Elastic demand with weibit stochastic user equilibrium flows and application in a motorised and non-motorised network

In this paper, we propose a new elastic demand (ED) stochastic user equilibrium (SUE) model with an application to the combined modal split and traffic assignment (CMSTA) problem. This new model, called the path-size weibit (PSW) SUE model with ED, is derived based on the Weibull distribution, which does not require the identically distributed assumption typically imposed in the multinomial logit (MNL) model with the Gumbel distribution. In addition, a path-size factor is included to correct the choice probabilities of routes that are not truly independent (i.e. another assumption typically required in the MNL model). Equivalent mathematical programming (MP) formulation of the PSW-SUE-ED model is developed to simultaneously consider both travel choice and route choice. The travel choice is determined based on the ED function that explicitly considers the network level of service based on the logarithmic expected perceived cost of the Weibull distribution to determine the travel demand, while the route choice accounts for both route overlapping and non-identical perception variance with respect to different trip lengths. Qualitative properties of the proposed MP formulation are rigorously proved. A path-based partial linearisation algorithm combined with a self-regulated averaging line search strategy is developed for solving the PSW-SUE-ED model and its application to the CMSTA problem. Numerical examples are also provided to demonstrate the features of the proposed PSW-SUE-ED model as well as a real-case study in a bi-modal network with motorised and non-motorised mode choices.