Proofs for some conjectures of Rajaratnam and Takawira on the peakedness of handoff traffic

The purpose of this paper is to supplement a recent paper by M. Rajaratnam and F. Takawira (see ibid., vol.49, p.817-34, 2000), which deals with a model for the performance analysis of cellular mobile networks. The key performance measure is a second-order characteristic (peakedness) of the traffic stream that serves as a model for handoff traffic. We show that this 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 the uniqueness of the solution to a system of nonlinear equations, required in the performance analysis, as conjectured by Rajaratnam and Takawira.