Modeling and analysis of hierarchical cellular networks with general distributions of call and cell residence times

We present an analytic model for the performance evaluation of hierarchical cellular systems, which can provide multiple routes for calls through overflow from one cell layer to another. Our model allows the case where both the call time and the cell residence time are generally distributed. Based on the characterization of the call time by a hyper-Erlang distribution, the Laplace transform of channel occupancy time distribution for each call type (new call, handoff call, and overflow call) is derived as a function of the Laplace transform of cell residence time. In particular, overflow calls are modeled by using a renewal process. Performance measures are derived based on the product form solution of a loss system with capacity limitation. Numerical results show that the distribution type of call time and/or cell residence time has influence on the performance measure and that the exponential case may underestimate the system performance.