In an earlier work, Xu et al formulated the schedule-based passenger flow assignment problem in high-speed railway (HSR) system with rigid capacity constraints as a linear programming (LP) model and considered advance ticket booking cost endogenously. In this paper the authors formulate the assignment model with arc flow variable based on space-time network. Then we apply the Dantzig-Wolfe (D-W) decomposition method to reformulate and solve the equilibrium assignment with less calculated amount and memories, and of which we use rooftop method to solve the sub-problem (minimum cost flow problem without capacity constraints) in each iteration. We find that exist the discrete time-varying demand equilibrium assignment (DDEA) convergent to the continuous time-varying demand equilibrium assignment (CDEA) when the discrete parameter of time-varying demand convergent to infinity, and exist a LP model to describes CDEA problem. Finally, a numerical experiment with real HSR network is presented to demonstrate and illustrate the proposed method.

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