A congested schedule-based dynamic transit passenger flow estimator using stop count data

A dynamic transit flow estimation model based on congested schedule-based transit equilibrium assignment is proposed using observations from stop count data. A solution algorithm is proposed for the mathematical program with schedule-based transit equilibrium constraints (MPEC) with computational complexity of O(N^2 L) where N and L represent the number of stops and transit lines respectively. The equilibrium constraints corresponding to the schedule-based hyperpath flow is adapted from the literature with some modifications to fit it into an estimation problem. Computational experiments are conducted first to verify the methodology with two synthetic data sets (one of which is Sioux Falls), followed by a validation of the method using bus data from Qingpu District in Shanghai, China from July 1, 2016, with 4 bus lines, 120 segments, 55 bus stops, and 120 one-minute intervals; this is one of the largest implementation of the schedule-based assignment model with congestion effects in the literature and the first for passenger flow estimation based on it. The estimation model converged to 0.005 tolerance of relative change in 10 iterations. The estimated average of segment flows are only 2.5% off from the average of the observed segment flows; relative errors among segments are 42.5%, which compares well with OD estimation methods applied to real data in the literature (e.g. Irvine network, Brescia motorway).