Equilibrium analysis of corridor problem with joint charging of departure time and travel distance

This paper investigates the impact of joint time and distance charging on many-to-one origin-destination travel behaviour, as a preliminary exploration of congestion charging in the continuous corridor model. Firstly, the equilibrium trip cost is analyzed to capture the departure time selection characteristics and flow dynamics. Secondly, we perform a mathematical analysis to reveal equilibrium flow patterns and deduce the properties of the departure set (set of departure space-time points). Next, we propose an ingenious mathematical approach to solve the continuous corridor model and conduct a numerical analysis to derive the equilibrium solution for three cases. Compared with the no-toll equilibrium, the departure set under congestion charging is still horn-shaped with its tip located somewhere close to the central business district. As a result, the departure time-based charging encourages commuters to leave earlier to avoid congestion, and the joint charging can ensure effective congestion relief while avoiding unfair charges.