Spatial blocking in Poisson cellular networks with random channel reuse

In this paper, we consider a static Poisson cellular network, where the base stations (BSs) and mobiles are located according to two independent spatial Poisson processes. Voronoi cells are formed based on the locations of BSs. Mobiles falling into a Voronoi cell communicate with the BS in the same cell. Assuming a channelised multiple access technique, a BS randomly assigns available channels to the mobiles within the cell. Under such a setting, we introduce the concept of spatial blocking. Spatial blocking occurs when the number of users in a cell is greater than the number of channels available. We derive expressions for the spatial blocking probability under three random frequency reuse schemes: fixed-channel-available, random-channel-available and cell-dependent-channel-available.