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Multilayer parking with screening on a random tree. (English) Zbl 1191.82030
Summary: We present a multilayer particle-deposition model on a random tree. We derive the time-dependent densities of the first and second layer analytically and show that for all trees the limiting density of the first layer exceeds the density in the second layer. We also provide a procedure to calculate higher-layer densities and prove that random trees have a higher limiting density in the first layer than regular trees. Finally, we compare densities between the first and second layer and between regular and random trees.

82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
90B20 Traffic problems in operations research
05C80 Random graphs (graph-theoretic aspects)
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