An exact optimization method for coordinating the arrival times of urban rail lines at a common corridor

The trips of a high-frequency urban rail line are typically planned with the aim of achieving even time headways. This results in reliable services for each urban rail line, where successive trips have the same time headway. Maintaining even time headways for each service line has significant advantages for the passengers of the line, but it might result in safety issues, vehicle bunching, and increased transfer times at a common corridor served by multiple urban rail lines. This study investigates the problem of urban rail corridor coordination and develops an exact optimization method for coordinating the vehicle trips of different lines that serve stations along a joint corridor. The proposed formulation is a non-convex mathematical program which is reformulated as a mixed-integer quadratic program with a convex objective function. A branch-and-bound algorithm coupled with the Active-set method is proposed for solving the model to global optimality. Results from a toy network and a case study of the light rail service in The Hague, The Netherlands, demonstrate the improvement potential of time headways at a common corridor, while accounting for the effect on the variation of time headways at isolated segments of the individual service lines.