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The evolution of a spatial stochastic network

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  • Robert, Philippe

Abstract

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]+

Suggested Citation

  • Robert, Philippe, 2010. "The evolution of a spatial stochastic network," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1342-1363, July.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:7:p:1342-1363
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    References listed on IDEAS

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    1. Ferrari, Pablo A. & Fernández, Roberto & Garcia, Nancy L., 2002. "Perfect simulation for interacting point processes, loss networks and Ising models," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 63-88, November.
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    Cited by:

    1. Veeraruna Kavitha & Eitan Altman, 2012. "Continuous polling models and application to ferry assisted WLAN," Annals of Operations Research, Springer, vol. 198(1), pages 185-218, September.
    2. Lasse Leskelä & Falk Unger, 2012. "Stability of a spatial polling system with greedy myopic service," Annals of Operations Research, Springer, vol. 198(1), pages 165-183, September.
    3. Sergey Foss, 2018. "Comments on: Polling: past, present and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 374-378, October.

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