image/svg+xml Optimization Models for Energy-efficient Railway Timetables Shuvomoy Das GuptaSystems Control GroupDepartment of Electrical & Computer EngineeringUniversity of Toronto Outline • Background• Literature review• Creating a feasible railway timetable• A robust mixed integer optimization model (ACC 2015)• A two-stage linear optimization model (Transportation Research Part B, accepted)• Concluding remarks Time Speed Accelerating Coasting Speed Holding Braking Power Time --- -- - Energy Produced Regenerative Braking Energy EnergyConsumed How a train moves Platform i Platform j Temporal representation of the phases of train t around platform i • Our goal is to maximize the overlapping time between the acceleration phase of with the braking phase of braking accelerating accelerating braking braking accelerating dwelling dwelling dwelling Notation: accelerating braking dwelling accelerating braking dwelling accelerating braking dwelling accelerating braking dwelling accelerating braking dwelling braking accelerating accelerating braking braking accelerating dwelling dwelling dwelling braking accelerating dwelling braking accelerating dwelling = The temporally closest train of t to the right = The temporally closest train of t to the left = The temporally closest train of t = or = accelerating braking dwelling braking accelerating dwelling (exclusively) Train Platform Braking Dwelling Accelerating Time Speed = Duration of braking phase of train t during arrival at platform i = Duration of accelerating phase of train t during departure from platform i Known: Unknown: = Start time of the braking phase of train t during arrival at platform i = End time of the accelerating phase of train t during departure from platform i } Decision Variables Train Relevant event times of a train around a platform } Uncertain Power Time Characterization of suitable train pairs Power Time