A stochastic model of traffic flow: Theoretical foundations

Saif Eddin Jabari, Henry X. Liu

Research output: Contribution to journalArticlepeer-review


In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.

Original languageEnglish (US)
Pages (from-to)156-174
Number of pages19
JournalTransportation Research Part B: Methodological
Issue number1
StatePublished - Jan 2012


  • Cell transmission
  • Counting processes
  • Fluid limit
  • Random time headways
  • Stochastic traffic flow

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


Dive into the research topics of 'A stochastic model of traffic flow: Theoretical foundations'. Together they form a unique fingerprint.

Cite this