Predicting Travel Times for On-demand Public Transport in Sofia

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This document describes the methodical approaches for Module 5 of INNOAIR On-demand Public Transport Platform for route optimization and, in particular, for travel times predictions. The text presents the chosen models of travel time between stops. There are four predictive models presented – all of which have been tested on a particular use-case data. The procedure to implement a prediction model goes through three phases: model identification, parameter estimation/optimization, and prediction, with their corresponding sub-phases. With business understanding and data understanding done already in general for the study, each applied model should be explained in terms of data preparation, data modeling and model validation. In the current text a use-case is used as a numerical experiment to play through the various modeling procedures under study. The input data used in these modeling procedures have two sources – traffic data for times of arrival for 4 consecutive stops of a bus line in Sofia and weather data. Based on the literature review, the researchers have chosen to use several models to predict the target data: Seasonal autoregressive moving average models with exogenous input with Fourier terms; Vector Autoregression and Vector Error-Correction Models; Bayesian Fourier model; Back-Propagation Neural Network models. Root-mean-square error measured in seconds, calculated on the forecast for the test set (last week of observations), is used for comparison of the proposed models.