Study of the Response of PW Traffic Flow Model to a Bottleneck on a Circular Road and its Suitability for Heterogeneous Traffic Conditions

The traffic flow conditions in developing countries are predominantly heterogeneous. The early developed traffic flow models have been derived from fluid flow to capture the behavior of the traffic. The very first two-equation model derived from fluid flow is known as the Payne-Whitham or PW Model. Along with the traffic flow, this model also captures the traffic acceleration. However, the PW model adopts a constant driver behavior which cannot be ignored, especially in the situation of heterogeneous traffic.This research focuses on testing the PW model and its suitability for heterogeneous traffic conditions by observing the model response to a bottleneck on a circular road. The PW model is mathematically approximated using the Roe Decomposition and then the performance of the model is observed using simulations.

Download Full-text

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

Applied Sciences ◽

10.3390/app11094278 ◽

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.

Download Full-text

Analysis and Comparison of Microscopic Traffic Flow Models with Real Traffic Microscopic Data

Transportation Research Record Journal of the Transportation Research Board ◽

10.1177/0361198105193400106 ◽

2005 ◽

Vol 1934 (1) ◽

pp. 53-63 ◽

Cited By ~ 42

Author(s):

Vincenzo Punzo ◽

Fulvio Simonelli

Keyword(s):

Traffic Flow ◽

Simulation Models ◽

Microscopic Traffic Simulation ◽

Flow Models ◽

Traffic Conditions ◽

Measure Model ◽

Road Systems ◽

Traffic Flow Models ◽

Real Traffic ◽

Better Than

The evermore widespread use of microscopic traffic simulation in the analysis of road systems has refocused attention on submodels, including car-following models. The difficulties of microscopic-level simulation models in the accurate reproduction of real traffic phenomena stem not only from the complexity of calibration and validation operations but also from the structural inadequacies of the submodels themselves. Both of these drawbacks originate from the scant information available on real phenomena because of the difficulty with the gathering of accurate field data. In this study, the use of kinematic differential Global Positioning System instruments allowed the trajectories of four vehicles in a platoon to be accurately monitored under real traffic conditions on both urban and extraurban roads. Some of these data were used to analyze the behaviors of four microscopic traffic flow models that differed greatly in both approach and complexity. The effect of the choice of performance measures on the model calibration results was first investigated, and intervehicle spacing was shown to be the most reliable measure. Model calibrations showed results similar to those obtained in other studies that used test track data. Instead, validations resulted in higher deviations compared with those from previous studies (with peaks in cross validations between urban and extraurban experiments). This confirms the need for real traffic data. On comparison of the models, all models showed similar performances (i.e., similar deviations in validation). Surprisingly, however, the simplest model performed on average better than the others, but the most complex one was the most robust, never reaching particularly high deviations.

Download Full-text

Car-Following Under Congested Conditions: Empirical Findings

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/1644-03 ◽

1998 ◽

Vol 1644 (1) ◽

pp. 20-28 ◽

Cited By ~ 35

Author(s):

Thomas Dijker ◽

Piet H.L. Bovy ◽

Raymond G. M. M. Vermijs

Keyword(s):

Traffic Flow ◽

Flow Analysis ◽

Truck Drivers ◽

Road User ◽

Flow Conditions ◽

Microscopic Simulation ◽

Flow Models ◽

Car Following ◽

Traffic Flow Models ◽

Macroscopic Findings

In traffic flow analysis several regimes are distinguished, such as congested and noncongested flow conditions. Indications exist that driving behavior differs by regime and that it may change discontinuously between regimes. In contrast most traffic flow models used today basically assume the same car-following behavior irrespective of the traffic flow regime. It is hypothesized that, because of this deficiency, these models do not always perform satisfactorily. To clarify this issue, differences in car-following between congested and noncongested flow are analyzed with data from two sites on Dutch freeways. It is shown that, at the same speeds, passenger car drivers follow with smaller headways in noncongested than in congested flow. Car-following of truck drivers does not show differences between regimes. Microscopic distance gap-speed models are established for several road-user classes, valid for each of the two flow regimes. To show the improvements resulting from these new microscopic relationships, the latter are implemented in a microscopic simulation model with which macroscopic patterns in traffic flow are modeled. The macroscopic findings produced with the regime-specific car-following rules show a considerable improvement in modeling performance.

Download Full-text

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.

Download Full-text

MATHEMATICAL MODELLING OF NETWORK TRAFFIC FLOW

Transport ◽

10.3846/1648-4142.2009.24.333-338 ◽

2009 ◽

Vol 24 (4) ◽

pp. 333-338 ◽

Cited By ~ 28

Author(s):

Raimundas Junevičius ◽

Marijonas Bogdevičius

Keyword(s):

Traffic Flow ◽

Network Traffic ◽

Flow Model ◽

Flow Speed ◽

Complex Model ◽

Traffic Flows ◽

Flow Models ◽

Traffic Flow Models ◽

Single Complex ◽

Made In

The article describes mathematical models of traffic flows to initiate different traffic flow processes. Separate elements of traffic flow models are made in a way to be connected together to get a single complex model. A model of straight road with different boundary conditions is presented as a separate part of the network traffic flow model. First testing is conducted in case the final point of the whole modelled traffic line is closed and no output from that point is possible. The second test is performed when a constant value of traffic flow speed and traffic flow rate is entered. Mathematical simulation is carried out and the obtained results are listed.

Download Full-text