Traditionally, travel demand models predict or forecast volumes or flows with point values. Since all predictions will be inaccurate, it would be valuable to add uncertainty measures to the model predictions. It is proposed that differences between observations and model-based predictions of the observations, which are often used in validation studies of travel demand models, should be used to produce error distributions that can represent model prediction errors.
An empirical study is presented to illustrate and evaluate the approach. The study is based on predicting bus route origin-destination (OD) flows from boarding and alighting counts and the state-of-the-practice Iterative Proportional Fitting (IPF) model. Error distributions are formed by comparing IPF-based OD predictions to extensively collected, directly observed (“ground truth”) OD flows in “calibration” time periods. The error distributions are used with IPF-based predictions to estimate various “events” – e.g., flow for a randomly selected OD pair on a given bus trip, flow for a specified OD pair, proportion of “short passenger trips” on a bus trip – in “validation” time periods. To capture uncertainty, the predictions are made in terms of probability distributions of the event outcomes.
Multiple measures are proposed to evaluate the quality of the predicted probability distributions with respect to the ground truth distributions for the validation periods. Empirical comparisons are conducted for multiple calibration period-vs-validation period scenarios and for multiple predicted events. To interpret the performance, as portrayed by the validation measures, event distributions are also produced using two other approaches – one that forms the distribution using only ground truth observations, without model prediction, in the calibration period and one that only uses the model prediction, without error distribution, in the validation period. The empirical results obtained to date (at the time of the abstract submission) demonstrate that using the proposed “model-plus-error” approach outperforms the other approaches. Results also show that refining the calibrated error distributions – for example, having different error distributions for low OD flow predictions and for high OD flow predictions – improves the performance.
An analogous approach for incorporating uncertainty in regional travel demand models and analogous validations studies are proposed.