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On the Dynamics of Systems of Urns

Abstract : In this paper we present an analysis of some generalization of the classic urn and balls model. In our model each urn has a fixed capacity and initially is filled with white balls. Black balls are added to the system of connected urns and gradually displace white balls. We show a general form of formulas for the expected numbers of black balls in a given urn and we analyze some special cases (parallel and serial configurations). We are mainly interested in a counterpart of the Coupon Collector Problem for the model considered. The primary motivation for our research is the formal analysis of the mix networks (introduced by D. Chaum) and its immunity to so-called flooding (blending) attacks.
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Marek Klonowski, Jacek Cichoń, Rafał Kapelko. On the Dynamics of Systems of Urns. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.235-250. ⟨hal-01349058⟩

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