On Thu, 21 Jun 2001, Paul Rosen wrote:
> > In addition i also wondered if any members of the list had come across any
> > literature concerning the application of chaos theory to traffic flows and
> > traffic congestion
>
> I haven't, but I'd be very interesting to see any replies sent to the
> list rather than privately - would a chaos theory analysis challenge or
> reinforce conventional traffic modelling/planning wisdom?
Paul,
It's clear that there are various levels at which a traffic system
might be "chaotic" - some of which would challenge and some of which would
reinforce conventional wisdom. We could consider a heirarchy of levels at
which the system might be considered: "chaotic" at the two extremes we
could have the following two scenarios:
(Note here that I'm taking the very loose definition of "chaos" as being
a system with "sensitive dependence on initial conditions".)
1) A driver brakes suddenly - this causes the driver behind him to brake
suddenly and so on - the resulting cascade can cause a traffic jam "for no
good reason" which might well not have happened if that driver had not
braked at that point. There's a lot of good work done both in the UK (on
M25 data) and in Germany (on equivalent motorway data) showing the
spontaneous formation of traffic jams. We could consider this kind of
thing a chaotic phenomenon - but it doesn't really challenge existing
theory. Most practitioners already believe (in my experience anyway) that
within certain bounds levels of congestion will naturally vary from day to
day.
2) This kind of micro behavioural change could influence day-to-day
behaviour. For example, a number of people in the traffic jam in 1)
decide to take a different route the next day. Enough of them do so that
responsive traffic signals change their behaviour encouraging others to
swap onto that route. After a number of weeks the whole system behaves
differently.
Possibility 2 sounds the least likely but there is no compelling reason
to say it couldn't happen. Most practitioners proceed on the assumption
that the system is to a high degree predictable (indeed most assume it
will tend to an equilibrium) and that within day microscopic differences
in behaviour will wash out in the long run. However, that was the case in
weather forecasting thirty years ago.
I'd be interested in hearing of any references people have on teh
subject.
Richard
Richard G. Clegg, Networks & NonLinear Dynamics Group,
Department of Mathematics, University of York.
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