On the Dynamics of Systems of Urns
Marek Klonowski, Jacek Cichoń, Rafał Kapelko
Abstract
IIn 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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