Robust train regulation for metro lines with stochastic passenger arrival flow

- A train traffic model of metro line with stochastic passenger arrival flow is developed.
- The stochastic stability condition of metro line is given in terms of LMIs.
- Robust train regulation strategy is designed to reduce the total delays of the trains.
- The proposed method significantly improves the operation efficiency of the metro system.

This paper investigates the robust train regulation problem for metro lines with a stochastic passenger arrival flow. The passenger arrival flow is assumed to be dependent on a discrete Markovian process. A constrained state-space model for the train traffic of a metro-line operation is developed from a system-theoretic standpoint. According to stochastic stability theory, we give a sufficient condition for the existence of state-feedback control as the train regulation strategy in terms of linear matrix inequalities, which ensures the stochastic stability of the train traffic of metro lines. By considering the uncertain disturbances to the train operation, a robust train regulation strategy that guarantees that the practical train timetable tracks the nominal timetable with a disturbance attenuation level is designed, and the total delays of the trains at each station are reduced. Moreover, a nonlinear optimization problem is formulated to determine the optimal robust train regulation strategy that ensures the minimization of the disturbance attenuation level. Numerical examples are given to illustrate the effectiveness of the proposed methods.