The Dynamics of Probabilistic Population Protocols
Abstract
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.
Cite
@article{arxiv.0807.0140,
title = {The Dynamics of Probabilistic Population Protocols},
author = {Ioannis Chatzigiannakis and Paul G. Spirakis},
journal= {arXiv preprint arXiv:0807.0140},
year = {2008}
}
Comments
To appear as a Brief Announced in Proc. of 22nd International Symposium on Distributed Computing (DISC 2008), September 22-24, 2008, Arcachon, France