On spectrum sharing in narrowband cellular wireless networks

We study secondary spectrum sharing in narrowband cellular networks in which calls in neighboring cells need to be assigned different channels. Analysis of such networks are in general difficult due to large state spaces and lack of closed form expressions. Here we consider linear topologies and show that they lend themselves to exact analysis. We analyze four sharing policies where equilibrium distribution of cell occupancies is a Markov random field. For each policy we derive closed form expressions for the equilibrium distributions in the form of a product of certain stochastic matrices. This characterization leads to tractable computation of equilibrium distributions and blocking probabilities. We use the obtained results to compare the policies in terms of (i) maximum revenue, and (ii) secondary price-demand pairs that lead to positive profit for the network service provider.