Uncertainty Estimation of Connected Vehicle Penetration Rate

Knowledge of the connected vehicle (CV) penetration rate is crucial for realizing numerous beneficial applications during the prolonged transition period to full CV deployment. A recent study described a novel single-source data penetration rate estimator (SSDPRE) for estimating the CV penetration rate solely from CV data. However, despite the unbiasedness of the SSDPRE, it is only a point estimator. Consequently, given the typically nonlinear nature of transportation systems, model estimations or system optimizations conducted with the SSDPRE without considering its variability can generate biased models or suboptimal solutions. Thus, this study proposes a probabilistic penetration rate model for estimating the variability of the results generated by the SSDPRE. An essential input for this model is the constrained queue length distribution, which is the distribution of the number of stopping vehicles in a signal cycle. An exact probabilistic dissipation time model and a simplified constant dissipation time model are developed for estimating this distribution. In addition, to improve the estimation accuracy in real-world situations, the braking and start-up motions of vehicles are considered by constructing a constant time loss model for use in calibrating the dissipation time models. VISSIM simulation demonstrates that the calibrated models accurately describe constrained queue length distributions and estimate the variability of the results generated by the SSDPRE. Furthermore, applications of the calibrated models to the next-generation simulation data set and a simple CV-based adaptive signal control scheme demonstrate the readiness of the models for use in real-world situations and the potential of the models to improve system optimizations. Funding: This work was supported by The University of Hong Kong [Francis S Y Bong Professorship in Engineering and Postgraduate Scholarship] and by the Council of the Hong Kong Special Administrative Region, China [Grants 17204919 and 17205822]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2023.1209 .