This study addressed the modeling of route travel times (including their associated uncertainty) in urban networks based on taxi floating car data. The model decomposes observed link travel speeds into the expected speed (modeled with daily and seasonal profiles) and deviations thereof. The latter were shown to be strongly heteroscedastic by providing an explicit model for the time variance. Temporal and spatial correlations were considered with a vector autoregression framework. Modeling was supported by automatic model selection methods for identifying the relevant effects and providing one-step-ahead predictions. The potential of the proposed model was investigated with taxi floating car data from a real-world test site near the city core of Vienna, Austria. Various specifications of the vector autoregression model were tested and compared. Taxi floating car measurements of local speeds were found to be strongly heteroscedastic, a factor that must be considered in estimation of models for expected travel speeds. The modeling of the mean suggested no remaining daily or weekly patterns, and it was superior to simple models explaining travel speeds as a linear function of the travel speeds in the last time period. The variance model successfully captured heteroscedasticity. More complex models for link travel speeds, including temporal and spatial correlation, do not increase prediction accuracy consistently; the lack indicates that a sampling frequency of 15 min for floating car data in urban settings is too low for use of temporal dependencies for prediction. An introduced method for computing route travel time uncertainty showed variability over the day for a highly frequented route.

Purpose: Travel time predictions are of importance for individual trip planning as well as for logistics applications. Since travel time and travel speed have a one-one correspondence, the modeller has the choice to model travel times directly or model the corresponding travel speeds and infer the associated time from the speed predictions. A priori it is not clear which of these is the superior approach. In this paper we investigate the implications of the choice of the methodology for the accuracy of the travel time predictions. Methods: For a selection of links, travel time prediction models, both in a direct way as well as indirectly via the implied link travel speeds, are obtained. The respective predictions are compared on a validation data set with respect to their accuracy as measured by mean error, root mean square error, mean percentage error as well as mean absolute percentage error. Additionally, the accuracy of route travel time predictions is evaluated based on the raw GPS data from the floating taxis. Results: The empirical results overwhelmingly make the case for using direct modelling if the goal of prediction is to obtain a RMSE-optimal prediction. If the MAPE is to be minimized, however, the indirect method provides the better results. Conclusion: Thus the goal of the prediction determines the better method of modelling: if one is interested in minimizing the RMSE, then, for the data investigated in this paper, the direct method should be selected. However, if one is interested in obtaining a small MAPE, the indirect method achieves better results.

The prediction of the uncertainty of route travel time predictions for all possible routes in an urban road network is of importance for example for logistics. Such predictions need to take the essential features of the data set as well as the underlying traffic dynamics into account. In this paper a large floating taxi data set is used in order to derive predictions of route travel time uncertainty based on link travel time uncertainty predictions. Prediction errors, that is actual travel times minus predicted travel times, are differentiated from model errors, that is measured travel times minus predicted travel times. These two errors are related, but not identical, as model errors contain measurement noise while the prediction errors do not. Detailed models for the variance of the link travel time prediction errors as well as the correlation between the model errors for different links are derived. The models are validated in depth using two different validation data sets. Estimates for the variance of prediction errors are obtained. The standardized model error distributions show a remarkable stability, such that modelling the variance appears to be sufficient for quantifying the uncertainty of the model errors. Furthermore we show that the model errors for adjacent links are highly correlated but correlations fade with increasing distance. Additionally usage of the road network plays a role with high correlation for links along common routes and low correlations for links along seldom used routes. We assume identical features for the prediction errors which is partly validated based on additional data. The paper provides a way to estimate the complete distribution of route travel time prediction errors for any given route in the street network.