Dynamic inference for left behind probabilities on congested metro routes

Passengers left behind is an important measure to describe the degree of congestion in metro systems. Note that passengers' left behind probabilities are different for their different tap-in times. This paper proposes a methodology for inferring these dynamic probabilities on congested metro routes using automated data. The EM algorithm is used to compute the maximum likelihood estimators of passengers' dynamic boarding probabilities, and then formulas for estimating dynamic left behind probabilities are presented based on the estimated boarding probabilities. Monte Carlo simulations and a real case application show the effectiveness of the proposed method.