How to leave Devon, if you need to!

Major sporting events have used deal with the problem of getting spectators to and from the venue by public transport.  The organisers of the last three Olympic Games have all done so (and maybe others as well; not everyone involved with such planning publishes or publicises their work).  There is a problem that most readers will recognise - they have attended an event which finishes at a particular time, and the whole audience wants to get away at the same time.  A similar problem arises in airports where a jumbo jet lands and all its passengers spill out at the same time.  The capacity of the system for people needs to recognise that large peaks will occur.

One day several years ago, soon after I had written about the use of capacitated networks for transport planning, I had a phone call at work.  The caller asked whether what I had written might be applied to help plan evacuation routes.  It wasn't something that I had direct experience of, though I had been taught a little about the theoretical concept.  So there followed a conversation about the way that evacuation of an area in an emergency might use the capacity of the arcs in a network of roads, and I remember drawing attention to the problems of how the flow of people at road junctions would mean that there were capacities of the nodes as well, and some of the problems of measuring the data.  Towards the end of the call, I asked why the caller was interested in the subject.  That was when he revealed that he was drawing up plans in case of a nuclear accident affecting a town near one of the UK's nuclear power stations.  I never heard from that caller again, so I do not know what happened next.

The south-west of England, Devon (where I live) and the neighbouring county of Cornwall, are popular destinations for holiday-makers.  These days, the majority travel by car.  Unfortunately, the geography of the peninsula means that there are few major roads into the two counties. 
Devon; major roads in green, and the thick blue line is motorway.
The most popular change-over day is a Saturday, so these major roads become congested with the traffic of holiday-makers coming and going.  It's not really an evacuation, though sometimes it may seem like one.  And there is traffic in and out of the counties.  As the map shows, there are two major roads and a motorway connecting Devon with the country to the east.  I only travel when I really need to on a Saturday in the summer, as I know that there will be hold-ups!  The border between Devon and Cornwall also has three major roads; and for much of the border, there is a river (the River Tamar) to be crossed, with very few bridges. 

Soon after coming to live in Exeter, I heard a story that made an interesting claim about those holiday-makers.  If everyone who had to leave Devon and Cornwall on a given date were to set out at exactly the same time, then there would be no problems on the roads.  All the holiday-makers would be spread out uniformly across the roads.  There must be a grain of truth in the story, because in 1999, when the counties were crowded with people wanting to see the solar eclipse, the traffic flowed extremely smoothly.  Once the eclipse was over, then many people returned home, leaving their various vantage points within a short space of time after the event. 

In the January 2014 issue of the Journal of the Operational Research Society, DR Bish, HD Sherali and AG Hobeika have written a paper "Optimal Evacuation Planning using Staging and Routing" (JORS volume 65, issue 1, pp124-140, DOI 10.1057/jors.2013.3).  Their models include the concept of staging, where the evacuation plan for people in an emergency specifies both the route that they should take, and the time they should start to move.  There would probably be some resistance to such an idea in some kinds of an emergency because the natural reaction is flight.  Could it be used for summer Saturdays in Devon?  Unfortunately, the number of holiday-makers in Devon and Cornwall who want to change-over on a summer Saturday is too big for their model! 


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