Microscopic Car-following Model Research Articles

Microscopic car-following model for the traffic flow: the state of the art

Car-following theory is an important research direction in the field of intelligent transportation systems (ITS), it describes the one-by-one following process of vehicles on the same lane in traffic flow, and one of its important issues is congestion control. To explore the strategy for controlling traffic congestion, this paper introduces and analyzes some classic car-following models, and gives a systematic review of their developments. Moreover, in order to introduce the approach to analyze the stability, taking the full velocity difference (FVD) model for example, the local and asymptotic stability analysis is discussed, while the corresponding nonlinear analysis is also conducted. Then, some perspectives of the car-following model are given in the final.

The Physical Foundation of Car-following Model

Based on the Newton’s law of motion, the motion equation of the microscopic car-following model is introduced. The moving vehicles comply with the idea of Newton's equations of motion. But the interaction between vehicles is different from their traction. The inertia of the car is not its mass. We discuss the differences and present how to treat them. This article can deepen and widen the students' understanding of Newton's laws of motion. It can also provide the materials for university physical teaching. It is suitable for the students to exploratory study.

The Impact of Automated Truck Lanes on Intercity Expressways: A Study Using Hybrid Simulator

Automated truck lanes (ATL) is a future technology for alleviating high proportion of truck usage. This paper proposes a hybrid microscopic-mesoscopic traffic simulator that can be used to precisely estimate the changes in traffic flows that would result from introduction of ATL on large-scale road networks. An integration framework is designed to ensure consistency of route choice and synchronization between mesoscopic and microscopic simulators. Microscopic car-following and lane-changing models are extended to reflect detailed interactions between cars and trucks. Three cases are simulated to evaluate the impact of ATL on traffic flows, proportion of trucks, travel time, and performance in total travel time saving. Finally, an analysis of safety and the effect of road incidents on travel time are also conducted using the hybrid simulator. Simulation results indicate that ATL can change traffic volumes not only on the expressway itself (New Tomei-Meishin Expressway) but also on the other expressways in the network, leading to shorter travel times and improved safety. For a more precise evaluation, the ATL system should be analyzed as part of a large-scale road network.

A new continuum traffic model with the effect of viscosity

Through considering the connection between microscopic car-following model and macroscopic continuum model, a new viscous vehicular flow model is proposed, in which the viscosity coefficient is determined by a more realistic constitutive relationship between averaged reaction time of drivers and the car density. Further analysis indicates that two traffic sound speeds in this viscous model may determine the existence and the stability of traveling wave solutions with an analytical method.

Continuum modeling for two-lane traffic flow with consideration of the traffic interruption probability

Considering the effects that the probability of traffic interruption and the friction between two lanes have on the car-following behaviour, this paper establishes a new two-lane microscopic car-following model. Based on this microscopic model, a new macroscopic model was deduced by the relevance relation of microscopic and macroscopic scale parameters for the two-lane traffic flow. Terms related to lane change are added into the continuity equations and velocity dynamic equations to investigate the lane change rate. Numerical results verify that the proposed model can be efficiently used to reflect the effect of the probability of traffic interruption on the shock, rarefaction wave and lane change behaviour on two-lane freeways. The model has also been applied in reproducing some complex traffic phenomena caused by traffic accident interruption.

Stability of car following with human memory effects and automatic headway compensation

This paper addresses the study of some appropriate control strategies in order to guarantee the exponential stability of a class of deterministic microscopic car-following models including human drivers' memory effects and automated headway controllers. More precisely, the delayed action/decision of human drivers is represented using distributed delays with a gap and the considered automated controller is of proportional derivative type. The analysis is performed in both delay parameter and controller gain parameter spaces, and appropriate algorithms are proposed. Surprisingly, large delays and/or gains improve stability for the corresponding closed-loop schemes. Finally, some illustrative examples as well as various interpretations of the results complete the presentation.

Empirical Results of Effects of Various Causal Factors on Car-Following Behavior

Experimentation and analysis methodologies for data intended for the development of microscopic car-following models are presented. The data methodology centers on the notion that it is better to sample a varied group of real drivers when the subjects are unaware that an experiment is being conducted. This contrasts with the methods used to calibrate most conventional models. The analysis focuses on determining possible causal factors, beyond the kinematic variables most often used, that could play a role in real traffic. These factors include various human characteristics (e.g., gender and distractions related to in-vehicle conditions like telephoning and vehicle occupancy); traffic and road characteristics (e.g., type of vehicle, congestion level, and location of driving lane); and environmental characteristics (e.g., time of day and weather conditions). The paper shows the magnitudes of the relationships that are discovered and offers suggestions as to how these results might contribute to the development of better models.

Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use a smooth particle hydrodynamic approach and to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the ``traffic pressure'', which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.

Selecting Noise Source and Traffic Representations that Capture Road Traffic Noise Dynamics Near Traffic Signals

Considering trafic dynamics greatly improves noise estimation in urban area. This can be achieved by coupling a dynamic trafic model with both noise emission laws and sound propagation calculation. Determining the relevant noise source and trafic representations to estimate classical noise descriptors (L-Aeq and statistical descriptors) near trafic signals has been recently studied. This research topic is extended in this paper to more specific descriptors which are able to capture noise dynamics at the trafic signal scale, for usual urban trafic situations (upstream, in front of, and downstream a trafic signal) and different distances from the road (5.5, 10 and 15 m). It appears that 14m-line sources ensure an estimation of all descriptors with errors below 2 dB(A) if trafic dynamics is precisely described. Macroscopic and microscopic car-following models are both relevant to highlight noise dynamics triggered by the trafic signal, but some differences between those traffic representations are observed.

Microscopic Car-Following Models Revisited: From Road Works to Fundamental Diagrams

We analyze the dynamics of the classical optimal velocity model for the case of road works. We introduce a new viewpoint, the so-called rotation solutions, which in case of an additional symmetry leads to Ponies-on-a-Merry-Go-Round-solutions (POMs) [D. G. Aronson, M. Golubitsky, and J. Mallet-Paret, Nonlinearity, 4 (1991), pp. 903–910]. This approach, which is also useful for the case without road works, opens the possibility of analytical and numerical bifurcation studies, which show a wide variety in the possible dynamics of this very simple model. In addition, we mimic different measurement approaches and recover the famous inverse Greek $\lambda$ structure in the fundamental diagram.

Stability of Traffic Flow Behavior with Distributed Delays Modeling the Memory Effects of the Drivers

Stability analysis of a single-lane microscopic car-following model is studied analytically from the perspective of delayed reactions of human drivers. In the literature, the delayed reactions of the drivers are modeled with discrete delays, which assume that drivers make their control decisions based on the stimuli they receive from a point of time in the history. We improve this model by introducing a distribution of delays, which assumes that the control actions are based on information distributed over an interval of time in history. Such an assumption is more realistic, as it takes into consideration the memory capabilities of the drivers and the inevitable heterogeneity of their delay times. We calculate exact stability regions in the parameter space of some realistic delay distributions. Case studies are provided demonstrating the application of the results.

Micro- and macro-simulation of freeway traffic

We present simulations of congested traffic in circular and open systems with a nonlocal, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and macro-simulations with these models for identical vehicles on a single lane produce the same traffic states, which also qualitatively agree with empirical traffic observations. Moreover, the phase diagrams of traffic states in the presence of bottlenecks for the microscopic car-following model and the macroscopic gas-kinetic-based model almost agree. In both cases, we found metastable regimes, spatially coexistent states, and a small region of tristability. The distinction of different types of vehicles (cars and long vehicles) yields additional insight and allows us to reproduce empirical data even more realistically, including the observed fluctuation properties of traffic flows like the wide scattering of congested traffic data. Finally, as an alternative to the gas-kinetic approach, we propose a new scheme for deriving nonlocal macroscopic traffic models from given microscopic car-following models. Assuming identical (macroscopic) initial and boundary conditions, we show that there are microscopic models for which the corresponding macroscopic version displays an almost identical dynamics. This enables us to combine micro- and macro-simulations of road sections by simple algorithms, and even to simulate them simultaneously.

Micro- and macro-simulation of freeway traffic

We present simulations of congested traffic in circular and open systems with a nonlocal, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and macro-simulations with these models for identical vehicles on a single lane produce the same traffic states, which also qualitatively agree with empirical traffic observations. Moreover, the phase diagrams of traffic states in the presence of bottlenecks for the microscopic car-following model and the macroscopic gas-kinetic-based model almost agree. In both cases, we found metastable regimes, spatially coexistent states, and a small region of tristability. The distinction of different types of vehicles (cars and long vehicles) yields additional insight and allows us to reproduce empirical data even more realistically, including the observed fluctuation properties of traffic flows like the wide scattering of congested traffic data. Finally, as an alternative to the gas-kinetic approach, we propose a new scheme for deriving nonlocal macroscopic traffic models from given microscopic car-following models. Assuming identical (macroscopic) initial and boundary conditions, we show that there are microscopic models for which the corresponding macroscopic version displays an almost identical dynamics. This enables us to combine micro- and macro-simulations of road sections by simple algorithms, and even to simulate them simultaneously.

Macroscopic traffic models from microscopic car-following models.

We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of a conservation equation and a momentum equation, and the latter contains a relaxation term, an anticipation term, and a diffusion term. Properties of the resulting macroscopic model are compared with those of the optimal velocity model through numerical simulations, and reasonable agreement is found although there are deviations in the quantitative level. The derivation is also extended to general car-following models.

Multi-anticipative car-following model

The microscopic car-following model by Bando et al. [1-4] is extended by incorporating multi-vehicle interactions. It is shown that the reaction to more than one vehicle ahead leads to a stabilization of the dynamical behavior, i.e. the stable region increases. Still the fundamental macroscopic properties of traffic, free flow and congested flow, are described. More important, due to the multi-anticipative driving behavior driving in narrow platoons is forced such that a third fundamental property of traffic flow, the so-called synchronized flow [5], is modeled as well.