Related papers: The Page-R{\'e}nyi parking process
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
An occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the…
Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…
Probability distributions of human displacements has been fit with exponentially truncated L\'evy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the…
During the attempt to line up into a dense traffic people have necessarily to share a limited space under turbulent conditions. From the statistical point view it generally leads to a probability distribution of the distances between the…
A ride sharing problem is considered where we are given a graph, whose edges are equipped with a travel cost, plus a set of objects, each associated with a transportation request given by a pair of origin and destination nodes. A vehicle…
A reversible adsorption-desorption parking process in one dimension is studied. An exact solution for the equilibrium properties is obtained. The coverage near saturation depends logarithmically on the ratio between the adsorption rate,…
Motivated by the applications of routing in PCB buses, the Rectangle Escape Problem was recently introduced and studied. In this problem, we are given a set of rectangles $\mathcal{S}$ in a rectangular region $R$, and we would like to…
In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed…
We consider a spatially distributed demand for electrical vehicle recharging, that must be covered by a fixed set of charging stations. Arriving EVs receive feedback on transport times to each station, and waiting times at congested ones,…
Parking accurately and safely in highly constrained spaces remains a critical challenge. Unlike structured driving environments, parking requires executing complex maneuvers such as frequent gear shifts and steering saturation. Recent…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…
We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the…
We study an one-dimensional stochastic model of vehicular traffic on open segments of a single-lane road of finite size $L$. The vehicles obey a stochastic discrete-time dynamics which is a limiting case of the generalized Totally…
We consider the problem of selfish agents in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet each step to one of the servers, which will attempt to serve…
We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk…
In urban environments, parking has proven to be a significant source of congestion and inefficiency. In this study, we propose a methodology that offers a systematic solution to minimize the time spent by drivers in finding parking spaces.…
Empty buses are standing at a bus station. $n$ passengers arrive, and they each board a bus completely at random (meaning that they choose uniformly and independently). Then all buses depart. We show that the more buses there are, the more…
We propose a generalized car parking problem where cars of two different sizes are sequentially parked on a line with a given probability $q$. The free parameter $q$ interpolates between the classical car parking problem of only one car…
We analyse the equilibrium pile-up configurations of infinite periodic walls of edge dislocations which are forced against an impenetrable obstacle by a constant applied shear stress. Numerically generated density distributions exhibit two…