相关论文: Modelling gap-size distribution of parked cars usi…
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…
The matching problem and the distribution law of Galton boards with interactions are studied in this paper. The general matching problem appeals at many scenarios, such as the reaction rate of molecules and the hailing rate of ride-hailing…
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…
Many-particle simulations of vehicle interactions have been quite successful in the qualitative reproduction of observed traffic patterns. However, the assumed interactions could not be measured, as human interactions are hard to quantify…
We consider a one-dimensional gas of $N$ charged particles confined by an external harmonic potential and interacting via the one-dimensional Coulomb potential. For this system we show that in equilibrium the charges settle, on an average,…
Different from previous models based on scatter theory and random matrix theory, a new interpretation of the observed log-normal type time-headway distribution of vehicles is presented in this paper. Inspired by the well known Galton Board,…
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices. We…
During the attempt to park a car in the city the drivers have to share limited resources (the available roadside). We show that this fact leads to a predictable distribution of the distances between the cars that depends on the length of…
Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random matrix theory are expressed in terms of solutions of coupled differential equations. Series solutions up to order 50 in the level spacing are obtained, thus…
We present a theoretical discussion of the reversible parking problem, which appears to be one of the simplest systems exhibiting glassy behavior. The existence of slow relaxation, nontrivial fluctuations, and an annealing effect can all be…
We present a theoretical approach to study the dynamics of spherical, cylindrical and ellipsoidal charge distributions under their self-Coulomb field and a stochastic force due to collisions and random motions of charged particles. The…
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…
Coulomb gases are special probability distributions, related to potential theory, that appear at many places in pure and applied mathematics and physics. In these short expository notes, we focus on some models, ideas, and structures. We…
We consider the frequency at which avoided crossings appear in an energy level structure when an external field is applied to a quantum chaotic system. The distribution of the spacing in the parameter between two adjacent avoided crossings…
We consider Coulomb gas models for which the empirical measure typically concentrates, when the number of particles becomes large, on an equilibrium measure minimizing an electrostatic energy. We study the behavior when the gas is…
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…
A special type of binomial splitting process is studied. Such a process can be used to model a high-dimensional corner parking problem, as well as the depth of random PATRICIA tries (a special class of digital tree data structures). The…
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…
We propose a generalized car parking problem where either a car of size $\sigma$ or of size $m\sigma$ ($m>1$) is sequentially parked on a line with probability $q$ and $(1-q)$, respectively. The free parameter $q$ interpolates between the…
We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded…