Urban Multimodal Traffic Assignment

Many countries have set the target of becoming carbon-neutral to achieve the goals of the Paris Agreement, which was recently finalized, and an operational agreement was reached with the closing of Cop26 (UNCC, 2021). For the transport sector, achieving such a target requires, among other things, encouraging travelers to shift to a combination of different sustainable transport modes without compromising urban mobility. This requirement underpins the rising market of multimodal mobility services as well as the growing interest from academics in developing cutting-edge methodologies to promote the usage and enhance the efficiency of a multimodal transport system. Despite the methodological diversity, one of the fundamental modeling components involved is the prediction of travelers’ mode and route choice behavior and the usages of different transport means. This is known as the multimodal traffic assignment problem.

The multimodal traffic assignment problem emerged almost 50 years ago. The earliest journal publication related to the multimodal assignment problem can be traced to Florian (1977)1. The paper applied a multinomial logit discrete choice model to split the travel demand between car and public transport on the condition that travelers’ route choice behavior follows the user equilibrium principle with respect to each model separately. A mathematical programming model was devised and solved by a decomposition type algorithm. Transit vehicles were considered to be equivalent to multiple private cars, allowing for computing the travel time via the conventional BPR type function2, which is continuous and monotonic. This work established most of the key elements that should be considered in a multimodal traffic assignment problem, such as the modes to be considered, the interaction between different modes, travelers’ mode and route choice principle, a rigorous mathematical formulation established on certain assumptions and lead to a convergent solution algorithm for an application, etc.

Since then, many models have been developed, and significant progress has been made. It has attracted more and more attention in the last two decades, as observed from the increasing number of publications in Fig. 1. To date, surprisingly, we have not noticed any work that critically reviews the development in this area3 other than a brief mention in the review of the multimodal network design problem (Farahani et al., 2013). In view of this, we conducted a review to analyze the research progress and status in multimodal traffic assignment models. In what follows, we will provide our comments and observations.