  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 polynomial
computational complexity. The equilibrium constraints corresponding to the
schedule-based hyperpath flow are modified from the literature to fit 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, with 4 bus lines, 120 segments, 55 bus stops, and 120
one-minute intervals. 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%.
