Related papers: Parking on the integers
In the Page parking (or packing) model on a discrete interval (also known as the discrete R{\'e}nyi packing problem or the unfriendly seating problem), cars of length two successively park uniformly at random on pairs of adjacent places,…
We present a queuing model of parking dynamics and a model-based prediction method to provide real-time probabilistic forecasts of future parking occupancy. The queuing model has a non-homogeneous arrival rate and time-varying service time…
In this article, we establish new results on the probabilistic parking model (introduced by Durm\'ic, Han, Harris, Ribeiro, and Yin) with $m$ cars and $n$ parking spots and probability parameter $p\in[0,1]$. For any $ m \leq n$ and $p \in…
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…
The notion of parking sequences is a new generalization of parking functions introduced by Ehrenborg and Happ. In the parking process defining the classical parking functions, instead of each car only taking one parking space, we allow the…
Consider $n$ cars $C_1, C_2, \ldots, C_n$ that want to park in a parking lot with parking spaces $1,2,\ldots,n$ that appear in order. Each car $C_i$ has a parking preference $\alpha_i \in \{1,2,\ldots,n\}$. The cars appear in order, if…
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…
In 1966, Konheim and Weiss [33] introduced a now classical parking protocol. The deterministic process and its resultant objects, known as parking functions, have since become a favorite object of study in enumerative combinatorics. In our…
Parking problems derive from works in combinatorics by Konheim and Weiss in the 1960s. In a memorable contribution, Lackner and Panholzer (2016) studied parking on a random tree and established a phase transition for this process when \(m…
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,…
Current navigation systems conflate time-to-drive with the true time-to-arrive by ignoring parking search duration and the final walking leg. Such underestimation can significantly affect user experience, mode choice, congestion, and…
In the classical parking problem, unit intervals ("car lengths") are placed uniformly at random without overlapping. The process terminates at saturation, i.e. until no more unit intervals can be stowed. In this paper, we present a…
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…
Parking plays a central role in transport policies and has wide-ranging consequences: While the average time spent searching for parking exceeds dozens of hours per driver every year in many Western cities, the associated cruising traffic…
There are so many vehicles in the world and the number of vehicles is increasing rapidly. To alleviate the parking problems caused by that, the smart parking system has been developed. The parking planning is one of the most important parts…
R\'enyi's parking problem (or $1D$ sequential interval packing problem) dates back to 1958, when R\'enyi studied the following random process: Consider an interval $I$ of length $x$, and sequentially and randomly pack disjoint unit…
We apply the random-matrix theory to the car-parking problem. For this purpose, we adopt a Coulomb gas model that associates the coordinates of the gas particles with the eigenvalues of a random matrix. The nature of interaction between the…
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…
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…
The increasing availability and adoption of shared vehicles as an alternative to personally-owned cars presents ample opportunities for achieving more efficient transportation in cities. With private cars spending on the average over 95\%…