Related papers: The Page-R{\'e}nyi parking process
Traditional car-sharing services are based on the two-way scheme, where the user picks up and returns the vehicle at the same parking station. Some services permits also one-way trips, which allows the user to return the vehicle in another…
Many studies suggest that searching for parking is associated with significant direct and indirect costs. Therefore, it is appealing to reduce the time which car drivers spend on finding an available parking lot, especially in urban areas…
This paper develops a computational framework based on a car-following model to study traffic instability and lane changes. Building upon Newell's classical first-order car-following model, we show that, both analytically and numerically,…
At each site of a supercritical Galton-Watson tree place a parking spot which can accommodate one car. Initially, an independent and identically distributed number of cars arrive at each vertex. Cars proceed towards the root in discrete…
Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…
The global electric car sales in 2020 continued to exceed the expectations climbing to over 3 millions and reaching a market share of over 4%. However, uncertainty of generation caused by higher penetration of renewable energies and the…
Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of…
The car-sharing problem, proposed by Luo, Erlebach and Xu in 2018, mainly focuses on an online model in which there are two locations: 0 and 1, and $k$ total cars. Each request which specifies its pick-up time and pick-up location (among 0…
We consider the notion of classical parking functions by introducing randomness and a new parking protocol, as inspired by the work presented in the paper ``Parking Functions: Choose your own adventure,'' (arXiv:2001.04817) by Carlson,…
We introduce a generalization of parking functions in which cars are limited in their movement backwards and forwards by two nonnegative integer parameters $k$ and $\ell$, respectively. In this setting, there are $n$ spots on a one-way…
In this paper we focus on the map matching problem where the goal is to find a path through a planar graph such that the path through the vertices closely matches a given polygonal curve. The map matching problem is usually approached with…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
Consider a supercritical Bienaym\'e--Galton--Watson tree $ \mathcal{T}$ with geometric offspring distribution. Each vertex of this tree represents a parking spot which can accommodate at most one car. On the top of this tree, we add $(A_u :…
Smart-parking solutions use sensors, cameras, and data analysis to improve parking efficiency and reduce traffic congestion. Computer vision-based methods have been used extensively in recent years to tackle the problem of parking lot…
Parking infrastructure is pervasive and occupies large swaths of land in cities. However, on-demand (OD) mobility -- such as commercial services Uber, Grab or Didi -- has started reducing parking needs in urban areas around the world. This…
In this article a multilayer parking system with screening of size n=3 is studied with a focus on the time-dependent particle density. We prove that the asymptotic limit of the particle density increases from an average density of 1/3 on…
We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…
For any integers $1\leq k\leq n$, we introduce a new family of parking functions called $k$-vacillating parking functions of length $n$. The parking rule for $k$-vacillating parking functions allows a car with preference $p$ to park in the…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
In discrete time, $\ell$-blocks of red lights are separated by $\ell$-blocks of green lights. Cars arrive at random. The maximum line length of idle cars is fully understood for $\ell = 1$, but only partially for $2 \leq \ell \leq 3$.