A Lane-Based Optimization Method for Minimizing Delay at Isolated Signal-Controlled Junctions

Abstract

This paper presents a lane-based optimization method for minimizing delay at isolated signal-controlled junctions. The method integrates the design of lane markings and signal settings, and considers both traffic and pedestrian movements in a unified framework. While the capacity maximization and cycle length minimization problems are formulated as Binary-Mix-Integer-Linear-Programs (BMILPs) that are solvable by standard branch-and-bound routines, the problem of delay minimization is formulated as a Binary-Mix-Integer-Non-Linear Program (BMINLP). A cutting plane algorithm and a heuristic line search algorithm are proposed to solve this difficult BMINLP problem. The integer variables include the permitted movements on traffic lanes and successor functions to govern the order of signal displays, whereas the continuous variables include the assigned lane flows, common flow multiplier, cycle length, and starts and durations of green for traffic movements, lanes and pedestrian crossings. A set of constraints is set up to ensure the feasibility and safety of the resultant optimized lane markings and signal settings. A numerical example is given to demonstrate the effectiveness of the proposed methodology. The heuristic line search algorithm is more cost-effective in terms of both optimality of solution and computing time requirement.