1 Pricing Mechanisms and Equilibrium Behaviors of Noncooperative Users in Cognitive Radio Networks Nguyen H. Tran, Cuong T. Do, Seung Il Moon, Choong Seon Hong Department of Computer Engineering, Kyung Hee University, 446-701, Republic of Korea Email: {nguyenth, dtcuong, moons85, cshong}@khu.ac.kr Abstract—We study the pricing mechanisms and their effects on equilibrium behaviors of self-optimizing secondary users (SUs) sharing a single channel of primary users (PUs) operated by a service provider (SP) in cognitive radio networks. From SUs’ point of view, a spectrum access decision on whether to join a queue or not is characterized through an individual optimal strategy. With this strategy, we show that there exists a unique equilibrium in terms of SUs’ joining probability. This strategy also requires each SU to know its average queueing delay, which is a non-trivial problem because of multiple SUs service’s interruptions from the returns of PUs; we, however, can analyze this queueing delay based on the general distribution of SUs’s service time and PUs’ traffic model by using renewal theory. We also provide a sufficient condition and iterative algorithms for the convergence of equilibrium points. From the SP’s point of view, two pricing mechanisms are proposed with different goals: revenue maximization and social welfare maximization. And the optimal price can be solved efficiently using numerical methods. I. I NTRODUCTION Cognitive radio (CR) is expected to mitigate spectrum shortage by enabling the spectrum sharing for secondary users (SUs) who opportunistically capture the temporal and spatial “spectrum holes” in spectral white spaces of primary users (PUs). Among many spectrum access control methods, pricing has long been considered an important approach due to its simplicity yet effectivity. By considering delay-sensitive SUs wishing to share a PU’s single channel operated by an SP, we examine the SP’s pricing effect on the equilibrium behaviors of non-cooperative SUs. This behavior is represented by a SU’s spectrum access decision it has to make upon arrival: joining the list of other SUs who also want to share the same channel, or balking. When all arriving SUs are considered as price-takers, two important questions are raised: (1) Given an admission price charged by the SP, what is the equilibrium point of SUs’ individual optimal strategies and how to achieve it? (2) What are the pricing policies of the SP to maximize its revenue and the network social welfare? Considering the first question, we introduce an individual optimal strategy employed by each SU in order to make its spectrum access decision based on a utility function that cap- tures the delay-sensitivity heterogeneity of SUs. We next show This research was supported by Next-Generation Information Computing Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2010- 0020728). Dr. CS Hong is the corresponding author. that there exists a unique equilibrium of the SUs’ behaviors. Each SU has to evaluate its average queueing delay of a virtual queue that is used to model a congestion effect happening when many SUs intend to share the same PUs’ channel. By using renewal theory, we provide a queueing delay analysis based only on the statistical information of PUs’ activities and SUs’ service time since SUs cannot observe exactly how many others SUs being in the CR networks. Finally, we examine the equilibrium dynamics through iterative algorithms and provide a sufficient condition for the equilibrium convergence. Considering the second question, we devise two pricing mechanisms for different SP’s perspectives. If the SP is oper- ated by a commercial planner, we propose a revenue-optimal pricing policy to maximize the SP’s revenue. Otherwise, if the SP is a social planner, we propose a socially optimal pricing policy to maximize the network social welfare. Both can be solved efficiently using numerical methods with single variable. II. RELATED WORK The pricing mechanisms and its impact on the equilibrium strategies of users in a queueing system can be traced back from the original work of [1] and surveyed in the monograph [2]. In the context of CR networks, even though pricing-based methods have been employed extensively for spectrum access control [3]–[6], few papers are in the category of pricing effect on equilibrium behavior of queueing systems [7]–[10]. Simi- larly to [7], we use the unobservable queue system, which ap- propriately models the non-cooperative and distributed nature of SUs, whereas [8], [10] employ the observable queue system, which requires either a centralized control server or a feedback mechanism with time overhead. We apply the renewal theory for the queueing analysis on general distributions of PUs’ channel and SUs’ service, whereas the others with Markov chain analysis either restricted their models to Bernoulli [8], or exponential [7], [9] distributions. Furthermore, these authors consider only either socially-optimal pricing [8], [9] or revenue-optimal pricing [7] in the shared-use model with homogeneous SUs, whereas we provide not only both social and revenue maximization pricing mechanisms but also the price competition between the shared-use and exclusive-use models with heterogeneous SUs. III. SYSTEM MODEL We consider a CR network with a single licensed channel operated by a SP. This licensed band is used exclusively by Globecom 2013 - Cognitive Radio and Networks Symposium 978-1-4799-1353-4/13/$31.00 ©2013 IEEE 935