An analysis of logit and weibit route choices in stochastic assignment paradox

Paradox in the transportation literature is about improving an existing link or adding a new link can actually increase network-wide travel costs or travel costs of each traveler. In this paper, we investigate the stochastic assignment paradox using the multinomial weibit (MNW) model, a new route choice model developed by Castillo et al. (2008), and compare it to the counter-intuitive results of the multinomial logit (MNL) model when an inferior travel alternative is marginally improved. Using a simple two-link network, we derive the conditions for paradoxical phenomenon to occur for both route choice models, and graphically compare and contrast the paradoxical regions. The results show the stochastic assignment paradox depends on how the cost difference is being considered in the route choice model (i.e., absolute cost difference in the MNL model and relative cost difference in the MNW model) to some extent. Hence, the stochastic paradox analysis is extended to a hybrid model that considers both MNW and MNL models (i.e., both relative cost difference and absolute cost difference). The paradox area of the hybrid model is shown to be a combination of the paradox areas of the two models. In addition, the stochastic assignment paradox conditions derived for a simple two-link network are generalized to three cases: (a) one O-D pair with multiple links on a route, (b) multiple O-D pairs, and (c) adding a new link. Analytical solutions, graphical illustrations, and numerical results are provided to demonstrate the stochastic paradox under different conditions. Future research directions are also discussed in the paper.