Deriving Link Travel-Time Distributions via Stochastic Speed Processes

Jeffrey P. Kharoufeh, Natarajan Gautam

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We derive an analytical expression for the cumulative distribution function of travel time for a vehicle traversing a freeway link of arbitrary length. The vehicle's speed is assumed to be modulated by a random environment that can be modeled as a stochastic process. We first present a partial differential equation (PDE) describing the travel time distribution and obtain a solution in terms of Laplace transforms. Next, we present a numerical inversion algorithm to invert the transforms. The technique is demonstrated on two example problems. Numerical results indicate great promise for this approach to the link travel-time problem.

Original languageEnglish (US)
Pages (from-to)97-106
Number of pages10
JournalTransportation Science
Issue number1
StatePublished - Feb 2004
Externally publishedYes


  • Highway link
  • Markov chain
  • Stochastic processes
  • Travel time

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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