A New Stability Index for Metro Lines

Abstract

In this work a new method to analyze the stability of metro lines with respect to a previously constructed time schedule is presented. For this purpose, metro lines are modelled using a nonlinear real time discrete space state representation and then the Lyapunov-based stability analysis is applied considering time delays of trains as disturbances. As a result a new set of indexes which relate time delays with the validity of the actual time schedule when falling inside a particular ‘stability area’ are defined. Results obtained in a simulated environment show that the new stability indexes are able to evaluate quantitatively and qualitatively the effects of saturation in metro lines as well as predict the need for rescheduling