A class of bush-based algorithms for the traffic assignment problem

Yu (Marco) Nie*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

104 Scopus citations


This paper studies a class of bush-based algorithms (BA) for the user equilibrium (UE) traffic assignment problem, which promise to produce highly precise solutions by exploiting acyclicity of UE flows. Each of the two building blocks of BA, namely the construction of acyclic sub-networks (bush) and the solution of restricted master problems (RMP), is examined and further developed. Four Newton-type algorithms for solving RMP, which can be broadly categorized as route flow and origin flow based, are presented, of which one is newly developed in this paper. Similarities and differences between these algorithms, as well as the relevant implementation issues are discussed in great details. A comprehensive numerical study is conducted using both real and randomly generated networks, which reveals that the relative performance of the algorithms is consistent with the analysis. In particular, the results suggest that swapping flows between shortest and longest route segments consistently outperforms other RMP solution techniques.

Original languageEnglish (US)
Pages (from-to)73-89
Number of pages17
JournalTransportation Research Part B: Methodological
Issue number1
StatePublished - Jan 2010


  • Acyclicity
  • Bush-based algorithm
  • User equilibrium traffic assignment

ASJC Scopus subject areas

  • Transportation
  • Civil and Structural Engineering


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