Comparative analysis of three user equilibrium models under stochastic demand

Zhong Zhou, Anthony Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

78 Citations (Scopus)


Recent empirical studies on the value of time and reliability reveal that travel time variability plays an important role on travelers' route choice decision process. It can be considered as a risk to travelers making a trip. Therefore, travelers are not only interested in saving their travel time but also in reducing their risk. Typically, risk can be represented by two different aspects: acceptable risk and unacceptable risk. Acceptable risk refers to the reliability aspect of acceptable travel time, which is defined as the average travel time plus the acceptable additional time (or buffer time) needed to ensure more frequent on-time arrivals, while unacceptable risk refers to the unreliability aspect of unacceptable late arrivals (though infrequent) that have a travel time excessively higher than the acceptable travel time. Most research in the network equilibrium based approach to modeling travel time variability ignores the unreliability aspect of unacceptable late arrivals. This paper examines the effects of both reliability and unreliability aspects in a network equilibrium framework. Specifically, the traditional user equilibrium model, the demand driven travel time reliability-based user equilibrium model, and the a-reliable mean-excess travel time user equilibrium model are considered in the investigation under an uncertain environment due to stochastic travel demand. Numerical results are presented to examine how these models handle risk under travel time variability.
Original languageEnglish
Pages (from-to)239-263
Number of pages25
JournalJournal of Advanced Transportation
Issue number3
Publication statusPublished - 1 Jan 2008
Externally publishedYes


  • Mean-excess travel time
  • Travel time budget
  • Travel time reliability
  • User equilibrium
  • Variational inequality

ASJC Scopus subject areas

  • Automotive Engineering
  • Economics and Econometrics
  • Mechanical Engineering
  • Computer Science Applications
  • Strategy and Management

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