User-equilibrium route flows and the condition of proportionality

Hillel Bar-Gera*, David Boyce, Yu Nie Marco

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


User-equilibrium (UE) static deterministic traffic assignment is a widely accepted model among researchers, and is extensively applied in travel forecasting practice. UE route flows are also quite commonly used in methodological research as well as in practical applications, even though it is well known that route flows are not uniquely determined by the UE conditions. One way to resolve this dilemma is by imposing an additional condition, such as the condition of proportionality.The purpose of the research findings presented here is to examine the nature and magnitude of the differences in route flows and multi-class link flows in a realistic setting by applying three assignment software tools in a case study based on the network of the Chicago region. The case study includes a single class version as well as a multi-class version with two classes: private cars and trucks. The assignment tools represent three categories of algorithms: link-based, route-based and pairs-of-alternative-segments-based. For each of the first two types we chose one tool that is commonly used in practice. For the third type, a research tool was used.Select link analyses from the various solutions are compared in a pair-wise manner, showing that the differences in the results cannot be neglected. A method to evaluate the satisfaction of proportionality for each assignment solution by itself is presented, and applied to all the solutions. The link-based solutions satisfy proportionality reasonably well, but satisfactory levels of UE convergence require very substantial computation times. The route-based assignment tool offers quick and precise convergence, but the resulting solutions deviate considerably from the condition of proportionality. The pairs-of-alternative-segments-based tool offers quick and precise convergence and generally satisfies proportionality. The authors believe that these findings stem from the nature of link-based and route-based algorithms, and thus apply to most algorithms in these categories.These conclusions should be taken into consideration by researchers in developing new algorithms, as well as by practitioners in choosing which software tool to apply.Additional assignment tools that aim to offer quick and precise convergence as well as proportionality have been announced more recently; however, they were not available for evaluation at the time the research was conducted. Their evaluation is a task that remains for future studies.

Original languageEnglish (US)
Pages (from-to)440-462
Number of pages23
JournalTransportation Research Part B: Methodological
Issue number3
StatePublished - Mar 2012


  • Multiple-class link flows
  • Proportionality
  • Route flows
  • User-equilibrium

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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