First-order traffic flow models incorporating capacity drop: Overview and real-data validation

Much work has been done to compare traffic-flow models with reality; so far, this has been done separately for microscopic, as well as for fluid-dynamical, models of traffic flow. This paper compares directly the performance of both types of models to real data. The results indicate that microscopic models, on average, seem to have a tiny advantage over fluid-dynamical models; however, one may admit that for most applications, the differences between the two are small. Furthermore, the relaxation times of the fluid-dynamical models turns out to be fairly small, of the order of 2 s, and are comparable with the results for the microscopic models. This indicates that the second-order terms are weak; however, the calibration results indicate that the speed equation is, in fact, important and improves the calibration results of the models.

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A Finite Acceleration Scheme for First Order Macroscopic Traffic Flow Models

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)43918-8 ◽

1997 ◽

Vol 30 (8) ◽

pp. 787-792 ◽

Cited By ~ 12

Author(s):

J.P. Lebacque

Keyword(s):

Traffic Flow ◽

Flow Models ◽

First Order ◽

Macroscopic Traffic Flow ◽

Traffic Flow Models ◽

Macroscopic Traffic Flow Models

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First-order Macroscopic Traffic Flow Models

Transportation and Traffic Theory ◽

10.1016/b978-008044680-6/50021-0 ◽

2005 ◽

pp. 365-386 ◽

Cited By ~ 47

Author(s):

Jean-Patrick Lebacque ◽

Megan M. Khoshyaran

Keyword(s):

Traffic Flow ◽

Flow Models ◽

First Order ◽

Macroscopic Traffic Flow ◽

Traffic Flow Models ◽

Macroscopic Traffic Flow Models

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Introducing Buses into First-Order Macroscopic Traffic Flow Models

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/1644-08 ◽

1998 ◽

Vol 1644 (1) ◽

pp. 70-79 ◽

Cited By ~ 52

Author(s):

J.P. Lebacque ◽

J.B. Lesort ◽

F. Giorgi

Keyword(s):

Simple Model ◽

Traffic Flow ◽

Supply And Demand ◽

Interaction Model ◽

Macroscopic Model ◽

Moving Frame ◽

Large Measure ◽

Flow Models ◽

First Order ◽

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.

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Two-Phase Bounded-Acceleration Traffic Flow Model: Analytical Solutions and Applications

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/1852-27 ◽

2003 ◽

Vol 1852 (1) ◽

pp. 220-230 ◽

Cited By ~ 47

Author(s):

J. P. Lebacque

Keyword(s):

Traffic Flow ◽

Analytical Solutions ◽

Flow Model ◽

Second Phase ◽

Traffic Equilibrium ◽

Two Phase ◽

Traffic Flow Model ◽

Flow Models ◽

First Order ◽

Traffic Flow Models

A two-phase traffic flow model is described. One phase is traffic equilibrium: flow and speed are functions of density, and traffic acceleration is low. The second phase is characterized by constant acceleration. This model extends first-order traffic flow models and recaptures the fact that traffic acceleration is bounded. Calculation of analytical solutions of the two-phase model for dynamic traffic situations is shown, a set of calculation rules is provided, and some examples are analyzed.

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