Bus arrival time prediction and measure of uncertainties using survival models

This study uses survival models to estimate the arrival time of buses at the downstream stops and intersections. Both accelerated failure time (AFT) and Cox regression based hazard models were considered in this study. Two different types of events: (i) buses arriving at bus stops and (ii) buses arriving at signalised intersections were included for measuring arrival times. Weibull and log-logistic distribution models were fitted for obtaining the arrival times against both the events separately. Various other factors such as distance, speed, bus stop dwell time, passenger count, gradient of the road, intersection length and signal details which included green time, red time, cycle length and so on were considered as explanatory variables. The proposed study was tested on a study corridor of length 59.48 km in the Mumbai arterial roads using public transport (buses). The results reveal that arrival times predicted using the developed models provided smaller uncertainties for 70% of the prediction and reduced prediction variation by 10%. The mean absolute percentage error value obtained for the AFT survival models was 10.04. Overall, the AFT model approach appears to be a promising method compared to Cox regression to predict bus arrival times and the associated uncertainties.