Network-wide adaptive signal control with partial connectivity: A stochastic optimization model for uncertain vehicle locations

The increasing adoption of connected vehicles (CVs) has facilitated the development of CV-based traffic signal control. However, most methods rely on deterministic control models that do not account for uncertainty in input traffic states. This can lead to suboptimal signal timing and even control failure, particularly in highly dynamic, nonlinear transportation systems. Additionally, while adaptive signal control for isolated intersections and corridors has been extensively studied, relatively little attention has been given to the more complex challenge of network-wide signal coordination in common grid networks. This paper addresses these gaps by developing a cycle-by-cycle adaptive and stochastic signal control for grid networks. To this end, a CV-based traffic pattern model is first proposed for estimating various correlated traffic patterns across all network lanes using estimated vehicle locations. A CV-based coordinated signal control framework is then formulated, incorporating a queue pattern-based delay model, a set of signal optimization constraints, and two vehicle location control strategies: deterministic vehicle location control (DVLC) and stochastic vehicle location control (SVLC). Unlike DVLC, SVLC explicitly and realistically considers uncertainty in vehicle locations arising from uncertain CV penetration rates. To efficiently solve the high-dimensional, non-convex, non-analytical integer optimization problems, a hierarchical max-green optimization algorithm is developed, which decomposes the original problem into a series of integer linear programming subproblems. Extensive VISSIM simulations demonstrate the effectiveness of the proposed model, highlighting its ability to enhance network-wide traffic performance and the importance of incorporating uncertainty in traffic state estimation for signal optimization.