Re: best braking technique as one approaches red light


"quasi" <quasi@xxxxxxxx> wrote in message
news:fjsqc39e3qatnlst6517o3ddmfbbl2fuok@xxxxxxxxxx
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 light
ahead 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) that
maximizes 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 standard
functional
cauchy-riemann type problem. Has anyone an insight
how 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

And

Do these lights have an amber stage?

Haven't done the sums but it could be that you would slow as you approach
the lights and then speed up knowing that it they go amber you will still
get across before they go red. (Assuming that you know how long they stay
amber.)


.

Relevant Pages

  • Re: Analyses of Mistake on Proof about Perfect Secrecy of One-time-pad
    ... "the ciphertext is not known" do not coexist, ... So the probability of the key now changes for that person ... Since knowing the ciphertext "does not coexist" with not knowing the ... If you do not admit the probabilities changes when c is fixed, ...
    (sci.crypt)
  • Re: best braking technique as one approaches red light
    ... No, the probability is relevant. ... then I should go the speed d/5. ... What makes the probability function irrelevant is the fact that you ...
    (sci.math)
  • Re: The Dreaded Spelling Category
    ... I wonder if Alex will issue a correction on "tomorrow"'s show. ... Scintillating 17th Century", but that doesn't mean it isn't ... It assigns the probability to the knowing, ... Of each individual from the original "us", knowing nothing else about ...
    (alt.usage.english)
  • Re: Food for Thought
    ... *A test administered without knowing it is test has a random ... probability of being passed, since the context can admit carelessness. ...
    (sci.econ)
  • Re: Hatto Chopin-Godowsky confirmed by waveforms
    ... "knowing" means the kind of corroboration that Farhan ... The ear is not realiable ... feeling that Hatto was a miracle (probability zero), ... Or maybe iTunes did reveal the hoax early on, ...
    (rec.music.classical.recordings)