Related papers: Parking on the integers
Vehicle-sharing systems are becoming important for urban transportation. In these systems, users arrive at a station, pick up a vehicle, use it for a while and then return it to another station of their choice. Depending on the type of…
We illustrate the experimental, empirical, approach to mathematics (that contrary to popular belief, is often rigorous), by using parking functions and their "area" statistic, as a case study. Our methods are purely finitistic and…
In this paper, we mainly study two notions of pattern avoidance in parking functions. First, for any collection of length 3 patterns, we compute the number of parking functions of size $n$ that avoid them under the first notion. This is…
Suppose that $n$ drivers each choose a preferred parking space in a linear car park with $m$ spaces. Each driver goes to the chosen space and parks there if it is free, and otherwise takes the first available space with larger number (if…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
This paper proposes a totally asymmetric simple exclusion process on a traveling lane, which is equipped with a queueing system and functions of site assignments along the parking lane. In the proposed system, new particles arrive at the…
In this paper, we propose a new macro-micro approach to modeling parking. We first develop a microscopic parking simulation model considering both on- and off-street parking with limited capacity. In the microscopic model, a parking search…
By analyzing data from a car-following experiment, it is shown that drivers control their car by a simple scheme. The acceleration $a(t)$ is held approximately constant for a certain time interval, followed by a jump to a new acceleration.…
We have carried out car-following experiments with a 25-car-platoon on an open road section to study the relation between a car's speed and its spacing under various traffic conditions, in the hope to resolve a controversy surrounding this…
In a carsharing system, a fleet of cars is distributed at stations in an urban area, customers can take and return cars at any time and station. For operating such a system in a satisfactory way, the stations have to keep a good ratio…
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…
With increased travelling needs more than ever, traffic congestion has become a major concern in most urban areas. Allocating spaces for on-street parking, further hinders traffic flow, by limiting the effective road width available for…
Double parking that often negatively affects traffic operations and safety is not a new phenomenon on urban streets. This study proposes a novel data-driven integrated framework for estimating the actual frequency of double parking so that…
Understanding city-scale vehicular mobility and trip patterns is essential to addressing many problems, from transportation and pollution to public safety, among others. Using spatio-temporal analysis of vehicular mobility, promising…
We show that the spacing distribution between parked cars can be obtained as a solution of certain linear distributional fixed point equation. The results are compared with the data measured on the streets of Hradec Kralove. We also discuss…
Let $(A_u : u \in \mathbb{B})$ be i.i.d.~non-negative integers that we interpret as car arrivals on the vertices of the full binary tree $ \mathbb{B}$. Each car tries to park on its arrival node, but if it is already occupied, it drives…
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
With the sharp increase in the number of vehicles, the issue of parking difficulties has emerged as an urgent challenge that many cities need to address promptly. In the task of predicting large-scale urban parking data, existing research…
The choice of forward and reverse parking in a parking lot is studied as a stochastic process. An $M/M/c/c$ queueing system is used as an initial framework. We use Monte Carlo simulation to get the relationship between vehicle orientation…
Autonomous parking is a crucial task in the intelligent driving field. Traditional parking algorithms are usually implemented using rule-based schemes. However, these methods are less effective in complex parking scenarios due to the…