it is transmitted, and this impatient behavior inevitably has an impact on the system performance. Aiming to investigate the influence of the aggregate behavior of requests and the likelihood of impatience on a dynamic spectrum allocation scheme in CRNs, in this paper a batch arrival queueing model with possible reneging and potential transmission interruption is established. By constructing a Markov chain and presenting a transition rate matrix, the steady-state distribution of the queueing model along with a dynamic spectrum allocation scheme is derived to analyze the stochastic behavior of the system. Accordingly, some important performance measures such as the loss rate, the balk rate and the average delay of secondary user packets are given. Moreover, system experiments are carried out to show the change trends of the performance measures with respect to batch arrival rates of secondary user packets for different impatience parameters, different batch sizes of secondary user packets, and different arrival rates of primary user packets. Finally, a pricing policy for secondary users is presented and the dynamic spectrum allocation scheme is socially optimized.