Abstract

Point processes recently gained recognition in modelling different aspects of telecommunication systems: network components, mobile customers, infrastructure, etc. In many cases though the underlying system shows highly irregular spatial characteristics: number requests serviced by a web-server varies hugely as a function of popularity and happening events. Number of active mobile users calling during popular events: football match, rock concert differs in order of magnitudes from normal periods. This calls for development of point process models exhibiting such bursty behaviour, in time or in space.

We introduce a wide class of point processes which generally have infinite expected number of points in a bounded domain, yet they appear unavoidably as limit in the thinning-superposition of point processes schemes. We show that these processes are necessarily Cox processes driven by strictly stable parameter measure and give insight into their cluster structure and further distributional properties.