Headway Optimisation for Metro Lines Based on Timetable Simulation and Simulated Annealing

Abstract

To improve the capacity of metro systems, it is important to evaluate and minimise headway, which is defined as the time interval calculated from “head to head” between two successive trains in this paper. With existing approaches for headway optimisation, the headway for moving block systems is often calculated based on the safe braking distance. However, the blocking time at movable elements (e.g., switches and crossings) and stops has special characteristics. Since train separation is dominated by a signalling system, the distance between two successive trains at movable elements and stops exceeds the safe braking distance. In this work, the theory for building a blocking time model and calculating line headway for moving block systems is investigated. A workflow to minimise line headway is designed to derive an optimised velocity profile before the identified bottlenecks. Several different optimisation algorithms, including grid search, Monte Carlo, and simulated annealing, are developed and compared. Among them, simulated annealing shows the best optimisation capability with the least computational effort. The designed algorithm has been tested for Hefei-Metro Line 1, and the line headway can be reduced from 116.776 seconds to 105.806 seconds. If the acceptable rate of the increased transport is set at 1%, the line capacity will increase by 6.5%.