Project staff and support

Peter (Kin Po) Tam (Intern, University of Birmingham)
Keith Briggs (Company Supervisor, BT)
Peter Butkovic (Academic Mentor, University of Birmingham)
Tristram Armour (Technology Translator, Industrial Mathematics KTN)

This Internship project was carried out at BT, in conjunction with the University of Birmingham. It is part of the KTN's Industrial Mathematics Internships Programme, co-funded by EPSRC. Start date: September 2009; duration: 3 months.

Project description

To determine the quickest route between two points in a timetabled transport network is easy with standard algorithms if the vehicles can be assumed to adhere to the timetable. This is not the case with trains. Recent work at BT allows very accurate modelling of the delays with respect to the timetable. This project would develop new route-planning algorithms which take account of this known delay distribution. The ultimate aim would be a better website for buying train tickets. But at the first stage, the work was to find the solution of a combinatorial optimisation problem.

"This was an ideal internship project, combining rigorous mathematics and statistical modelling with a problem of genuine practical interest. Along the way we developed new results in the field of generalized order statistics (classical order statistics deals with e.g. the distribution of the minimum of a set of iid random variables; we are able to remove the iid condition and also compute conditional order statistics). And to write a program for the problem which is sufficiently fast is quite a challenge, since it must deal with a potentially large number of combinations of trains and routes. This was achieved by some clever programming," said industrial supervisor Keith Briggs, BT.

Project overview

At the end of this project, BT were able to develop a program which can be used internally by their staff when they need to travel. Ideally, this program will be used by a public transport company, for example National Rail, to improve their journey planning system on their website. BT were also able to obtain some new results in generalized order statistics and they have developed ways to decrease the number of calculations required in a problem with exponential computational complexity.

“For the duration of the internship, I was able to gain valuable knowledge and experiences, which I believe are not only useful for my PhD study, but it also provided me an excellent insight into the work involved in this industry. I was also able to learn the programming languages Python and C and understand the method and style of writing programs so that it can be read and run efficiently,” said intern Peter Tam, University of Birmingham.