Estimating journey time for two-point vehicle re-identification survey with limited observable scope using 2-dimensional truncated distributions

In transportation, Weigh-in motion (WIM) stations, Electronic Toll Collection (ETC) systems, Closed-circuit Television (CCTV) are widely deployed to collect data at different locations. Vehicle re-identification, by matching the same vehicle at different locations, is helpful in understanding the long-distance journey patterns. In this paper, the potential hazards of ignoring the survivorship bias effects are firstly identified and analyzed using a truncated distribution over a 2-dimensional time-time domain. Given journey time modeled as Exponential or Weibull distribution, Maximum Likelihood Estimation (MLE), Fisher Information (F.I.) and Bootstrap methods are formulated to estimate the parameter of interest and their confidence intervals. Besides formulating journey time distributions, an automated framework querying the observable time-time scope are proposed. For complex distributions (e.g, three parameter Weibull), distributions are modeled in PyTorch to automatically find first and second derivatives and estimated results. Three experiments are designed to demonstrate the effectiveness of the proposed method. In conclusion, the paper describes a very unique aspects in understanding and analyzing traffic status. Although the survivorship bias effects are not recognized and long-ignored, by accurately describing travel time over time-time domain, the proposed approach have potentials in travel time reliability analysis, understanding logistics systems, modeling/predicting product lifespans, etc.