The Dynamics of Probabilistic Population Protocols

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We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large populations. For the general model we give a sufficient condition for stability that can be checked in polynomial time. We also study two interesting subcases: (a) protocols whose specifications (in our terms) are configuration independent. We show that they are always stable and that their eventual subpopulation percentages are actually a Markov Chain stationary distribution. (b) protocols that have dynamics resembling virus spread. We show that their dynamics are actually similar to the well-known Replicator Dynamics of Evolutionary Games. We also provide a sufficient condition for stability in this case.
To appear as a Brief Announced in Proc. of 22nd International Symposium on Distributed Computing (DISC 2008), September 22-24, 2008, Arcachon, France

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Distributed, Parallel, and Cluster Computing, Computer Science and Game Theory, C.2.4; C.2.1; F.1.1; F.1.2

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http://salesiana.dossiersoluciones.com/handle/123456789/163952

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.0140
 http://arxiv.org/abs/0807.0140

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arXiv