Bounds for call completion probabilities in large-scale mobile communication networks

In this paper, we propose a method to obtain upper and lower bounds of call completion probabilities in a mobile communication network having a large number of base stations. Each base station has its own zone where its radio wave reaches. These zones are overlapping with neighboring zones, and handovers become possible. However, the existence of overlapping zones makes the analysis of a network difficult. To overcome this difficulty, we introduce two smaller size models and show that the upper and lower bounds can be represented in terms of certain performance measures obtained from the smaller size models. Using our method, we can get the values of the bounds by standard methods such as simulation with less computational burden, where the tightness of the bounds can be controlled by choosing a set of focused base stations with appropriate size.