Constructing a Transit Origin-Destination Table Using the Uncertainty Maximization Concept

Document Type

Journal Article

Publication Date


Subject Area

mode - mass transit


Uncertainty, Trip tables, Transit, Public transit, Passenger counting, Origin and destination, O&D, Maximization, Maximisation, Mass transit, Local transit, Entropy (Statistical mechanics), Case studies, Boarding and alighting


An origin–destination (O-D) table contains information essential for making decisions about the operation and management of a transit system, such as determining the schedule, train composition, and fare structure. The table needs to be updated frequently. However, the collection of O-D data is time-consuming, costly, and cumbersome. This paper proposes a method that produces an O-D table on the basis of generally available data: passenger boarding and alighting counts at individual stations and the analyst’s knowledge, either qualitative or quantitative, about the values for some station pairs; for example, the number of trips (i, j) is approximately 100 or the number of trips (i, j) is much greater than the number of trips (m, n) (where i, j, m, and n are stops). The method applies the entropy maximization principle, in which the values for the O-D pairs whose information is not available are maximally unbiased and the available information is used as a constraint in the optimization problem. The uniqueness of the proposed approach is its ability to deal with qualitative and often language-based information, which the analyst often possesses. An example from a real transit line is presented to show the usefulness of the method and also to show how the additional information about select O-D pairs affects the quality of the solution.