A modelling and simulation study of a metro line as a time-delayed switched system

In public transportation systems, there is a linear relationship between the passenger quantities in a station and the headway of the vehicles. An optimized headway is beneficial for both passenger satisfaction and cost reduction, since reducing the headway will increase operational costs. The headway update starts from the first station and propagates to the other stations with a time delay, τ, originating from the train's travel time between the first station and the affected station. A well-defined model of the passenger quantities in the transportation line is required for tuning the headway efficiently. In this study, the transportation system is considered as a switched time-delayed system since the change in passenger quantities is dependent on the state of a train arriving at the station and travel time is a pure delay between stations. A sample metro line has been modelled as a switched time-delayed system and simulated on MATLAB Simulink® utilizing real-world data provided by Metro Istanbul. The results of the simulations of this new model have been compared to the traditional discrete event simulations of the Arena®. Both results were consistent and the simulation based on our switched time-delayed system mathematical model was significantly faster and dynamically adjustable.