Analysis of a multiplicative hybrid route choice model in stochastic assignment paradox

In recent years, a multiplicative hybrid (MH) route choice model was proposed to overcome the drawbacks of the multinomial logit (MNL) model and the multinomial weibit (MNW) model. This paper compares the conditions for the stochastic traffic assignment paradox of the three models. We analyze the condition when improving a link in an uncongested network counterintuitively increases total travel costs. Using three typical flow-independent networks (two links, (Formula presented.) independent links, and (Formula presented.) routes with (Formula presented.) overlapping links), we reveal the strong relationships in the paradox conditions of the three models. We further study the paradoxical features of the three models in the Sioux-Falls network, where the model parameters are estimated from simulated route sets. The case study shows that (1) the MH model fits the data the best, (2) using the MNL or the MNW model to identify paradox links exhibits intrinsic tendencies that are consistent with the theoretical analysis, and (3) the paradox links identified by the MH model is a compromise of the other two models. This paper delves into the relationships of the three models in the stochastic assignment paradox and provides suggestions and caveats to the application of the three models.