Limiting Behavior of Some Spatial Particle Systems

作者：Jones Matthew O^*

来源：Stochastic Models, 2015, 31(2): 208-225.

DOI：10.1080/15326349.2014.994367

• Poisson process
• Stochastic geometry
• Hard core process
• Convergence in distribution
• Point process
• Marked point process
• Laplace functional
• Spatial queueing

Particles (representing customers, or species) arrive to a general space according to a Poisson process and are removed randomly upon future arrivals based on randomly assigned attributes. These systems are similar to the Matern II generalizations in Teichmann et al. ([)(12)(]), but evolve temporally as Markov processes on spaces of marked point processes. We analyze their limiting behavior by viewing them as transformations of marked point processes and obtain expressions for their mean measure and Laplace functional. Such models are popular with applications to include spatial service systems, species competitions, and wireless networks.

• 出版日期2015-4-3