A Phase Space Model for Spatial BMAPs

Introducing spatial arrival processes is of great help for modeling mobile communication, since users can be characterized more adequately by properties deriving from their positions. BAUM [1] creates a stochastic model for Spatial BMAPs. It generalizes the concept of LUCANTONI [2]. The paths of a BMAP are determined by the evolution of the phase process and the distribution of batch sizes, given that an arrival occurs. If we decribe a phase by a function we need a suitable topological and stochastic enviroment for this class of functions, namely we need an adequate measurable space ( ;S( )) for the phases 2 . Due to the generator of the phase process we need the condition that our measurable space must have the property that its -algebra contains the single sets f g, 2 . The aim of this paper is to develop an adequat measurable space ( ;S( )) which has the properties mentioned above.