A multi-modal network equilibrium model with captive mode choice and path size logit route choice

In this paper, we consider captive mode travelers (those who have no other choices but rely on one specific travel mode for daily commuting trips) in a multi-modal network equilibrium (MMNE) problem. Specifically, the dogit model is adopted to account for captive mode travelers in the modal split problem, and the path-size logit (PSL) model is used to capture route overlapping effects in the traffic assignment problem. The dogit-PSL MMNE model is formulated as an equivalent entropy-based mathematical programming (MP) problem, which admits solution existence and uniqueness. Three numerical examples are provided. The first example examines the effects of mode captivity and route overlapping on network performances and observes that accounting for captive mode travelers would produce different equilibrium states and hence the network performance indicators. The second example applies the dogit-PSL MMNE model for evaluating the exclusive bus lane (EBL) expansion plans, in which a consistent synthetic proportional index is proposed. Numerical results show that considering mode captivity may produce substantial impacts on the odds (up to 50 percent of odds in the given scenarios) of making different EBL line expansion decisions. The third example implements the dogit-PSL MMNE model in the Seoul network to show the applicability of the dogit-PSL MMNE model in a real-size multi-modal system.