The Tube Challenge and Underground Mathematics

The Tube Challenge is a race around the London Underground system.  The rules are that participants must pass through all 270 stations as quickly as possible, using the trains, or walking or using public transport between stations.

Harry Beck's map of the London Underground system pioneered such maps of public transport systems around the world.  It transforms the geography of London into a network - essentially,, it is a public demonstration of topology.  It is also one of the best known network diagrams in Britain, if not the world.  This year, the underground system has celebrated its 150th birthday.  One part of that celebration is the installation of 270 different labyrinths in the stations, numbered according to the sequence taken by the current holder of the record time for the Tube Challenge.

Details can be found here; there is a link from that page to the challenge, where an animated diagram shows the journey, and the stations are highlighted as they are "visited".  If you watch the route develop you will see the stages where it is optimal to leave the underground system to travel on the surface between stations.

Now, consider the O.R. problem that underlies this challenge.  It has links to both the travelling salesperson problem, and to the Chinese postperson problem, but the timetable of the public transport is also part of the complexity.  Not all edges of the network need to be traversed, one doesn't have to return to the start.

Do other transport systems have similar challenges?

One of our O.R. students at Exeter had a summer holiday job working for London Underground.  His job was to deliver new electronic devices to each of the 270 stations and install them.  He could carry six machines at a time, and that was a a day's work, so he had to plan his trips to reach the stations in groups of at most six, another interesting piece of O.R.  He wrote it up and analysed the problem as a project.


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