Prediction intervals to account for uncertainties in travel time prediction

The accurate prediction of travel times is desirable but frequently prone to error. This is mainly attributable to both the underlying traffic processes and the data that are used to infer travel time. A more meaningful and pragmatic approach is to view travel time prediction as a probabilistic inference and to construct prediction intervals (PIs), which cover the range of probable travel times travelers may encounter. This paper introduces the delta and Bayesian techniques for the construction of PIs. Quantitative measures are developed and applied for a comprehensive assessment of the constructed PIs. These measures simultaneously address two important aspects of PIs: 1) coverage probability and 2) length. The Bayesian and delta methods are used to construct PIs for the neural network (NN) point forecasts of bus and freeway travel time data sets. The obtained results indicate that the delta technique outperforms the Bayesian technique in terms of narrowness of PIs with satisfactory coverage probability. In contrast, PIs constructed using the Bayesian technique are more robust against the NN structure and exhibit excellent coverage probability.