1. Introduction
The network equilibrium model is one part of the four-step travel forecasting model and a useful tool for longterm
transportation planning. Since the beginning of the network equilibrium models only consider one mode
(mostly, automobile), one of the drawback of the beginning network equilibrium model is the inconsistency between
other steps. To overcome this drawback, many researchers proposed network equilibrium model which combines
mode and route choice (Oppenheim (2005) , Nagao .et. al. (2009)) or which further combines trip generation, mode
choice and route choice (Oppenheim (2005)). Although many of the traditional combined equilibrium models treat
the passengers’ assignment to the public transportation network as the same methodology of the traditional road
network assignment, it is well know that “common lines problem” is one of the key essences to be considered in the
passengers’ assignment to the urban public transportation network. Common lines problem is defined as a feature
that a passenger who takes the first vehicle to come on his/her “attractive lines” can get to his or her destination
earliest (See Chiriqui et al. (1975)). The set of “attractive lines” is referred as “hyperpath”. (Nguyen et. al. (1988)).