A method of time-varying demand distribution estimation for high-speed railway networks with user equilibrium model

Time-varying demand distribution (TDD) is a critical input data for operation and management in HSR systems. This paper proposed a bi-level model to estimate the TDD with the ticket booking date and using the schedule-based User Equilibrium (UE) assignment. The up-level aims to determine the TDD with maximum entropy value and minimal error between the path flow (ticket booking volumes) and the corresponding equilibrium flows (determined from lower-level); the lower-level is a schedule-based UE assignment with rigid capacity constraints to reflect the interactions of ticket booking choices behaviors between different OD pairs in the HSR networks, and further, the advance booking cost is considered endogenously as a part of passenger choice equilibrium. The bi-level model is converted into a single-level model through equivalent complementary constraints. Then, based on linear relaxation, the single-level model is transformed into a mixed-integer quadratic program (MIQP). Furthermore, in order to improve the computational efficiency of the MIQP, the approach of reducing the calculation size of our problem is proposed. By solving the MIQP we get the information about the upper and lower bounds of our original problem, and then a global optimal solution algorithm with four piecewise interval strategies is proposed. The effectiveness and applicability of the proposed algorithm are illustrated with a simple case and three real-world cases.