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Speed–density functional relationship for heterogeneous traffic data: a statistical and theoretical investigation

Authors
  • Gaddam, Hari Krishna1
  • Rao, K. Ramachandra1
  • 1 Indian Institute of Technology, Delhi, Department of Civil Engineering, Hauz Khas, New Delhi, Delhi, 110016, India , Hauz Khas, New Delhi (India)
Type
Published Article
Journal
Journal of Modern Transportation
Publisher
Springer Singapore
Publication Date
Dec 05, 2018
Volume
27
Issue
1
Pages
61–74
Identifiers
DOI: 10.1007/s40534-018-0177-7
Source
Springer Nature
Keywords
License
Green

Abstract

This study is an attempt to establish a suitable speed–density functional relationship for heterogeneous traffic on urban arterials. The model must reproduce the traffic behaviour on traffic stream and satisfy all static and dynamic properties of speed–flow–density relationships. As a first attempt for Indian traffic condition, two behavioural parameters, namely the kinematic wave speed at jam (Cj) and a proposed saturation flow (λ), are estimated using empirical observations. The parameter Cj is estimated by developing a relationship between driver reaction time and vehicle position in the queue at the signalised intersection. Functional parameters are estimated using Levenberg–Marquardt algorithm implemented in the R statistical software. Numerical measures such as root mean squared error, average relative error and cumulative residual plots are used for assessing models fitness. We set out several static and dynamic properties of the flow–speed–density relationships to evaluate the models, and these properties equally hold good for both homogenous and heterogeneous traffic states. From the numerical analysis, it is found that very few models replicate empirical speed–density data traffic behaviour. However, none of the existing functional forms satisfy all the properties. To overcome the shortcomings, we proposed two new speed–density functional forms. The uniqueness of these models is that they satisfy both numerical accuracy and the properties of fundamental diagram. These new forms would certainly improve the modelling accuracy, especially in dynamic traffic studies when coupling with dynamic speed equations.

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