scholarly journals A non-local traffic flow model for 1-to-1 junctions

2019 ◽  
Vol 31 (6) ◽  
pp. 1029-1049
Author(s):  
F. A. CHIARELLO ◽  
J. FRIEDRICH ◽  
P. GOATIN ◽  
S. GÖTTLICH ◽  
O. KOLB
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Approximate Solutions ◽  
Well Posedness ◽  
Local Conservation ◽  
Flow Modelling ◽  
Vehicle Density ◽  
Proposed Model ◽  
Non Local ◽  
Traffic Flow Modelling

We present a model for a class of non-local conservation laws arising in traffic flow modelling at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes (hence their maximal vehicle density). We use an upwind type numerical scheme to construct a sequence of approximate solutions, and we provide uniform L∞ and total variation estimates. In particular, the solutions of the proposed model stay positive and below the maximum density of each road segment. Using a Lax–Wendroff type argument and the doubling of variables technique, we prove the well-posedness of the proposed model. Finally, some numerical simulations are provided and compared with the corresponding (discontinuous) local model.

scholarly journals Macroscopic Traffic-Flow Modelling Based on Gap-Filling Behavior of Heterogeneous Traffic

2021 ◽  
Vol 11 (9) ◽  
pp. 4278
Author(s):  
Muhammad Umair Khan ◽  
Salman Saeed ◽  
Moncef L. Nehdi ◽  
Rashid Rehan
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Gap Filling ◽  
New Model ◽  
Flow Models ◽  
Flow Modelling ◽  
Complex Interactions ◽  
Proposed Model ◽  
Traffic Flow Models ◽  
Traffic Flow Modelling

Traffic-flow modelling has been of prime interest to traffic engineers and planners since the mid-20th century. Most traffic-flow models were developed for the purpose of characterizing homogeneous traffic flow. Some of these models are extended to characterize the complex interactions involved in heterogeneous traffic flow. Existing heterogeneous traffic-flow models do not characterize the driver behavior leading to gap filling in heterogeneous traffic conditions. This study aimed at explaining the gap-filling behavior in heterogeneous traffic flow by using the effusion model of gas particles. The driver’s behavior leading to gap filling in heterogeneous traffic was characterized through developing analogies between the traffic flow and the Maxwell–Boltzmann equation for effusion of gases. This model was subsequently incorporated into the Payne–Whitham (PW) model by replacing the constant anticipation term. The proposed model was numerically approximated by using Roe’s scheme, and numerical simulation of the proposed model was then carried out by using MATLAB. The results of the proposed and PW models were therefore compared. It is concluded that the new model proposed in this study not only produces better results compared to the PW model, but also better captures the expected reality. The main difference between the behavior of the two models is that the effect of bottleneck in the density of traffic is propagated in the form of a shockwave travelling backwards in time in the new model, while the PW model does not exhibit this effect.

scholarly journals Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity

2016 ◽  
Vol 11 (1) ◽  
pp. 107-121 ◽  
Author(s):  
Paola Goatin ◽  
Sheila Scialanga
Keyword(s):  
Traffic Flow ◽  
Finite Volume ◽  
Flow Model ◽  
Well Posedness ◽  
Local Velocity ◽  
Traffic Flow Model ◽  
Non Local

Network-Level Heterogeneous Traffic Flow Modelling in VISSIM

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ranju Mohan ◽  
Susan Eldhose ◽  
Gautham Manoharan
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Flow Modelling ◽  
Traffic Flow Modelling

BOND-GRAPHS TRAFFIC FLOW MODELLING AND FEEDBACK CONTROL

2006 ◽  
Vol 39 (3) ◽  
pp. 345-350
Author(s):  
Violina IORDANOVA ◽  
Hassane ABOUAÏSSA ◽  
Daniel JOLLY
Keyword(s):  
Feedback Control ◽  
Traffic Flow ◽  
Bond Graphs ◽  
Flow Modelling ◽  
Traffic Flow Modelling

scholarly journals A traffic flow model with non-smooth metric interaction: Well-posedness and micro-macro limit

2017 ◽  
Vol 15 (1) ◽  
pp. 261-287 ◽  
Author(s):  
Paola Goatin ◽  
Francesco Rossi
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Well Posedness ◽  
Traffic Flow Model

scholarly journals A macroscopic traffic flow model with finite buffers on networks: well-posedness by means of Hamilton–Jacobi equations

2020 ◽  
Vol 18 (6) ◽  
pp. 1569-1604
Author(s):  
Nicolas Laurent-Brouty ◽  
Alexander Keimer ◽  
Paola Goatin ◽  
Alexandre M. Bayen
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Well Posedness ◽  
Finite Buffers ◽  
Traffic Flow Model ◽  
Macroscopic Traffic Flow ◽  
Jacobi Equations

Heterogeneous traffic flow modelling for an arterial using grid based approach

2008 ◽  
Vol 42 (4) ◽  
pp. 467-491 ◽  
Author(s):  
P. J. Gundaliya ◽  
Tom V. Mathew ◽  
S. L. Dhingra
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Flow Modelling ◽  
Traffic Flow Modelling ◽  
Grid Based
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