Re: best braking technique as one approaches red light
- From: quasi <quasi@xxxxxxxx>
- Date: Thu, 23 Aug 2007 08:07:37 -0400
On Thu, 23 Aug 2007 07:40:45 -0400, quasi <quasi@xxxxxxxx> wrote:
On Thu, 23 Aug 2007 07:10:36 EDT, jeremy rutman
<jeremy_spagnet@xxxxxxxxxxx> wrote:
I'm traveling at a speed V when I see a red lightahead at distance d with probability to change to green > as function of time p(t), which for example could be
gaussian.
I would like to find the velocity profile v(t) thatmaximizes my velocity (averaged over all scenarios
knowing p(t)) as I pass the light, with the condition
that I have to stop if I hit the light when its still
red.
It doesnt seem to fit the form of a standardfunctional
cauchy-riemann type problem. Has anyone an insighthow to solve it?
If you absolutely have to stop on red, then the
probability function
p(t) is irrelevant. You always should go at the
maximum speed subject
to the requirement that you must be able to brake to
a full stop at
the light if it's still red.
quasi
No, the probability is relevant. If for instance the probability of being green is:
p(t)=0 for t<5 and
p(t)=1 for t=>5
then I should go the speed d/5.
The 5 in d/5 comes from the probability of being green.
Maybe I'm missing something, but it seems to me that you can't
possibly do better than to go at the maximum possible speed for which
it is still possible to stop. And there's no reason to do worse.
What makes the probability function irrelevant is the fact that you
are not allowed to fail to stop if it's still red.
Ok, I just noticed -- p(t) can be zero on an interval.
Perhaps that does make p(t) relevant.
I have a few questions (although I won't be back until later):
p(t) represents the probability that the light will go green within t
seconds, right?
Does the function p itself change based on how long the light has been
seen as red?
V is the maximum speed, right? But what about the maximum acceleration
and deceleration values? Don't we need to be given that info?
quasi
.
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