Modeling The Origin-Destination Matrix With Incomplete Information

Different methods exist for the estimation of trips in public transportation systems based on automatized fare collection data. Some of the widely adopted estimation strategies are based on the traceability of passenger transfers. They may be effective in large cities, but fall short for trip estimation of single-routes, which are mostly the case in small-to-medium cities. We present a model to estimate the Origin-Destination Matrix, independent of transfers and passenger identification, using only boarding and alighting counts. The model is based on a system of linear diophantine equations, together with a method that computes the general solution and reduces the evaluation space, achieving useful estimations in polynomial time.