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.

中文翻译：

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公交车到站时间预测和不确定性的生存模型测量

这项研究使用生存模型来估算公交车在下游站点和十字路口的到达时间。这项研究考虑了加速故障时间（AFT）和基于Cox回归的风险模型。两种不同类型的事件：（i）到达公交车站的公交车和（ii）到达信号交叉口的公交车用于测量到达时间。拟合了Weibull和log-logistic分布模型，以分别获取两个事件的到达时间。其他各种因素，例如距离，速度，公交车站的停留时间，乘客人数，道路坡度，交叉路口长度和信号细节（包括绿灯时间，红色时间，周期长度等）均被视为解释性变量。拟议的研究在长度为59的研究走廊上进行了测试。使用公共交通工具（公共汽车）在孟买干线公路上行驶48公里。结果表明，使用开发的模型预测的到达时间为70％的预测提供了较小的不确定性，并将预测偏差降低了10％。从AFT生存模型获得的平均绝对百分比误差值为10.04。总体而言，与Cox回归相比，AFT模型方法似乎是一种有前途的方法，可以预测公交车的到站时间和相关的不确定性。