Traffic flow theory

Pushkin Kachroo, Kaan M.A. Özbay

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter presents the basic traffic flow theory which is used in the following chapters for control problem formulations. The theory develops the Lighthill–Whitham–Richards (LWR) model that uses the conservation law for traffic. Additionally, a density-dependent speed formula is used. There are many relationships available for this fundamental diagram, the chapter uses Greenshields’ formula for further analysis. Elementary partial differential equations (PDE) theory is also presented including the method of characteristics needed for the analysis of the traffic model. Shockwaves and weak solutions are discussed followed by a brief discussion of traffic measurements.

Original languageEnglish (US)
Title of host publicationAdvances in Industrial Control
PublisherSpringer International Publishing
Number of pages31
StatePublished - 2018

Publication series

NameAdvances in Industrial Control
ISSN (Print)1430-9491
ISSN (Electronic)2193-1577

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Industrial and Manufacturing Engineering


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