A superstatistical model of vehicular traffic flow

Abstract

In the analysis of vehicular traffic flow, a myriad of techniques have been implemented. In this study, superstatistics is used in modeling the traffic flow on a highway segment. Traffic variables such as vehicular speeds, volume, and headway were collected for three days. For the superstatistical approach, at least two distinct time scales must exist, so that a superposition of nonequilibrium systems assumption could hold. When the slow dynamics of the vehicle speeds exhibit a Gaussian distribution in between the fluctuations of the system at large, one speaks of a relaxation to a local equilibrium. These Gaussian distributions are found with corresponding standard deviations 1/β. This translates into a series of fluctuating beta values, hence the statistics of statistics, superstatistics. The traffic flow model has generated an inverse temperature parameter (beta) distribution as well as the speed distribution. This beta distribution has shown that the fluctuations in beta are distributed with respect to a chi-square distribution. It must be mentioned that two distinct Tsallis q values are specified: one is time-dependent and the other is independent. A ramification of these q values is that the highway segment and the traffic flow generate separate characteristics. This highway segment in question is not only nonadditive in nature, but a nonequilibrium driven system, with frequent relaxations to a Gaussian

An entropy-based analysis of lane changing behavior: An interactive approach

“…A strong corroboration for this hypothesis by the authors comes from the research of Kosun and Ozdemir (2016) where the generalized entropy governs the traffic processes. In that work, the authors examined to what extent a given road segment displays Boltzmann-Gibbs characteristics.…”

“…Hence, both long and short-range interactive driving could be examined in this generalized framework. Of the vehicular traffic studies, the references (Kosun and Ozdemir 2016), and (Koşun 2015) are representative in terms of exhibiting the connection between traffic flow and generalized statistical mechanics. Nonadditivity is here discussed in terms of lane changing scenarios and driving safety.…”

Determining the complexity of multi-component conformal systems: A platoon-based approach

“…Under χ 2 distributed β, the generalized canonical distributions of nonextensive statistical mechanics become, Eq. (4), [2,21]…”

“…Traffic flow is a complex, many particle system where vehicles come into contact, forming possibly long-range, non-Markovian type memory, where the dominating form of thermostatistics is the nonextensive entropic domain, instead of the highly idealized Boltzmann-Gibbs (BG) framework. The existence of such interactions has been shown in detailed analysis in [1,2]. Unless interactions are ignored, and simplified, traffic flow would hardly harbor Gaussian distributions, and ergodic time series.…”

Guidance control strategy for air traffic flow in terminal areas

“…There have been a large number of research efforts made to study the traffic flow characteristics up to now; however, they mainly focused on vehicle traffic flow. It is a common method to establish traffic flow models to analyze traffic operation phenomena and traffic congestion rules, [3][4][5] particularly in the field of intelligent transportation system based on information guidance. A series of route guidance algorithms, traffic guidance information release strategies, and optimal location of traffic guidance information releasing devices were proposed.…”