Entropy production LO20070

Keith SANDROCK (KSAND@hertz.mech.wits.ac.za)
Thu, 3 Dec 1998 12:27:03 +2:00

Replying to LO19979 --

Dear LO systems thinkers

At de Lange's interesting series on entropy reminds me of some work I did
years ago on the study of traffic flow. Traffic flow (Vehicles/hour) is
related to traffic density (vehicles/mile) by a bell-shaped curve with
traffic density represented on the horizontal axis, and traffic flow on
the vertical axis. The 'bell' is not quite symmetrical but you can safely
think of it as being so.

It is very easy to visualise this picture. At the origin we have zero
density (no vehicles on the roadway) and hence zero flow. At the extreme
right hand side we have maximum density (traffic jam) and again zero flow
since nothing is moving. Somewhere about the midway point between these
two extremes traffic density is just right to produce maximum flow.

When densities are low there is little or no interaction between the
vehicles on the road and they are free to travel as they choose. As the
density increases interaction plays an increasingly important role and the
vehicles are no longer free to travel unhindered as before. At the point
of maximum flow (optimum density) and beyond the vehicle system behaves
like a compressible fluid and can be described using Boltzmann-like
equations. Prigogine (see At's posts) did some important work on traffic
flow modeling in the region of high density.

I am sure we have all experienced the situation where we have been happily
cruising along an open road only to suddenly come upon a traffic build up
of some kind. Immediately we are alert and forced to concentrate on the
vehicle ahead, and to keep a safe distance between our cars. The
behaviour of the two systems depicted in this illustration is radically
different. Both can be described fairly accurately using mathematical
models. (These results are well known to traffic engineers). And of
course the entropy situations are also vastly different for the two
systems. Viewing traffic flow systems in terms of entropy is an intriguing
avenue to explore.

What I found very interesting was the fact that when density is high
enough, shock waves are propagated through the traffic stream in much the
same way as through a compressible fluid. This can happen when we have an
erratic driver in our midst. This driver does not maintain a constant
distance between his car and the one in front. Instead he steps on the
gas as soon as the gap widens, only to jam on brakes when he is about to
whack the other guy's bumper. The wave he generates is propagated
backwards with increasing amplitude, and at about the third car back the
space between the vehicles measured in units of time (seconds) equals the
average human reaction time. Of course this results in a rear-end
collision. Who gets the blame? Well they guy who hit the car in front is
obviously guilty isn't he? Not necessarily. He could be the victim of
circumstances caused by the erratic blighter who generated the shock wave
in the first place.

The study of traffic flow and its modeling is an extremely rich field for
systems thinkers. Some really elegant work has been done in this area. I
won't go into this here, but recommend the field to you. The point I
wished to make is that entropy production and changes in entropy play a
significant role in our well known, everyday, traffic flow situations.
Using the knowledge you have gained from At, think about this aspect next
time you drive to work.


Keith Sandrock Systems/Johannesburg Technology (JOHANTEC)
FAX 27-11-339-7997 KSAND@hertz.mech.wits.ac.za


"Keith SANDROCK" <KSAND@hertz.mech.wits.ac.za>

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