Homogeneous Traffic Flow Research Articles

Third-order leader-following consensus protocol of traffic flow formed by cooperative vehicular platoons by considering time delay: constant spacing strategy

In this article, the problem of third-order consensus of homogeneous traffic flow formed by cooperative vehicular platoons is studied. This article is presented in two main parts. Inter-platoon stability analysis and intra-platoon stability analysis. For inter-platoon stability analysis, due to great length of traffic flow, it is assumed that lead vehicle is not available. Therefore, a new consensus algorithm based on bidirectional virtual leader-following strategy is introduced. Both communication and parasitic delays are involved in control design and stability analysis. By decoupling the closed-loop dynamics of cooperative leaders and employing the cluster treatment characteristic root method, necessary conditions on control parameters and stable regions of time delay satisfying internal stability of leaders’ network are derived. In continuance of this part, inter-platoon string stability is studied. In the second part, it is assumed that the communication topology of each platoon is generic. Therefore, some of the eigenvalues of network matrix are complex which complicates the intra-platoon stability analysis. After decoupling the closed-loop dynamics of each platoon, a new consensus algorithm is presented. It will be shown that by this algorithm, the control parameters are independent of eigenvalues of network matrix which simplifies the controller design and stability analysis. Several simulation results are provided to show the effectiveness of the proposed approaches.

An Enhanced Clustering-Based Method for Determining Time-of-Day Breakpoints Through Process Optimization

The fixed-time strategy is crucial in traffic signal control which applies signal plans to different time periods of the day. One critical step is to determine the optimal breakpoints to divide one day into periods with homogeneous traffic flow. Most existing methods are based on $k$ -means clustering algorithm and have to select the optimal number of clusters. Since direct $k$ -means and time-incorporated $k$ -means clustering will result to noncontiguous time periods, several adjustments are needed including further partitioning and re-clustering via empirically adjustment which merges short time periods into adjacent longer ones to finalize the time-of-day (TOD) partition plan. Such adjustments can make the previous optimal number of clusters selection suboptimal. This paper proposes an enhanced method to determine optimal TOD breakpoints through optimizing the process. Instead of choosing the optimal partition plan before adjustments, we propose to determine the optimum after all the adjustments. A case study based on Qingdao City in China is presented to evaluate the added value of the enhanced method. It is shown through simulation experiments that the enhanced method can avoid over-partitioning and substantially improve the traffic operational efficiency especially during high demand periods.

Heterogeneous platoon flow dispersion model based on truncated mixed simplified phase‐type distribution of travel speed

SummaryExisting research on platoon dispersion models either describe homogeneous traffic flow feature, or are in lack of analytical solutions. By analyzing the field data, the truncated mixed simplified phase‐type distribution is proved to be capable of capturing the characteristics of heterogeneous traffic flow with an excellent fitting result. In light of this, we derive a generic heterogeneous platoon dispersion model with truncated mixed simplified phase‐type of speed in the forms of integrable functions. Numerical case studies are conducted to compare the performance of the proposed model and the conventional models (i.e., the Robertson model and truncated mixed Gaussian model). The results show that the proposed model not only better captures the platoon dispersion laws of heterogeneous traffic flow, but also presents higher computational efficiency, which provides practical implications on traffic signal control. Copyright © 2017 John Wiley & Sons, Ltd.

Dynamic route guidance strategy in a two-route pedestrian-vehicle mixed traffic flow system

With the rapid development of transportation, traffic questions have become the major issue for social, economic and environmental aspects. Especially, during serious emergencies, it is very important to alleviate road traffic congestion and improve the efficiency of evacuation to reduce casualties, and addressing these problems has been a major task for the agencies responsible in recent decades. Advanced road guidance strategies have been developed for homogeneous traffic flows, or to reduce traffic congestion and enhance the road capacity in a symmetric two-route scenario. However, feedback strategies have rarely been considered for pedestrian-vehicle mixed traffic flows with variable velocities and sizes in an asymmetric multi-route traffic system, which is a common phenomenon in many developing countries. In this study, we propose a weighted road occupancy feedback strategy (WROFS) for pedestrian-vehicle mixed traffic flows, which considers the system equilibrium to ease traffic congestion. In order to more realistic simulating the behavior of mixed traffic objects, the paper adopted a refined and dynamic cellular automaton model (RDPV_CA model) as the update mechanism for pedestrian-vehicle mixed traffic flow. Moreover, a bounded rational threshold control was introduced into the feedback strategy to avoid some negative effect of delayed information and reduce. Based on comparisons with the two previously proposed strategies, the simulation results obtained in a pedestrian-vehicle traffic flow scenario demonstrated that the proposed strategy with a bounded rational threshold was more effective and system equilibrium, system stability were reached.

Density-based mixed platoon dispersion modelling with truncated mixed Gaussian distribution of speed

In China, urban arterial traffic presents a mixed-flow feature because the percentage of bus flow is relatively high. This affects the applicability of traditional platoon dispersion models, which are generally only suitable for homogeneous traffic flow. Based on field observations, this paper proposes a mixed platoon dispersion model (MPDM) to macroscopically simulate the mixed platoon dispersion process along the road segment between two successive signalised intersections from the density view. In order to capture the heterogeneity in mixed platoon speeds, the truncated mixed Gaussian distribution is adopted here to fit the speed data collected in the field, and expectation–maximisation (EM) algorithm is employed to estimate the distribution parameters. Later, the piecewise platoon density function is developed to examine the platoon dispersion characteristics. By applying this density function, the formulations of the expected number of vehicles in the front of the platoon that have passed and the expected number of vehicles at the rear of the platoon that have not passed a downstream intersection, as well as the downstream arriving flow function, are derived. Furthermore, numerical calculation for signal coordination verifies the effectiveness of the proposed MPDM.

A car-following model accounting for the driver’s attribution

In this paper, we use the FVD (full velocity difference) model to develop a car-following model with consideration of the driver’s attribution. The numerical results show that the proposed model can qualitatively reproduce the effects of the driver’s attribution on each vehicle’s speed, acceleration, fuel consumption and exhaust emissions under two typical traffic states, i.e., the aggressive driver enhances his speed, acceleration, fuel consumption and exhaust emissions while the conservative driver reduces his speed, acceleration, fuel consumption and exhaust emissions, so the aggressive driver’s speed, acceleration, fuel consumption and exhaust emissions are greater than those of the neutral driver and the neutral driver’s speed, acceleration, fuel consumption and exhaust emissions are greater than those of the conservative driver. In addition, we further study each vehicle’s speed, acceleration, fuel consumption and exhaust emissions when aggressive drivers, neutral drivers and conservative drivers are uniformly mixed. The numerical results show that there are no prominent differences between the mixed traffic flow and the homogeneous traffic flow consisting of neutral driver, i.e., each vehicle’s speed, acceleration, fuel consumption and exhaust emissions are similar to those of the neutral driver.

Variable Speed Limit Control Strategy with Collision Probability Assessments Based on Traffic State Prediction

An increasing number of vehicles on roadways has made traffic safety a serious challenge for transportation engineers. For the mitigation of traffic safety concerns, a variety of active traffic control measures, such as the variable speed limit (VSL), have been intensively investigated and deployed. VSL is usually adopted to advise drivers of a lower speed limit that is more appropriate to a congested traffic condition and takes advantage of the homogeneous traffic flow effect. However, in earlier studies, because of the absence of traffic state prediction, the impact of applied VSL control was not quantitatively analyzed. In this study, a model predictive control framework was adopted for predicting and assessing future traffic states. Taking into consideration the impact of VSL control, the study used a macroscopic traffic flow model. The collision probabilities of the predicted traffic states were assessed with a precursor-based collision prediction model to determine the optimized control signal. With this design, the proposed algorithm controller provided a robust method for determining the VSL control plan to optimize safety performance over a traffic network. The proposed control algorithm was evaluated with a simulation study based on field data that was conducted to reproduce a major ring road in Edmonton, Alberta, Canada. The proposed algorithm was used to implement VSL control on the studied 11-km freeway stretch. The proposed algorithm control scenario was then compared with the uncontrolled scenario. The evaluation proved that the proposed VSL control algorithm could effectively reduce the probability for collisions in a congested traffic network without significantly compromising mobility.

Traffic Safety and Sustainable Transport Systems in Developing Countries

Road safety problems and the efficiency of transport systems are influenced by factors outside the context of the infrastructure itself. This acknowledgement is of great importance when transferring transport systems and road safety policies developed in high-income countries to low-income countries. Policies and countermeasures that have proven to be effective in the mitigation of road safety problems in developed countries may not fit well with the safety needs in settings where road traffic is commonly characterized by a higher degree of heterogeneity. Such characteristic makes underlying concepts of traffic flows theory applied in high-income countries questionable when applied to low-income countries given that they are designed for homogeneous traffic flows. Because they do not account for such varying dynamic and static characteristics of transport modes they fail in delivering adequate results when applied to road environments characterized by heterogeneous traffic. Other important issues are the differences in the mobility habits of the population, the role and the quality of the public transport systems and its characteristics. The objective of this paper is to provide a better understanding on how all these factors correlate and influence the performance and safety of the transport systems and their importance in the development of infrastructures and transport policies that better fit the mobility patterns and safety needs of developing societies. 

Mixed traffic flow modeling near Chinese bus stops and its applications

To determine how bus stop design influences mixed traffic operation near Chinese bus stops, a new theoretical method was developed by using additive-conflict-flows procedure. The procedure was extended from homogeneous traffic flow to mixed traffic flow. Based on the procedure and queuing theory, car capacity and speed models were proposed for three types of bus stops including curbside, bus bay and bicycle detour. The effects of various combinations of bus stop type, traffic volume, bus dwell time, and berth number on traffic operations were investigated. The results indicate that traffic volume, bus dwell time and berth number have negative effects on traffic operations for any type of bus stops. For different types of bus stops, at car volumes above approximately 200 vehicles per hour, the bus bay and bicycle detour designs provide more benefits than the curbside design. As traffic volume increases, the benefit firstly increases in uncongested conditions and then decreases in congested conditions. It reaches the maximum at car volumes nearly 1 100 vehicles per hour. The results can be used to aid in the selection of a preferred bus stop design for a given traffic volume in developing countries.

VEHICLE CLASS WISE SPEED-VOLUME MODELS FOR HETEROGENEOUS TRAFFIC

Link performance functions commonly used for traffic assignment are often based on Volume Delay Functions (VDF) developed for homogeneous traffic. However, VDFs relating stream speed to the volume of traffic based on homogeneous lane-based traffic are not adequate for traffic assignment in developing countries due to the heterogeneous nature of traffic that is characterized by a mix of a wide range of vehicle classes with significant differences in static and dynamic characteristics and an imperfect lane discipline. Unfortunately, the use of VDFs similar to those for homogeneous traffic flow situations imposes strong restrictions considering two respects: 1) travel times at path and link levels can be obtained for an aggregated stream but not for individual vehicle types; 2) the effect of varying composition and asymmetric interactions is captured only to a limited extent by converting all vehicles into equivalent Passenger Car Unit (PCU). Hence, this paper proposes the development of VDFs specific to different classes of heterogeneous traffic, as it is more realistic in traffic assignment than the use of the same VDF for all classes of vehicles in a link. This study is aimed at developing models to determine the speed of each vehicle class as a function of flow and composition for six lane roads with heterogeneous traffic based on data obtained from Chennai city, India. Heterogeneity in this study mainly refers to differences in vehicle types (two-wheeler, car, bus, etc.) participating in mixed traffic. To develop multiple user class VDFs, the speed and flow of each vehicle class for a wide range of traffic flow conditions need to be recorded. As this is not possible using field measurements, an established micro-simulation model (HETEROSIM) is used for determining speeds for each vehicle type by systematically varying the volume and composition levels over a range of values that represent relevant and practical traffic conditions observed in six lane divided roads in Chennai city. The proposed delay functions are different from standard single user class VDFs in three key respects: first, they enable more realistic behaviour by modelling differences in class wise speeds at a given volume and composition level; second, they allow for capturing asymmetric interactions of different vehicle types on an average speed of a given vehicle class. Finally, speed-flow relationships for each class are also allowed to vary across volume levels which enable the representation of differential interactions at different levels of congestion in mixed traffic. The need for homogenizing the volumes in terms of a single class is obviated. The models significantly outperformed single class VDFs in both calibration and validation datasets. Further, the proposed models are used for analyzing heterogeneous traffic characteristics. Empirical evidence of asymmetric interactions and the impact of composition on classwise performance are also found and quantified. Finally, two applications of the proposed models are demonstrated for the level of service analysis of different classes and impact analysis of excluding some classes. The proposed models may have applications such as determining class wise road user costs and performance measures (e.g. emissions) that depend on class-specific speeds.

A Modified Cellular Automaton in Lagrange Form with Velocity Dependent Acceleration Rate

Based on Nasch model of single lane traffic flow, a modified Cellular Automaton traffic flow model incorporating s-t-s effect among vehicles given in Lagrange model for traffic flow is proposed to simulate homogeneous and mixed type traffic flow. The model is developed with modified cell size, incorporating different acceleration characteristics depending upon the speed of each individual vehicle. Comparisons are made between Nasch model and modified model. It is observed that slope of congested branch is changed for modified model due to variable acceleration rate.

Car capacity near bus stops with mixed traffic derived by additive-conflict-flows procedure

To determinate car capacity at bus stops with mixed traffic, a new theoretical approach was developed on the basis of additive-conflict-flows procedure. The procedure was extended from homogeneous traffic flow to mixed traffic flow. The conflicts among cars, buses and bicycles near the stop can be described by the extended procedure. The procedure can be understood more easily than the theory of gap acceptance. Car capacity near the stop is the function of both bus stream and bicycle stream. The proposed model can also analyze the cases of pedestrian effects and limited priority of bicyclists. Numerical results show that the car capacity decreases with the increasing flow rates of other streams. In addition, pedestrian effects and bicyclist’s limited priority have negative effects on car capacity near bus stops with mixed traffic flow.

Uncertainty Modeling and Robust Control in Urban Traffic

AbstractThe paper investigates the problem of uncertainty modeling and constrained robust control of urban traffic. Linear polytopic approach is used by state-space representations to describe the uncertain network system. In order to handle model mismatches, robust and infinite horizon model predictive control (MPC) method is proposed. The control strategy is an efficient method to reduce travel time and improve homogeneous traffic flow under changing model conditions. Centralized numerical solution has been carried out as a solution of Linear Matrix Inequalities (LMI) by using semidefinite programming (SDP). Closed-loop control results were tested in simulation environment taking alternative model uncertainty levels into account.

PERTURBATION AND STABILITY ANALYSIS OF THE MULTI-ANTICIPATIVE INTELLIGENT DRIVER MODEL

This paper discusses three kinds of IDM car-following models that consider both the multi-anticipative behaviors and the reaction delays of drivers. Here, the multi-anticipation comes from two ways: (1) the driver is capable of evaluating the dynamics of several preceding vehicles, and (2) the autonomous vehicles can obtain the velocity and distance information of several preceding vehicles via inter-vehicle communications. In this paper, we study the stability of homogeneous traffic flow. The linear stability analysis indicates that the stable region will generally be enlarged by the multi-anticipative behaviors and reduced by the reaction delays. The temporal amplification and the spatial divergence of velocities for local perturbation are also studied, where the results further prove this conclusion. Simulation results also show that the multi-anticipative behaviors near the bottleneck will lead to a quicker backwards propagation of oscillations.

Hydrodynamic modeling of traffic jams in intracellular transport in axons

Irregularities in intracellular traffic in axons caused by mutations of molecular motors may lead to “traffic jams”, which often result in swelling of axons causing such neurodegenerative diseases as Alzheimer's disease and Down syndrome. Hence, it is of particular interest to mathematically model the formation of traffic jams in axons. This paper adopts the hydrodynamic continuity equations for intracellular transport of organelles as developed by Smith and Simmons [D.A. Smith, R.M. Simmons, Models of motor-assisted transport of intracellular particles, Biophysical Journal 80 (2001) 45–68.] whereas the Kerner and Konhäuser [B.S. Kerner, P. Konhäuser, Cluster effect in initially homogeneous traffic flow, Physical Review E 48 (1993), R2335–R2338.] model for traffic jams in highway traffic is applied to predict the velocity field. It is observed that combination of the two sets of equations can comprehensively predict the traffic jams in axons without the need to any additional assumption or modification.

Navier-Stokes-like equations applicable to adaptive cruise control traffic flows

Under the scenario in which, within a traffic flow, each vehicle is controlled by adaptive cruise control (ACC), and the macroscopic one-vehicle probability distribution function fits the Paveri-Fontana hypothesis, a set of reduced Paveri-Fontana equations considering the ACC effect is derived. With the set, by maximizing the specially defined informational entropy deviating from a certain reference homogeneous steady state, the Navier-Stokes-like equations considering ACC are introduced. For a homogeneous steady traffic flow in a single circular lane, when the steady velocity or density is perturbed along the lane, numerical simulations indicate that ACC-controlled vehicles require less time for re-equilibration than manually driven vehicles. The re-equilibrated steady densities for ACC and manually driven traffic flows are all close to the original values; the same is true for the re-equilibrated steady velocity for manually driven traffic flows. For ACC traffic flows, the re-equilibrated steady velocity may be higher or lower than the original value, depending upon a parameter ω (introduced to solve the distribution function of the reference steady state), and the headway time (introduced in ACC models). Also, the simulations indicate that only an appropriate parameter set can ensure the performance of ACC; otherwise, ACC may result in low traffic running efficiency, although traffic flow stability becomes better.

Controlling traffic jams by a feedback signal

The aim of this paper is to control the vehicle system to move orderly by a feedback signal in the optimal velocity (OV) model under open boundary. Following the description of the OV model and its stability analysis, some problems about the definition of traffic jams in [12] are presented and illustrated by an example. Based on our analysis, a feedback signal acting on the traffic system has been introduced into the OV model. The signal will act in the system only if the state is inhomogeneous, and it will vanish in the homogeneous traffic flow. Theoretically, it is proved that the disorder state in traffic system could be suppressed by using the control method. Two kinds of noises are tested in our computer simulations. The simulation results demonstrate that the traffic system can move into a homogeneous phase by the control.

The direct simulation Monte Carlo method applied to a Boltzmann-like vehicular traffic flow model

In this paper a direct simulation Monte Carlo (DSMC) method is applied to a spatial homogeneous mesoscopic vehicular traffic flow model, based on a Boltzmann-like master equation. In contrast to gas kinetics, where in a collision a velocity jump change occurs, the interaction now changes the acceleration value of the following car in a leading car pair. There are no conservation laws in a single interaction. Therefore the Bird simulation scheme seems not to be the right choice for the approximation of the interaction integral. It is shown that a Nanbu like scheme is natural for this process. To avoid the typical double loop computational effort of the Nanbu scheme, a sampling algorithm developed by Babovsky is applied. Several car interaction profiles are examined and their resulting stochastic equilibrium solutions are discussed. First, simple interaction profiles are used to compare the simulation results with analytic calculated velocity distributions showing excellent agreement. Second, a realistic distance threshold interaction profile is applied to the simulation and the results are shown to be in qualitative agreement with measured traffic flow data. The simulation procedure seems to be applicable to study the influence of different interaction profiles to the macroscopic vehicular traffic flow quantities in stochastic equilibrium.

A numeric investigation of a vehicular traffic flow model based on a stochastic acceleration process

In this paper a new acceleration oriented mesoscopic vehicular traffic flow model based on a Boltzmann equation ansatz together with its numerical solving method is discussed. A direct simulation Monte Carlo method is adopted from gas dynamics to solve the model equation for a spatial homogeneous traffic flow and different driver interaction profiles. For a simple academic interaction case the numerical solution is found to be in very good agreement with the analytical calculated result. For a more applied interaction profile the numerical results are in good qualitative conformance to measurements or other traffic flow theories.

Editorial

Recently, considerable technological progress has been made in the field of AutomatedDriver Assistance Systems (ADAS). Electronic devices inform or support the driver inaccident-prone driving situations, in order to improve the critical task of driving a motorvehicle. Potentially, ADAS offers important advantages for road transportation: increasedcontrol with respect to the speed and the position of vehicles on the road is important forestablishing homogeneous traffic flows and reducing the number of accidents. As suchADAS is assumed to have a positive impact on the use of road infrastructure and trafficsafety (Boussuge & Valade, 1994). Moreover, this could lead to a reduction of energy useand polluting gas emissions (Barth, 1995; Michaelian & Browand, 2000). As soon as parts ofor the whole driving task are supported and/or executed automatically by ADAS, vehicledriving could become more comfortable and more convenient as compared to today’s manualdriving (Stevens, 1997; Hoedemaeker, 1999). These expectations imply a high potential inindividual and societal advantages. In various countries, therefore, transport policy makers areincreasingly interested in the automation of vehicle driving tasks. However, current policydevelopment regarding ADAS is highly complicated by, among others, much uncertainty onfuture ADAS development and implementation in terms of whether ADAS implementationwill contribute to or conflict with transport policy goals, and the basic societal conditionsrequired for ADAS implementation (Marchau, 2000)