Method for Balancing Observed Boarding and Alighting Counts on a Transit Line

Document Type

Journal Article

Publication Date


Subject Area

mode - bus


Travel patterns, Ridership, Patronage (Transit ridership), Passenger counting, Optimization, Optimisation, Mathematical analysis, Intracity bus transportation, Fuzzy sets, Bus transit, Boarding and alighting


The number of passengers boarding and alighting at each transit stop is basic information used in analyses of transit operations. Observed counts (manual or mechanical) of total boardings and total alightings, however, often do not match. This paper proposes a method that adjusts boarding and alighting counts so that their totals match and the cumulative boardings at each stop is greater than the cumulative alightings at that stop. The method considers observed values as approximate numbers, represents them with a range, and seeks the adjusted value within this range. In this fuzzy optimization search process, the range is represented by a fuzzy set of values, and the membership grades of the fuzzy set guide the direction of the search. The process is capable of incorporating knowledge about ridership patterns along the route and the accuracy of individual observed values. The method is tested with real-world data, and the results are compared with those obtained from the commonly used least squares method. The model yields solutions that are consistent with the available information and with degree of uncertainty.