Unconstrained weibit stochastic user equilibrium model with extensions

• An unconstrained minimization program is developed for the MNW-SUE model.
• The MNW-SUE model considers non-identical perception variances for different trip lengths.
• Equivalency and uniqueness of the MNW-SUE model are provided.
• A link-based algorithm is developed for solving the MNW-SUE model.
• Several extensions for future research are provided.

This study provides an unconstrained minimization program as an alternative formulation for the multinomial weibit (MNW) stochastic user equilibrium (SUE) model that explicitly considers the heterogeneous perception variances with respect to different trip lengths under congested conditions. Qualitative properties of the unconstrained minimization program are given to establish the equivalency and uniqueness of the MNW-SUE solution. The advantage of the unconstrained minimization programming formulation is that it allows the development of a link-based algorithm, which obviates path storage and enumeration. The methodological contributions lie in the derivation of the expected perceived travel cost (or the satisfaction function) that enables the development of an unconstrained MNW-SUE minimization program and a link-based stochastic loading mechanism combined with recent advances in line search strategies in the link-based algorithm. Numerical examples are also provided to illustrate the features of the MNW-SUE model and the link-based algorithm along with several extensions for future research.