Optimal driving strategies for a train journey with speed limits

How should a vehicle he driven to minimise fuel consumption? In this paper we consider the case where a train is to be driven along a straight, level track, but where speed limits may apply over parts of the track. The journey is to be completed within a specified time using as little fuel as possible.For a journey without speed limits, the optimal driving strategy typically requires full power, speed holding, coasting and full braking, in that order. The holding speed and braking speed can be determined from the vehicle characteristics and the time available to complete the journey. If the vehicle has discrete control settings, the holding phase should be approximated by alternate coast and power phases between two critical speeds.For a journey with speed limits, a similar strategy applies. For each given journey time there is a unique holding speed. On intervals of track where the speed limit is below the desired holding speed, the speed must be held at the limit. If braking is necessary on an interval, the speed at which braking commences is determined in part by the holding speed for the interval. For vehicles with discrete control, speed-holding is approximated by alternate coast and power phases between two critical speeds, or between a lower critical speed and the speed limit.