Mutual service processes in Euclidean spaces: existence and ergodicity

François Baccelli, Fabien Mathieu and Ilkka Norros ()
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François Baccelli: UT Austin
Fabien Mathieu: Nokia Bell Labs
Ilkka Norros: VTT

Queueing Systems: Theory and Applications, 2017, vol. 86, issue 1, No 4, 95-140

Abstract: Abstract Consider a set of objects, abstracted to points of a spatially stationary point process in $$\mathbb {R}^d$$ R d , that deliver to each other a service at a rate depending on their distance. Assume that the points arrive as a Poisson process and leave when their service requirements have been fulfilled. We show how such a process can be constructed and establish its ergodicity under fairly general conditions. We also establish a hierarchy of integral balance relations between the factorial moment measures and show that the time-stationary process exhibits a repulsivity property.

Keywords: Spatial birth and death process; Infinite particle system; Palm probability; Coupling from the past; Moment measure; Repulsion; 60D05; 60G55; 60D05; 60G10; 60G17; 60J25; 05C80; 70F45 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11134-017-9524-3

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