Market Equilibria in Spectrum Trading with Multi-Regions and Multi-Channels

We study the spectrum market equilibrium where multiple spectrum channels are available, and each of the secondary users has an initial endowment. Assume that each user, with a given endowment, is interested in buying spectrum channels over a specified set of geometric regions in the Euclidean plane. Regions may overlap, thus creating sub- regions where each subregion has a unique set of users interested in acquiring spectrum. Fraction timeshare on spectrum is acceptable. We utilize a price function wherein the price of timeshare on spectrum in a certain region is equal to the maximum price of timeshare amongst the sub-regions in that region. The utility function used is the logarithm utility function. We first prove the existence of equilibrium and then design efficient algorithms for computing the spectrum market equilibrium. We also analyze the utilization of the spectrum by extensive simulations.