Proofs for some conjectures of Rajaratnam and Takawira

The purpose of this note is to supplement a recent paper by Rajaratnam and Takawira ({\it IEEE Trans. Vehicular Technol.} {\bf 49} (2000) 817-834), which deals with a model for the performance analysis of cellular mobile networks. We show that the key performance quantity may be obtained by evaluating an explicit formula rather than by solving a set of equations. This result enables us to verify some conjectures formulated by Rajaratnam and Takawira on the basis of numerical experiments. We also show uniqueness of the solution to a system of nonlinear equations, required in the performance analysis, as conjectured by Rajaratnam and Takawira. \u