The objective

The objective is to find the latest time a passenger should start the train journey so that the passenger will reach the destination on time to a degree of certainty given known train delay distributions in the network.

The approach

First, it was assumed that the departure times of any two trains are statistically independent and that also the order of the departure for any two trains may vary due to delay. In reality, the order of the departure of trains will not change. Finally, it was assumed that the passengers will always catch the first train that departs to their next station on their route after they arrive at the station.

Train delay distributions were contructed using real delay data obtained by by comparing the actual departure times of the trains from different stations with the departure time scheduled on the timetable. From these distributions and with any given starting time, a method of calculating the time a passenger will take to travel between two stations was developed together with the probability the passenger will arrive before this time.

Using this model together with a bisection method, the latest time the passenger can start the trip can be calculated, given the time the passenger want to arrive the destination and the probability the passenger want to arrive on time.

A program was written (in Python and C) for the model was tested using several journeys; each with more than one route and real data was used for each route. The example shown here is of the journey between Ipswich and Manchester which has 5 different routes.

"This internship was a great opportunity for my PhD student to experience practical applications of knowledge gained during his study. It will be invaluable when he becomes involved with real-life applications after his PhD, but it also helps him now with the finalisation of his thesis. Great experience to be recommended to any research student in Applied Mathematics," said academic supervisor Peter Butkovic, University of Birmingham.

related resources:

	Optimal trip planning subject to known delay distributions
»	Technical summary

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