Related papers: The Page-R{\'e}nyi parking process
In this paper, we investigate the parking process on a uniform random rooted binary tree with $n$ vertices. Viewing each vertex as a single parking space, a random number of cars independently arrive at and attempt to park on each vertex…
Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each…
Suppose that $m$ drivers each choose a preferred parking space in a linear car park with $n$ spots. In order, each driver goes to their chosen spot and parks there if possible, and otherwise takes the next available spot if it exists. If…
We compute the correlation function in the equilibrium version of R\'enyi's {\sl parking problem}. The correlation length is found to diverge as $2^{-1}\pi^{-2}(1-\rho)^{-2}$ when $\rho\nearrow1$ (maximum density) and as…
We propose a model for optimizing the last-mile delivery of n packages, from a distribution center to their final recipients, using a strategy that combines the use of ride-sharing platforms (e.g., Uber or Lyft) with traditional in-house…
Place a car independently with probability $p$ at each site of a graph. Each initially vacant site is a parking spot that can fit one car. Cars simultaneously perform independent random walks. When a car encounters an available parking spot…
We present an algorithm to simulate random sequential adsorption (random "parking") of discs on constant-curvature surfaces: the plane, sphere, hyperboloid, and projective plane, all embedded in three-dimensional space. We simulate complete…
In this paper, we investigate a parking process on a uniform random rooted plane tree with $n$ vertices. Every vertex of the tree has a parking space for a single car. Cars arrive at independent uniformly random vertices of the tree. If the…
A parking function is a function $\pi:[n]\to [n]$ whose $i$th-smallest output is at most $i,$ corresponding to a parking procedure for $n$ cars on a one-way street. We refine this concept by introducing preference-restricted parking…
in this article a multilayer parking system of size n=3 is studied. We prove that the asymptotic limit of the particle density in the center approaches a maximum of 1/2 in higher layers. This means a significant increase of capacity…
Consider sequential packing of unit balls in a large cube, as in the Renyi car-parking model, but in any dimension and with Poisson input. We show after suitable rescaling that the spatial distribution of packed balls tends to that of a…
Parking sequences (a generalization of parking functions) are defined by specifying car lengths and requiring that a car attempts to park in the first available spot after its preference. If it does not fit there, then a collision occurs…
We study the problem of planning routes in road networks when certain streets or areas are closed at certain times. For heavy vehicles, such areas may be very large since many European countries impose temporary driving bans during the…
Recently, a phase transition phenomenon has been established for parking on random trees. We extend the results of Curien and H\'enard on general Galton--Watson trees and allow different car arrival distributions depending on the vertex…
Parking occupancy in the area is defined by three major parameters - the rate of cars arrivals, the dwell time of already parked cars, and the willingness of drivers who are searching but yet did not find a vacant parking spot, to continue…
We investigate parking in a one-dimensional lot, where cars enter at a rate $\lambda$ and each attempts to park close to a target at the origin. Parked cars also depart at rate 1. An entering driver cannot see beyond the parked cars for…
All over the world, especially in the university environment, planning managers and traffic engineers are constantly faced with the problem of inadequate allocation of car parking spaces to demanded users. Users could either prefer reserved…
We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…
An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes…
We investigate simple strategies that embody the decisions that one faces when trying to park near a popular destination. Should one park far from the target (destination), where finding a spot is easy, but then be faced with a long walk,…