Adaptive signal control at partially connected intersections: A stochastic optimization model for uncertain vehicle arrival rates

Optimizing traffic signal control is crucial for improving efficiency in congested urban environments. Current adaptive signal control systems predominantly rely on on-road detectors, which entail significant capital and maintenance costs, thereby hindering widespread implementation. In this paper, a novel connected vehicle (CV)-based adaptive signal control (CVASC) framework is proposed that optimizes signal plans on a cycle-by-cycle basis without the need for on-road detectors, leveraging partial CV data. The framework comprises a consequential system delay (CSD) model, deterministic penetration rate control (DPRC), and stochastic penetration rate control (SPRC). The CSD model analytically estimates vehicle arrival rates and, consequently, the total junction delay, utilizing CV penetration rates as essential inputs. Employing the CSD model without considering CV penetration rate uncertainty results in fixed vehicle arrival rates and leads to DPRC. On the other hand, incorporating CV penetration rate uncertainty accounts for uncertain vehicle arrival rates, establishing SPRC, which poses a high-dimensional, non-convex, and stochastic optimization problem. An analytical stochastic delay model using generalized polynomial chaos expansion is proposed to efficiently and accurately estimate the mean, variance, and their gradients for the CSD model within SPRC. To solve DPRC and SPRC, a gradient-guided golden section search algorithm is introduced. Comprehensive numerical experiments and VISSIM simulations demonstrate the effectiveness of the CVASC framework, emphasizing the importance of accounting for CV penetration rate uncertainty and uncertain vehicle arrival rates in achieving optimal solutions for adaptive signal optimizations.