### Abstract

This paper proposes a novel algorithm to determine the path flow solution that satisfies the proportionality condition from a given origin-based user equilibrium (UE) link flow solution. The algorithm iteratively refines the origin-based bush representation of the UE solution through constructing a list of "node-based arrival bushes" and solving the entropy maximization subproblems defined on them. Thanks to the special structure of bushes, these subproblems can be solved efficiently. The proposed algorithm thus obviates the knownhurdles to efficient implementation, such as enumerating allUE paths or collecting a set of paired alternative segments to cover them. We prove that the algorithm ensures convergence to a solution that perfectly satisfies the proportionality condition in general networks. Numerical experiments indicate that the proposed algorithm converges much faster than the known alternative, with a three- to eightfold speed-up on large networks.

Original language | English (US) |
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Pages (from-to) | 566-584 |

Number of pages | 19 |

Journal | Transportation Science |

Volume | 53 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2019 |

### Keywords

- bush representation
- entropy maximization
- paired alternative segments
- proportionality
- user equilibrium

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Transportation