Analysis of bus travel time distributions for varying horizons and real-time applications

Given the increasing interest in real-time bus arrival information, producing reliable estimation is essential to maximize the benefits of real-time systems. The primary objectives of this paper are to analyze the changes of bus travel time characteristics as pseudo horizon varies and how such characteristics can be applied to real-time bus arrival estimation. In this study, “horizon” refers to the distance between a real-time bus location and a bus stop, whereas “pseudo horizon” refers to the distance from a GPS point to an upstream GPS point. In contrast to existing methods that provide point estimates of bus arrival times, this study provides interval estimates that take into account the uncertainty of future bus arrival times given that early and late buses have their own respective ramifications. A methodology is developed to analyze the bus travel time distribution systematically based on different pseudo horizons since such distributions are critical to producing reliable bus arrival information. The analysis of real transit GPS data shows a significant change in bus travel time characteristics around a pseudo horizon range of 8 km. The analysis of changes in probability densities with pseudo horizons shows that bus travel time distribution converges from a rightly skewed distribution to a more symmetrical distribution from a shorter to a longer pseudo horizon. Lognormal and normal distributions are found to be the best models for before and after a cut-off horizon of 7-8 km, respectively. Instead of a single distribution, the outcomes of this study suggest a combination of probability distributions based on the estimation horizon to be used to provide better bus arrival time estimations.