A multiplicative regret-based stochastic user equilibrium model

Random regret minimization is an alternative decision rule to the overwhelmingly used random utility maximization in travel choice and network equilibrium models. Existing random regret models (RRMs) mainly adopt an additive error structure, which is inadequate to capture travelers’ magnitude-dependent perceptions of travel alternatives and is often difficult to reflect the impact of transportation network scales. This study proposes a novel multiplicative random regret model (MRRM) to address these issues by taking advantage of the multiplicative error structure. Compared with the traditional additive RRMs, the MRRM addresses the scale-invariance issue and enables alternative-specific travel perceptions while retaining the essential properties of RRMs. Specific distributional assumptions are made for the smooth approximation of the regret function and random perception of alternative-level regret, which guarantees the analytical expression of choice probability that facilitates the application in traffic assignment problems. The MRRM is further integrated into the stochastic user equilibrium (SUE) assignment to endogenously model the congestion effect on regret-based route choice behaviors. The MRRM-SUE model is formulated as a variational inequality problem and solved via a path-based algorithm. Numerical experiments are conducted on different networks to illustrate the features of the MRRM-SUE model and verify its applicability in real-world cases.