Axiomatization of Transit Flow Estimation

Transit flows between stations are typically estimated indirectly using fare collecting data rather than through direct measurement. Traditional methods approximate transit flows by adapting Origin-Destination (OD) trip estimation techniques. However, these approaches have two significant limitations. First, transit link flows represent the number of passengers remaining within the transit vehicles between stations, while OD flows specifically represent passengers entering at one station and exiting at another station. Second, traditional methods rely on the assumption that a cost function is necessary without providing mathematical justification. Consequently, there lacks a robust theoretical foundation explicitly tailored for transit flow estimation. This paper addresses this gap by developing an axiomatic framework based on the Ideal Flow Network. Through systematic mathematical derivations, we identify key balance conditions and necessary constraints to achieve more accurate transit flow estimation.