Uncertainty in connected vehicle penetration rate estimation : advanced modeling and applications for traffic signal optimization

Abstract

The emergence of connected vehicles (CVs) enables real-time traffic information sharing within a transportation network. The shared information provides invaluable opportunities to improve transportation systems. Nevertheless, the full deployment of CVs will either take a long time or never be achieved owing to issues posed by policy, privacy, and willingness. In the inevitable transition period, the CV penetration rate serves as the essential input for many beneficial applications and must be estimated. However, existing methods are solely point estimators for estimating the average CV penetration rate and overlook the uncertainty in this estimation. Direct application of point estimators may lead to biased models and suboptimal solutions in system modeling and optimization. This study, for the first time, explicitly models the uncertainty in CV penetration rate estimation by proposing an innovative and fully analytical probabilistic penetration rate model. A Markov-constrained queue length model is derived to account for complex residual-vehicle effects, fostering the establishment of a unified framework for CV penetration rate uncertainty estimation at any undersaturation condition. The availability of such uncertainty paves the way for the paradigm shift from deterministic to stochastic CV-based traffic signal optimization for isolated intersections and traffic networks.

For traffic signal optimization at isolated intersections, the total intersection delay, serving as the minimization objective measure, is estimated as a function of the real-time arrival rates and numbers of holding vehicles, where the former are derived by taking real-time CV penetration rates as inputs, while the latter are estimated through a CV-based holding vehicle model. Considering necessary signal optimization constraints, a CV-based adaptive signal control framework is established for isolated intersections. Ignoring the uncertainty in CV penetration rate estimation gives a deterministic arrival rate and optimization problem. In contrast, incorporating such uncertainty into real-time arrival rate estimation formulates a stochastic, high-dimensional, and non-convex optimization problem. An analytical stochastic delay model is proposed to effectively evaluate and differentiate the stochastic delay model based on generalized polynomial chaos expansion. This enables the development of an efficient gradient-guided golden section search algorithm for solving traffic signal optimization problems.

For network-wide traffic signal optimization, the objective becomes minimizing the total network delay, which is derived from the vehicle locations in all lanes in a network with a CV-based traffic pattern model. A dedicated model for CV-based vehicle location is developed for estimating vehicle locations in both source and intermediate lanes. Similarly, with a set of constraints, a CV-based coordinated signal control framework is established for traffic networks. Considering the uncertainty in CV penetration rate estimation gives rise to stochastic vehicle locations and control schemes; otherwise, the resulting vehicle locations and control schemes are deterministic. A hierarchical max-green optimization algorithm is proposed to solve the optimization problems by decomposing the complex original problem into subproblems at three different levels. Comprehensive vertical queue experiments, VISSIM simulations, real-world validations on the Next Generation Simulation dataset, and illustrative applications demonstrate the effectiveness and superiority of the proposed models, highlighting the significance and importance of incorporating CV penetration rate uncertainty into CV-based traffic signal optimization.