A customized two-stage parallel computing algorithm for solving the combined modal split and traffic assignment problem

•A block-decomposed model is proposed for solving the combined modal split and traffic assignment (CMSTA) problem.•A customized two-stage parallel algorithm is proposed to solve the CMSTA problem. The first parallel stage of the TP algorithm is used in the path generation phase, and the second parallel stage is used in the path flow adjustment phase.•An optimal parallel computing resource schedule is proposed to solve each block problem.•The parallel slowdown is uncovered in calculating each block problem of the path flow adjustment phase by using parallel resources.•To validate the two-stage parallel method with large-scale networks.