Estimation of people flow in public transportation network through the origin-destination problem for the South-Eastern corridor of Quito city in the smart cities context

The present work proposes a model for estimation of users demand in the public transportation network of the South-Eastern corridor of Quito-Ecuador typified in Origin-Destination Matrix (ODM), from the people account who aboard and descend from each bus that arrives at the different stops or stations. We propose a mathematical model, knowing the direct flows and destinations of passengers and the route matrix. We solve the system applying Bayesian inference, using the Monte Carlo technique which generates a large number of random samples that are accepted or rejected according to the Metropolis-Hasting criterion. The resulting value is the arithmetic mean value of all accepted samples. We validate the model through the analysis of the convergence of results, patterns of behavior of the origin-destination pairs and the sensitivity of the results to variations in the values of the links and destinations. Finally, we apply it to the South-East corridor network of Quito city, as particular case study.