First-order Macroscopic Model Research Articles

Framework for Deriving Macroscopic Demand Functions from Microscopic Acceleration Models

Vehicle acceleration plays an integral role in determining the operational capacity of roadway sections. Traditional first-order macroscopic models of traffic do not capture the boundedness of vehicle acceleration. In a recent study, it was shown that the cell transmission model could capture critical macroscopic effects of bounded acceleration if one modified the demand function such that traffic demand (sending flow) decreased in density for congested traffic. However, such a modified demand function was calibrated only with data. This paper introduces a framework for deriving such macroscopic demand functions corresponding to well-known microscopic acceleration models. Two mechanisms are explored for deriving the demand function with varying assumptions on how vehicles accelerate within a single discretized cell. The first mechanism is based on the assumption that vehicles within a single cell begin accelerating at the same time and that this information of the trigger of acceleration propagates instantaneously. The second mechanism assumes that the information for the trigger propagates within the cell at a finite speed such that following vehicles begin their acceleration process later than the leading vehicles. The derived demand functions are consistent with those calibrated with data. This study explicitly bridges macroscopic and microscopic models of bounded acceleration and can lead to more efficient evaluation of the effects of bounded acceleration on traffic systems.

Self-organized populations interacting under pursuit-evasion dynamics

We discuss the modeling of interacting populations through pursuit-evasion–or attraction–repulsion–principles : preys try to escape chasers, chasers are attracted by the presence of preys. We construct a hierarchy of models, ranging from ODEs systems with finite numbers of individuals of each population, to hydrodynamic systems. First-order macroscopic models look like generalized “two-species Keller–Segel equations”. But, due to cross-interactions, we can show that the system does not exhibit any blow up phenomena in finite time. We also obtain second-order models, that have the form of systems of balance laws, derived from kinetic models. We bring out a few remarkable features of the models based either on mathematical analysis or numerical simulations.

On the Consistency of Freeway Macroscopic Merging Models

Many first-order macroscopic models for freeway traffic have been developed since the seminal work on the well-known Lighthill–Whitham–Richards, or LWR, continuous model. The asymmetric cell transmission model (ACTM) is a widely accepted macroscopic model integrated into a variety of freeway traffic control frameworks. The model is based on the original cell transmission model; modified merge equations make it computationally tractable for optimization of ramp metering. However, when the common simplistic calibration of the model is used, an infeasible merging behavior is observed at uncontrolled merges, and the resulting queue lengths are not accurately estimated. This paper proposes an elegant analytical relationship, based on traffic flow theory, for calibrating the two parameters involved in the ACTM merge model. The method ensures the physical consistency of the dynamics involved in queue processes in the proximity of a noncontrolled merge junction. This method should be an essential feature of any freeway traffic model.

Second-Order Model and Capacity Drop at Merge

This study deals with the modeling of merge sections from a macroscopic point of view. It is well known that the first-order macroscopic model is not able to reproduce the capacity drop, that is, the fact that the maximal throughput just downstream of a merge is lower after the onset of congestion than just before. Second-order models, such as the one proposed recently by Bastin and Haut, claim to be able to reproduce this observed feature. The ability of this second-order model, chosen for its generality, to reproduce the capacity drop was studied by using numerical investigations. Definitions of the capacity drop are reviewed and some of the experimental observations are reported. The latest attempts to model the capacity drop are presented. Then the chosen model is presented briefly, and its numerical resolution is detailed. The study's main contribution can then be developed. From numerical experiments, it is shown that the studied approach allows the definition of a new framework for capacity drop modeling. Its limitations are also explored.

Integrating the Impact of Rain into Traffic Management

A new approach to the integration of the effects of inclement weather into traffic management strategies is presented. Adverse weather conditions are a critical factor affecting traffic operations and safety. Previously, a methodology for the analysis of the impact of rain has been addressed, and this impact on key traffic indicators (e.g., free-flow speed, capacity) has been quantified. As a result of these quantification studies, a first parameterization of the fundamental diagram according to rain intensity has been proposed. Since the fundamental diagram represents the basis of many simulation tools, the goal is to develop weather-responsive traffic state estimation tools that can be useful for control applications and traffic management. More precisely, the online traffic state estimation takes place within a Bayesian framework with particle-filtering techniques (i.e., sequential Monte Carlo simulations) in combination with a parameterized first-order macroscopic model. This approach has already been validated for sensor diagnosis and accident detection. In this paper the goal is to show how the integration of the weather effects can improve this efficient tool. The approach is validated with real-world data from the ring road section in Lyon, France (eight sensors from a homogeneous section). The results from different scenarios show the benefits of integrating the impact of rain into traffic state estimation. Strategies to detect a rain event in time and space are also suggested.

Introducing Buses into First-Order Macroscopic Traffic Flow Models

The aim of this paper is to provide a simple model of the interaction between buses and the surrounding traffic flow. Traffic flow is assumed to be described by a first-order macroscopic model of the Lighthill-Whitman-Richards type. As a consequence of their kinematics, which in large measure can be considered to be independent of the flow of other vehicles, buses should be considered as a moving capacity restriction from the point of view of other drivers. This simple interaction model is analyzed, mainly by considering the moving frame associated with the bus in order to derive analytical computation rules for derivation of the effects of the presence of the bus in the traffic flow. After deriving traffic equations in the moving frame associated with a bus, the usual basic concepts of first-order models, including those of relative traffic supply and demand, are generalized to the moving frame. A simple model for the bus-traffic interaction, assuming that the dimension of the bus can be neglected, can be derived from analytical calculations in the moving frame. Finally, some tentative results for the inclusion of buses into first-order traffic flow models, discretized according to Godunov’s scheme, are given.