Related papers: Parking on the integers
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 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…
We present a traffic model that extends the linear car-following model as well as the min-plus traffic model (a model based on the min-plus algebra). A discrete-time car-dynamics describing the traffic on a 1-lane road without passing is…
Graphical parking functions, or $G$-parking functions, are a generalization of classical parking functions which depend on a connected multigraph $G$ having a distinguished root vertex. Gaydarov and Hopkins characterized the relationship…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
By observing their environment as well as other traffic participants, humans are enabled to drive road vehicles safely. Vehicle passengers, however, perceive a notable difference between non-experienced and experienced drivers. In…
Parking has been a painful problem for urban drivers. The parking pain exacerbates as more people tend to live in cities in the context of global urbanization. Thus, it is demanding to find a solution to mitigate d rivers' parking…
We present an analytical and numerical study of the parking lot model (PLM) of granular relaxation and make a connection to the aging dynamics of dense colloids. As we argue, the PLM is a Kinetically Constrained Model which features…
Travellers in autonomous vehicles (AVs) need not to walk to the destination any more after parking like those in conventional human-driven vehicles (HVs). Instead, they can drop off directly at the destination and AVs can cruise for parking…
This paper presents a method to predict the evolution of a complex traffic scenario with multiple objects. The current state of the scenario is assumed to be known from sensors and the prediction is taking into account various hypotheses…
In this paper, we extend some ideas of statistical physics to describe the properties of human mobility. From a physical point of view, we consider the statistical empirical laws of private cars mobility, taking advantage of a GPS database…
Mobility-on-demand systems are transforming the way we think about the transportation of people and goods. Most research effort has been placed on scalability issues for systems with a large number of agents and simple pick-up/drop-off…
There are interesting extensions of the problem of determining a joint probability with known marginals. On the one hand, one may impose size constraints on the joint probabilities. On the other, one may impose additional constraints like…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…
Given a strictly increasing sequence $\mathbf{t}$ with entries from $[n]:=\{1,\ldots,n\}$, a parking completion is a sequence $\mathbf{c}$ with $|\mathbf{t}|+|\mathbf{c}|=n$ and $|\{t\in \mathbf{t}\mid t\le i\}|+|\{c\in \mathbf{c}\mid c\le…
Intelligent systems sometimes need to infer the probable goals of people, cars, and robots, based on partial observations of their motion. This paper introduces a class of probabilistic programs for formulating and solving these problems.…
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…
The capability of traffic-information systems to sense the movement of millions of users and offer trip plans through mobile phones has enabled a new way of optimizing city traffic dynamics, turning transportation big data into insights and…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…