Operations research: principles and practice, 2nd ed.
Operations research: principles and practice, 2nd ed.
Market equilibria for homothetic, quasi-concave utilities and economies of scale in production
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Mathematical Programming: Series A and B
A Microeconomic Model for Hierarchical Bandwidth Sharing in Dynamic Spectrum Access Networks
IEEE Transactions on Computers
A secondary market for spectrum
INFOCOM'10 Proceedings of the 29th conference on Information communications
Near-optimal power control in wireless networks: a potential game approach
INFOCOM'10 Proceedings of the 29th conference on Information communications
Dynamic spectrum management with the competitive market model
IEEE Transactions on Signal Processing
Price dynamics in competitive agile spectrum access markets
IEEE Journal on Selected Areas in Communications
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We model cognitive radio networks (CRNs) as a spectrum market where every primary user (PU) offer her subchannels with certain interference bound indicating the interference limit the PU can tolerate, and secondary users (SUs) purchase the right to access the subchannels while observing their budget constraints as well as the inference bound. In this spectrum market model, the utility of SU is defined as the achievable transmission rate in free space, and the utility of PU is given by the net profit the PU can make. Then we develop a market equilibrium in the context of Fisher model, and show that the equilibrium is obtained by solving an optimization problem called Eisenberg-Gale convex program. Furthermore, we develop a distributed algorithm with best response dynamics and price dynamics, and prove that its asymptotic solutions are equivalent to the solutions given by the convex program. Besides, we introduce adaptive step size to the price dynamics for faster convergence. With some numerical examples, we show that it helps to achieve faster convergence.