Convexity and global optimisation of lane-based fixed-time signal model for delay minimisation at an isolated intersection

Lane-based fixed-time signal is basic to various signal control strategies. It performs well in maximizing road capacity, but is faced with significant challenge in minimizing traffic delay. This study validates the convexity of lane-based fixed-time signal model for delay minimization, when lane markings are determined as well as flow factors. Thus Breadth first search algorithm is developed to enumerate the feasible lane markings, which are then screened with flow factors. Cutting plane algorithm is applied to the CMINLP for each feasible lane markings, where the non-linear delay function is converted to a series of linear ones, until the relaxed delay converges to the actual delay. Branch pruning strategy is established for efficiency, to eliminate the lane markings with uncompetitive delay. Numerical analyses follow to validate the proposed algorithm. This research promotes the redesign of lane-based fixed-time signal control.