Theoretical predictions for vehicular headways and their clusters

This article presents a derivation of analytical predictions for steady-state distributions of netto time gaps among clusters of vehicles moving inside a traffic stream. Using the thermodynamic socio-physical traffic model with short-ranged repulsion between particles (originally introduced in [Physica A \textbf{333} (2004) 370]) we firstly derive the time-clearance distribution in the model. Consecutively, the statistical distributions for the so-called time multi-clearances are calculated by means of theory of functional convolutions. Moreover, all the theoretical surmises used during the above-mentioned calculations are proven by the statistical analysis of traffic data. The mathematical predictions acquired in this paper are thoroughly compared with relevant empirical quantities and discussed in the context of three-phase traffic theory.Comment: 23 pages, 10 figure

Inter-vehicle gap statistics on signal-controlled crossroads

We investigate a microscopical structure in a chain of cars waiting at a red signal on signal-controlled crossroads. Presented is an one-dimensional space-continuous thermodynamical model leading to an excellent agreement with the data measured.Moreover, we demonstrate that an inter-vehicle spacing distribution disclosed in relevant traffic data agrees with the thermal-balance distribution of particles in the thermodynamical traffic gas (discussed in [1]) with a high inverse temperature (corresponding to a strong traffic congestion). Therefore, as we affirm, such a system of stationary cars can be understood as a specific state of the traffic sample operating inside a congested traffic stream.Comment: 6 pages, 4 figures, accepted for publication in J. Phys. A: Math. Theo

The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles

We analyze statistical properties of the city bus transport in Cuernavaca (Mexico) and show that the bus arrivals display probability distributions conforming those given by the Unitary Ensemble of random matrices.Comment: 4 pages, 3 figure

Equilibrium distributions in thermodynamical traffic gas

We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0) depending on the distance r between the neighboring particles. The calculated distribution (for a=1) is successfully compared with the highway-traffic clearance distributions, which provides a detailed view of changes in microscopical structure of traffic sample depending on traffic density. In addition to that, the observed correspondence is a strong support of studies applying the equilibrium statistical physics to traffic modelling.Comment: 5 pages, 6 figures, changed content, added reference

Statistical mechanics of non-hamiltonian systems: Traffic flow

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 ahead. Distribution of car velocities for various densities of a group of cars are derived as well as probabilities of density fluctuations of the group for different velocities. For high braking abilities of cars free-flow and congested phases are found. Platoons of cars are formed for system of cars with inefficient brakes. A first order phase transition between free-flow and congested phase is suggested.Comment: 12 pages, 6 figures, presented at TGF, Paris, 200

A model for the bus system in Cuernavaca (Mexico)

The bus system in Cuernavaca, Mexico and its connections to random matrix distributions have been the subject of an interesting recent study by M Krbálek and P Šeba in [15, 16]. In this paper we introduce and analyse a microscopic model for the bus system. We show that introducing a natural repulsion does produce random matrix distributions in natural double scaling regimes. The techniques employed include non-intersecting paths, logarithmic potential theory, determinantal point processes, and asymptotic analysis of several orthogonal polynomial ensembles. In addition, we introduce a circular bus model and include various calculations of non-crossing probabilities.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48795/2/a6_28_s11.pd

The Wasteland of Random Supergravities

We show that in a general \cal{N} = 1 supergravity with N \gg 1 scalar fields, an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking the superpotential and Kahler potential to be random functions, we construct a random matrix model for the Hessian matrix, which is well-approximated by the sum of a Wigner matrix and two Wishart matrices. We compute the eigenvalue spectrum analytically from the free convolution of the constituent spectra and find that in typical configurations, a significant fraction of the eigenvalues are negative. Building on the Tracy-Widom law governing fluctuations of extreme eigenvalues, we determine the probability P of a large fluctuation in which all the eigenvalues become positive. Strong eigenvalue repulsion makes this extremely unlikely: we find P \propto exp(-c N^p), with c, p being constants. For generic critical points we find p \approx 1.5, while for approximately-supersymmetric critical points, p \approx 1.3. Our results have significant implications for the counting of de Sitter vacua in string theory, but the number of vacua remains vast.Comment: 39 pages, 9 figures; v2: fixed typos, added refs and clarification

ScienceDirect Experimental Study of Phase Transition in Pedestrian Flow

Abstract The transition between low and high density phases is a typical feature of systems with social interactions. This contribution focuses on simple evacuation design of one room with one entrance and one exit; four passing-through experiments were organized and evaluated by means of automatic image processing. The phase of the system, determined by travel time and occupancy, is evaluated with respect to the inflow, a controlled boundary condition. Critical values of inflow and outflow were described with respect to the transition from low density to congested state. Moreover, microscopic analysis of travel time is provided