Modeling link capacity constraints with physical queuing and toll in the bi-modal mixed road network including bus and car modes

In urban transportation network, the formation of traffic congestion is often caused by link capacity constraints, which is often accompanied by physical queuing phenomena. This paper proposes a bi-modal mixed traffic equilibrium model with capacity constraints under two cases: (1) the physical queuing case for both car and bus modes; (2) implementing a queuing toll policy only for car mode to eliminate physical queuing. Based on the method of successive averages, an improved bi-loop algorithm is designed to solve the model. By two classical networks, we compare the two proposed cases with the benchmark case without capacity constraints to analyze the impact of capacity constraints and queueing toll policy on travelers’ travel cost and travel choice behavior. Some general insights are concluded based on the numerical results.