RE: game theory, etc.

["Chris Landry" <chris@xxxxxxxxxxxxxxxxxxxxx>]

> Date: Tue, 12 Aug 2003 01:27:55 -0400 (EDT)
> From: Jim Sokoloff <jim@domain.elided>
> Subject: RE: game theory etc.
> 
> For this analysis, consider measuring the maximum number of Alfas
> that pass a given point on a one lane road in a 1 minute period.
> (This obviously scales linearly with number of lanes and number
> of minutes.)
> 
> If you take the safe following interval to be 2 seconds, you will
> get 30 vehicles per minute past that point REGARDLESS of what speed
> they are travelling. If you take the safe interval to be 3 seconds,
> guess what? Fewer cars/min (20), but still constant with speed.
> 
> For your assertion to be true, the formula for safe following
> interval would have to have a minima at 40-45 mph. I can't imagine
> that any reasonable formula for following interval has its minima
> there. (I'd like to see the proposal I suppose.)
> 
> - ---Jim

Ah, but you assumed that each car is of zero length.  If you assume that
the cars actually occupy some space, the road capacity does increase
significantly with speed, at lower speeds.  However, you get to within
10% of the theoretical max capacity at 36 mph for a 3 sec interval and
at 54 mph for a 2 sec interval.  Of course, at 36 mph, you'll have a
very efficient roadway full of very frustrated drivers who are going to
be late for dinner!

Chris
'84 GTV6
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