Macroscopic modeling of mixed bi-modal urban networks: A hybrid model of accumulation- and trip-based principles

Network-level traffic flow models either assume steady-state urban flows (i.e. accumulation-based models) or track the movement of all vehicles (i.e. trip-based models). The steady-state assumption present in the accumulation-based models may pose a challenge in light of the multi-modal nature of urban flows. It might be indeed a rough assumption for the flow of some transportation modes like buses, cruising-for-parking vehicles, taxis, and on-demand vehicles. Trip-based models address this concern, however, they need significant parameter calibration effort and are not computationally efficient, which substantially reduces the practicality of these models in real-world applications. Nevertheless, despite the critical importance of developing multi-modal traffic flow models, few attempts have been made to investigate these models in network macroscopic fundamental diagram (NMFD)-related literature. This paper bridges this gap by developing a hybrid network-level traffic flow model for mixed bi-modal (i.e. car and bus) networks. The present hybrid model reproduces the dynamics of car flows via accumulation-based model principles while tracking the movement of buses using the trip-based model. This effort also includes the development of a new FIFO-based entrance function to ensure different modes experience the same delay under saturated traffic conditions. Different numerical experiments are conducted to study the hybrid model performance and to compare it with that of accumulation-based and trip-based models in both steady-state and transition periods under different traffic conditions. Our observations reveal that the hybrid model simulates the dynamics of cars and buses by closely following the behavior of its components under free-flow conditions. The model also outperforms the accumulation-based model under saturated traffic conditions while being considerably less demanding than the trip-based model. A further investigation of the model performance is performed for networks with different bus shares in both free-flow and saturated traffic conditions, confirming the results of the initial numerical experiments. The hybrid model's computational efficiency is demonstrated. The potential real-world applications of the hybrid model in development of bi-modal network-level simulation models, NMFD-based control strategies along with bus space allocation policies, public transport operation problems, modeling of cruising-for-parking vehicles, taxis, and on-demand vehicles, and modeling and application of autonomous modular vehicles are discussed and future research directions are highlighted.