Multi-class Traffic Flow Model Research Articles

POLARIS-LC: A Multi-Class traffic Flow Model in Lagrangian Coordinates for Large-Scale Simulation

Agent-based modeling has become increasingly prevalent in transportation systems simulation as the scenarios around new technologies and policies become increasingly complex. This increased complexity, in terms of traveler behavior, traffic flow, modal operations, system management, and so on, requires increasingly sensitive and detailed representation of the core components of the simulation, especially as it relates to traffic flow. Many future mobility solutions rely on connectivity, communication, advanced sensing, and detailed information flows, while the simulation also needs to remain computationally tractable. In this paper, we propose a new Lagrangian Coordinate within the POLARIS Agent-Based-Modeling Framework (LC-POLARIS) of traffic flow, which combines computational efficiency while adding microscopic features. This model allows multi-class traffic flow by setting different speed-spacing relationships. In this modeling, automated vehicles have lower reaction time, while light-duty trucks have lower free-flow speed and higher jam spacing. The model captures the reduction in capacity and higher queue spillback because of higher jam spacing of trucks. Also, the model yields higher capacity for both passenger and light duty automated vehicles on expressways. The LC-ABM traffic flow model is validated in Bloomington, IL, USA, in a scenario with different rates of four vehicle types.

Multi-class traffic flow model based on three dimensional flow–concentration surface

This paper proposes a continuum model based on a three-dimensional flow-concentration surface for multi-class traffic. The model assumes that the flow of any vehicle class is a function of the class density as well as the fraction of road area occupied by other vehicle classes. By considering occupancy of road area instead of lane occupancy, the model effectively describes traffic flow that does not follow lane discipline. The propagation speed of small disturbance (PSSD), conventionally defined from the two-dimensional flow–density relationship, is reformulated for each class using a three-dimensional flow–concentration surface. Using the proposed PSSD and a speed–area occupancy (speed-AO) relationship, a second-order continuum model for multi-class traffic is formulated. The speed–AO relationship captures class-specific congestion and replicates the gap-filling behaviour commonly observed in lane-indisciplined traffic. Properties of the proposed model are validated theoretically where possible, and through numerical simulation when theoretical derivations are cumbersome. Numerical simulation of the proposed multi-class traffic model replicates field-observed phenomena such as shockwaves and rarefaction waves, local cluster effect, and gap-filling behaviour. Finally, the model is calibrated using field traffic data collected on a road section with bottleneck, and is found to replicate class-wise vehicle flows and speeds, and stop-and-go phenomena.

A two-dimensional multi-class traffic flow model

The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [ 21 ], where a two-dimensional model for a single class of vehicles is proposed, we extend the dynamics to a multi-class model leading to a coupled system of conservation laws in two space dimensions. Besides the study of the Riemann problems we also present a Lax-Friedrichs type discretization scheme recovering the theoretical results by means of numerical tests. We calibrate the multi-class model with real data and compare the fitted model to the real trajectories. Finally, we test the ability of the model to simulate the overtaking of vehicles.

Modeling multi-class disordered traffic flow subject to varying vehicle composition using the concept of traversable distance

Disordered traffic stream at the microscopic level can be described as a permeable medium. Each vehicle is considered to traverse through a series of lateral gaps created by other vehicles. We develop a multi-class traffic flow model that considers such viable and accessible gaps for individual vehicle classes to traverse downstream. The model accounts for the varying shares of different vehicle classes. The concept of traversable distance and modified equilibrium speed functions are used to model the interplay among multiple vehicle classes. Using a higher order finite volume approximation method, evolution for a two-class traffic stream is shown. This model replicates prominent empirical characteristics exhibited by multi-class disordered traffic such as overtaking and creeping. Varying shares of smaller vehicles affect queue formation and discharge characteristics, and have significant impacts on roadway capacity. The model also could compute dynamic class-specific travel times at different vehicular compositions more realistically.

Lagrangian-antidiffusive remap schemes for non-local multi-class traffic flow models

This paper focuses on the numerical approximation of the solutions of a class of non-local systems in one space dimension, arising in traffic modeling. We propose alternative simple schemes by splitting the non-local conservation laws into two different equations, namely the Lagrangian and the remap steps. We provide some properties and estimates recovered by approximating the problem with the Lagrangian-antidiffusive remap (L-AR) scheme, and we prove the convergence to weak solutions in the scalar case. Finally, we show some numerical simulations illustrating the efficiency of the L-AR schemes in comparison with classical first- and second-order numerical schemes.

Optimal control of a generalized multi-lane multi-class traffic flow model

Optimal control of a generalized multi-lane multi-class traffic flow model

Evaluating Impacts of Overloaded Heavy Vehicles on Freeway Traffic Condition by a Novel Multi-Class Traffic Flow Model

Overloaded heavy vehicles (HVs) have significant negative impacts on traffic conditions due to their inferior driving performance. Highway authorities need to understand the impact of overloaded HVs to assess traffic conditions and set management strategies. We propose a multi-class traffic flow model based on Smulders fundamental diagram to analyze the influence of overloaded HVs on traffic conditions. The relationship between the overloading ratio and maximum speed is established by freeway toll collection data for different types of HVs. Dynamic passenger car equivalent factors are introduced to represent the various impacts of overloaded HVs in different traffic flow patterns. The model is solved analytically and discussed in detail in the appendices. The model validation results show that the proposed model can represent traffic conditions more accurately with consideration for overloaded HVs. The scenario tests indicate that the increase of overloaded HVs leads to both a higher congestion level and longer duration.

Non-local multi-class traffic flow models

We prove the existence for small times of weak solutions for a class of non-local systems in one space dimension, arising in traffic modeling. We approximate the problem by a Godunov type numerical scheme and we provide uniform L ∞ and BV estimates for the sequence of approximate solutions. We finally present some numerical simulations illustrating the behavior of different classes of vehicles and we analyze two cost functionals measuring the dependence of congestion on traffic composition.

Model Predictive Control for Freeway Networks Based on Multi-Class Traffic Flow and Emission Models

The main aim of this paper is to use multi-class macroscopic traffic flow and emission models for Model Predictive Control (MPC) for traffic networks. In particular, we use and compare extended versions of multi-class METANET, FASTLANE, multi-class VT-macro, and multi-class VERSIT+. In addition, end-point penalties based on these multi-class traffic flow and emission models are also included in the objective function of MPC to account for the behavior of the traffic system beyond the prediction horizon. A simulation experiment is implemented to evaluate the multi-class models. The results show that the approaches based on multi-class METANET and the extended emission models (multi-class VT-macro or multi-class VERSIT+) can improve the control performance for the total time spent and the total emissions with respect to the non-control case, and they are more capable of dealing with the queue length constraints than the approaches based on FASTLANE. Including end-point penalties can further improve the control performance with a small sacrifice in the computational efficiency for the approaches based on multi-class METANET but not for the approaches based on FASTLANE.

A Heterogeneous Multiclass Traffic Flow Model with Creeping

A heterogeneous traffic model with two vehicle classes is developed to capture overtaking and creeping in highly heterogeneous traffic flows. Creeping is a special case of overtaking that occurs when small vehicles continue to advance in congestion even though larger vehicles have completely stopped. To motivate the new model, it is shown that a two class homogeneous multiclass model is equivalent to a class of second order models originally proposed by Aw, Rascle, and Zhang (ARZ). Based on the properties of the ARZ model, homogeneous models do not allow overtaking or creeping. The new creeping model is a phase transition model which applies a system of conservation laws in the noncreeping phase and a system equivalent to a scalar model in the creeping phase. The solution to the Riemann problem is obtained by investigating the elementary waves, particularly for the cases when one vehicle class is absent, as well as in the presence of a phase transition. Based on the proposed Riemann solver, the solution to the Cauchy problem is constructed using wavefront tracking. Numerical tests are carried out using a Godunov scheme to illustrate the creeping phenomenon. Source code for the numerical simulations is available at https://github.com/shimaof/heterogeneous-traffic-model.

Anisotropy in generic multi-class traffic flow models

Traffic flow models and simulation tools are often used for traffic state estimation and prediction. Recently several multi-class models based on the kinematic wave traffic flow model have been introduced. These multi-class models take into account the heterogeneity of both vehicles and drivers. We analyse two important properties of these models: hyperbolicity and anisotropy. Both properties relate to the propagation speed of disturbances, as can be observed in real traffic. We discuss the importance of traffic flow models to be hyperbolic and anisotropic. Moreover, we develop a framework to analyse whether traffic flow models have these properties. Therefore, we derive a generic formulation of multi-class kinematic wave traffic flow models, rewrite it in the Lagrangian formulation and apply eigenvalue analysis to the resulting system of equations. Our analysis shows that most multi-class kinematic wave traffic flow models are indeed hyperbolic and anisotropic under certain modelling conditions.

Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme

A high-resolution relaxed scheme which requires little information of the eigenstructure is presented for the multiclass Lighthill-Whitham-Richards (LWR) model on an inhomogeneous highway. The scheme needs only an estimate of the upper boundary of the maximum of absolute eigenvalues. It is based on incorporating an improved fifth-order weighted essentially non-oscillatory (WENO) reconstruction with relaxation approximation. The scheme benefits from the simplicity of relaxed schemes in that it requires no exact or approximate Riemann solvers and no projection along characteristic directions. The effectiveness of our method is demonstrated in several numerical examples.

A hybrid scheme for solving a multi-class traffic flow model with complex wave breaking

This paper extends the δ -mapping algorithm to solve a multi-class traffic flow model on an inhomogeneous highway, which is characterized by spatially varying fluxes and very complex waves. In the algorithm, the values of solution variables are mapped onto an intermediate state locally around the cell interface, and then the finite difference WENO reconstruction is applied. The hybrid scheme is consistent with steady flows, and resolves the waves more efficiently than the standard WENO scheme. The algorithm is also applicable to hyperbolic conservation laws with spatially varying fluxes in general.

Hyperbolicity and kinematic waves of a class of multi-population partial differential equations

This paper studies many fundamental aspects of a newly proposed multi-class traffic flow model. For the first time it presents a complete discussion on the hyperbolicity of the system; and based upon this, the admissible waves of the Riemann problem are deeply investigated. Many important conclusions are made in discussions, and the related physical meanings are interpreted. For the confirmation of main conclusions, numerical examples are given at the end.

A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway

As a new attempt to solve hyperbolic conservation laws with spatially varying fluxes, the weighted essentially non-oscillatory (WENO) method is applied to solve a multi-class traffic flow model for an inhomogeneous highway. The numerical scheme as well as an analytical study is based upon a modified equivalent system that is written in a “standard” hyperbolic conservation form. Numerical examples, which include the difficult traffic signal control problem, are used to demonstrate the effectiveness of the WENO scheme in which the results are in good agreement with the analytical counterparts.

A multi-class traffic flow model – an extension of LWR model with heterogeneous drivers

In this paper, a multi-class traffic flow model as an extension of the Lighthill, Whitham and Richards (LWR) model with heterogeneous drivers is formulated. The model takes into account the distribution of heterogeneous drivers characterized by their choice of speeds in a traffic stream, which models the dynamic behavior of heterogeneous users whereby faster vehicles could overtake slower ones under uncongested condition as well as congested condition (though less easily), and slower vehicles would slow down the faster ones. Numerical simulations show that the model can predict many of the puzzling traffic flow phenomena such as the two-capacity (or reverse-lambda) regimes occurred in the fundamental diagram, hysteresis and platoon dispersion.