A probabilistic stationary speed-density relation based on Newell's simplified car-following model

Saif Eddin Jabari, Jianfeng Zheng, Henry X. Liu

Research output: Contribution to journalArticlepeer-review


Probabilistic models describing macroscopic traffic flow have proven useful both in practice and in theory. In theoretical investigations of wide-scatter in flow-density data, the statistical features of flow density relations have played a central role. In real-time estimation and traffic forecasting applications, probabilistic extensions of macroscopic relations are widely used. However, how to obtain such relations, in a manner that results in physically reasonable behavior has not been addressed. This paper presents the derivation of probabilistic macroscopic traffic flow relations from Newell's simplified car-following model. The probabilistic nature of the model allows for investigating the impact of driver heterogeneity on macroscopic relations of traffic flow. The physical features of the model are verified analytically and shown to produce behavior which is consistent with well-established traffic flow principles. An empirical investigation is carried out using trajectory data from the New Generation SIMulation (NGSIM) program and the model's ability to reproduce real-world traffic data is validated.

Original languageEnglish (US)
Pages (from-to)205-223
Number of pages19
JournalTransportation Research Part B: Methodological
StatePublished - Oct 2014


  • Driver heterogeneity
  • Macroscopic traffic variables
  • Microscopic traffic variables
  • Newell's car-following
  • Probabilistic macroscopic traffic relations
  • Stationary traffic

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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