The evolution of a spatial stochastic network

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Robert, Philippe

关键词: Stochastic networks;    Queueing systems;    Birth and death processes;    Stationary recursive equations;    Random point processes;    Backward coupling;    Stationary point processes;   

DOI  :  10.1016/j.spa.2010.03.013

来源: Elsevier

【 摘 要 】

The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. In the births, particles are created at rate lambda(+) and their location is independent of the current configuration. Deaths are due to negative particles arriving at rate lambda(-). The death of a particle occurs when a negative particle arrives in its neighborhood and kills it. Several killing schemes are considered. The arriving locations of positive and negative particles are assumed to have the same distribution. By using a combination of monotonicity properties and invariance relations it is shown that the configurations of particles converge in distribution for several models. The problems of uniqueness of invariant measures and of the existence of accumulation points for the limiting configurations are also investigated. It is shown for several natural models that if lambda(+) < lambda(-) then the asymptotic configuration has a finite number of points with probability 1. Examples with lambda(+) < lambda(-) and an infinite number of particles in the limit are also presented. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free