How many people are coming to this event?

The Institute of Mathematics and its Applications is a UK-based professional society for mathematicians in industry and academic life.  Many of its members are also members of the OR Society, but the IMA extends to mathematics in many other areas, including engineering and computing.  The IMA has a high profile in education, and produces publicity material about interesting and unusual aspects of mathematical models.  The series is called "Mathematics Matters".  One of the most recent items is about crowd modelling, "Following the crowd" which draws on work by Professor Keith Still on managing crowds for safety and security. 

"Following the crowd" highlights the problem of deciding how many people are coming to an event, and how to control access.  The example taken is the attendance at London's New Year fireworks display.  It is free, so there are no advance bookings to work from.  The safety concern is when to close access to the viewing areas; leave it too late, and either people are herded into a dense mass, or the crowd is forced to turn round against the flow ("Those behind cried 'Forward', Those before cried 'Back' ").  The outline of the method is to take arrival rates at regular intervals, fit these to a model of the pattern of arrival rates, forecast attendance from this model (or at least forecast the arrivals for a few future time intervals) and close off access to feeder channels when the viewing areas hold about 80% of their capacity.  The feeders will supply the remaining 20%. 

Keith Still's website has numerous other stories of models of crowds, and of what happens when there is no organisation, or inadequate organisation.  It is instructive to see how this area of modelling brings together forecasting, queue models and network flows.  It extends to the design of feeder channels - as used in theme and adventure parks as well. 


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