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.

Analysis of Queues in a Random Environment with Impatient Customers

We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.

A Multi-server Queue in a Multi-phase Random Environment with Waiting Servers and Customers'Impatience Under Synchronous Working Vacation Policy

In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operative phase j,j=1,K¯,customers are served one by one.Once the system is empty,the servers have to wait a random period of time before leaving,causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate.Using the method of the probability generating functions,we establish the steady-state analysis of the system.Special cases of the queueing model are presented.Then,explicit expressions of the useful system characteristics are derived.In addition,a cost model is constructed to define the optimal values of service rates,simultaneously,to minimize the total expected cost per unit time via a quadratic fit search method.Numerical examples are provided to display the impact of different system characteristics.