Mobility models for cellular mobile radiotelephone networks: Product forms and blocking (Q2715926)

The author considers mobility models for mobile cellular communication systems with special emphasis on new call and handover blocking. The mobile communication system is described by a homogeneous Markov process with discrete locations. First, the mobility and the behaviour of the customers is modelled without capacity constraints. This leads to a Markov process which has a stationary distribution in product form. As channel allocation algorithm a maximum packing procedure is used where each cell admits the same number of channels. Interferences are described via hypergraphs: the vertices model the cells, the arcs describe which cells cannot be used at the same time because of interferences. Finding feasible solutions leads to coloring problems in hypergraphs. In particular conditions are given when the set of feasible solutions can be described as a polyhedral set. Finally, conditions are derived which guarantee that the stationary distribution keeps its product form under capacity constraints.