A multiclass simultaneous transportation equilibrium model

Single class travel forecasting models assume that all travelers are similar in their travel-decision characteristics, such as their money-value of the time and their sensitivity to travel times in choosing their origin, destination and mode of travel, etc. To obtain more realistic models, travelers are often divided into classes, either by socio-economic attributes (e.g., income level, car availability, etc.) or by the purpose (e.g., home-based-work, non-home-based-work, home-based-shopping, etc.) of their travel, assuming that travel-decision characteristics are the same within each class, but differ among classes. However, the development of this concept of multiple classes increases the mathematical complexity of travel forecasting models. All the existing multiclass combined models consider the trip generation step of transportation planning process is exogenous to the combined prediction process. In this paper we enhance the Simultaneous Transportation Equilibrium Model (STEM) that developed by Safwat and Magnanti in 1988, and explicitly combined trip generation step, to be a multiclass model in terms of socio-economic group, trip purpose, pure and combined transportation modes, as well as departure time, all interacting over a physically unique multimodal network. The developed Multiclass Simultaneous Transportation Equilibrium Model (MSTEM) is formulated as a Variational Inequality problem and a diagonalization algorithm is proposed to solve it.