Polynomial Approach and Non-linear Analysis for a Traffic Fundamental Diagram

Rosas-Jaimes, Oscar A.; Quezada-Téllez, Luis Alberto; Anaya, Guillermo Fernández

doi:10.7307/ptt.v28i4.1965

Cited by 3 publications

(2 citation statements)

References 7 publications

(32 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We want to treat these fundamental diagrams in a similar manner as is done in the paper by Rosas-Jaimes et al (2016). In that paper, only the flow-density fundamental diagram is tested by means of a polynomial expression.…”

Section: Greenberg's Modelmentioning

confidence: 99%

“…Lo & Cho (2005) develop an analysis over Greenshield's model, even though they adapt that model to a logistic-type mapping only for a flow-density relation. In Rosas-Jaimes et al (2016) a polynomial approach is suggested for the calculation of a flow-density fundamental diagram, and then it is used to perform a discrete dynamical analysis. In the present case of this article the velocity-density and the velocity-flow fundamental diagrams are also included, and they are not adapted versions of a fundamental diagram model, but they are directly derived from the solution of Greenberg's model and other basic expressions in traffic theory.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability analysis in Greenberg’s traffic model

Rosas-Jaimes

Quezada-Téllez²,

Fernández‐Anaya

2017

Int. J. Mod. Phys. C

Self Cite

View full text Add to dashboard Cite

Based on the classical traffic model by Greenberg, a linear differential equation, we analyze it by means of varying the critical velocity v o that appears in it as a parameter. In order to make such analysis we have obtained a solution for such a model and discretized it, obtaining related expressions for density k, flow q and velocity v to be treated as paired functions to obtained maps in phase-planes in which it is possible to observe distinct behaviors which span from monotonic and oscillatory stable trajectories, limit cycles of distinct periodicity, and chaotic ones. These behaviors are analyzed from a dynamical approach and then ilustrated with simulations performed in each case. As it is shown in this paper, these analyses are similar to those carried out in similar though simpler expressions (i.e. logistic-type functions), but taking in this case a new and direct approach through a nonlinear expression not used before to perform studies like these presented in this document, with a deep detail in the manner in which traffic variables are involved qualitatively and quantitatively.

show abstract

Section: Greenberg's Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability analysis in Greenberg’s traffic model

Rosas-Jaimes

Quezada-Téllez²,

Fernández‐Anaya

2017

Int. J. Mod. Phys. C

Self Cite

View full text Add to dashboard Cite

show abstract

MOD3D-PAT - A Novel Modified 3rd Degree Polynomial Approximation for Modelling Traffic Congestion in Urban Areas

Chan

Lim

Parthiban

2021

2021 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME)

View full text Add to dashboard Cite

Simulational analysis of two controllers for variable speed limit control

Ivanjko

Kušić

Gregurić

2022

Proceedings of the Institution of Civil Engineers - Transport

View full text Add to dashboard Cite

Variable speed limit control (VSLC) is one of the services from the domain of intelligent transport systems applied to alleviate or prevent congestion on urban motorways. The main idea of VSLC is to change the speed limit according to current traffic or weather in order to improve the traffic situation. Improvement of the traffic situation on urban motorways depends on the applied controller and its parameters. For this reason, the controllers chosen for implementation have to be tested in simulations using a realistic urban motorway segment, placement of sensors and traffic scenario, and a relevant set of control parameters. An analysis of two VSLC controllers, including the influence of their parameters on controller performance with respect to traffic and environmental aspects, is presented in this paper. To this end, an appropriate microscopic simulation framework was developed, the fundamental diagram of a simulated synthetic urban motorway segment was measured and traffic parameters, with vehicle emissions values, were obtained. The effectiveness of the two analysed controllers was compared based on the obtained simulation results. The results revealed that appropriate settings of the controller are crucial to ensure optimal use of urban motorways with minimum travel times and vehicle emissions.

show abstract

Polynomial Approach and Non-linear Analysis for a Traffic Fundamental Diagram

Abstract: ABSTRACT

Cited by 3 publications

References 7 publications

Stability analysis in Greenberg’s traffic model

Stability analysis in Greenberg’s traffic model

MOD3D-PAT - A Novel Modified 3rd Degree Polynomial Approximation for Modelling Traffic Congestion in Urban Areas

Simulational analysis of two controllers for variable speed limit control

Contact Info

Product

Resources

About