Multilayer parking with screening on a random tree

In this paper 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 in 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.Comment: 15 pages, 2 figure

Parking on a Random Tree

Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating function G(s). We consider the following variation of Renyi's parking problem, alternatively called blocking RSA: at every vertex of the tree a particle (or car) arrives with rate one. The particle sticks to the vertex whenever the vertex and all of its nearest neighbors are not occupied yet. We provide an explicit expression for the so-called parking constant in terms of the generating function.Comment: 7 page

A second row Parking Paradox

We consider two variations of the discrete car parking problem where at every vertex of the integers a car arrives with rate one, now allowing for parking in two lines. a) The car parks in the first line whenever the vertex and all of its nearest neighbors are not occupied yet. It can reach the first line if it is not obstructed by cars already parked in the second line (screening). b) The car parks according to the same rules, but parking in the first line can not be obstructed by parked cars in the second line (no screening). In both models, a car that can not park in the first line will attempt to park in the second line. If it is obstructed in the second line as well, the attempt is discarded. We show that both models are solvable in terms of finite-dimensional ODEs. We compare numerically the limits of first and second line densities, with time going to infinity. While it is not surprising that model a) exhibits an increase of the density in the second line from the first line, more remarkably this is also true for model b), albeit in a less pronounced way.Comment: 11 pages, 4 figure

Parking on a Random Tree

Abstract Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating function G(s). We consider the following variation of Rényi's parking problem, alternatively called blocking RSA (random sequential adsorption): at every vertex of the tree a particle (or "car") arrives with rate one. The particle sticks to the vertex whenever the vertex and all of its nearest neighbors are not occupied yet. We provide an explicit expression for the so-called parking constant in terms of the generating function. That is, the occupation probability, averaged over dynamics and the probability distribution of the random trees converges in the large-time limit to (1 − α 2 )/2 with 1 α xdx G(x) = 1

Measuring local autonomy: A decision-making approach

In studies on central-local relations it is common to assess local autonomy in a deductive way. The extent of local autonomy is determined by measuring the central legal and financial competence, after which the remaining room for local decision-making is determined. The outcome of this indirect method is that the autonomy of local government tends to be systematically underestimated. As an alternative this paper introduces a decision-making approach in which local decisions are systematically weighed on three dimensions: Agenda setting, freedom in choices, and dependency. Using Dutch data, the authors come to the conclusion that a locally oriented perspective leads to a more accurate and positive judgement of the autonomy of local government. © 2006 Taylor & Francis

A Second-row Parking Paradox

We consider two variations of the discrete car parking problem where at every vertex of a"currency sign cars (particles) independently arrive with rate one. The cars can park in two lines according to the following parking (adsorption) rules. In both models a car which arrives at a given vertex tries to park in the first line first. It parks (sticks) whenever the vertex and all of its nearest neighbors are not occupied yet. A car that cannot park in the first line will attempt to park in the second line. If it is obstructed in the second line as well, the attempt is discarded.In the screening model a) a car cannot pass through parked cars in the second line with midpoints adjacent to its vertex of arrival.In the model without screening b) cars park according to the same rules, but parking in the first line cannot be obstructed by parked cars in the second line.We show that both models are solvable in terms of finite-dimensional ODEs. We compare numerically the limits of first- and second-line densities, with time going to infinity. While it is not surprising that model a) exhibits an increase of the density in the second line from the first line, more remarkably this is also true for model b), albeit in a less pronounced way.</p