Traffic light approach strategy If approaching a red traffic light, it is obviously smart to decellerate as soon as possible to some lower, but highest possible velocity that allow the light switch green just as we cross the stop line. We save time and energy this way.
However,  is there still an optimal decelleration strategy, maximizing the speed on the stop line, if neither the schedule nor the current phase time is known if we first spot the red light? 
 A: I would use geometric progression for the speed. 
You drive at speed $v$.
As you first spot the red light, you are at a distance $d$ to the traffic light. Reduce your speed by a factor $a <1$. Now you drive with $a v$. After half the remaining distance to the traffic light, if the lights are still red, reduce again by the same factor. Now you drive with $a^2 v$. Repeat, as long as the light is red.
What happens is the following: The time $t_k$ you need to drive the $k$th segment, after having reduced your speed for the  $k$th time, is
 $t_k = \frac{0.5^k d}{a^k v}$. The total time elapsed for driving $n$ segments is thus
$T_n = \sum_{k=1}^n \frac{0.5^k d}{a^k v} = \frac{d}{v} \frac{1 - 1/(2a)^n}{1 - 1/(2a)}$
This formula allows you to adapt to your previous knowledge (or expectation or risk-aversiveness).
Note that it takes $n\to \infty$ to actually arrive at the traffic light since at $n$, the remaining distance to the traffic light is $0.5^n d$.
If you know nothing and want to take no risk of having to stop, choose $a < 0.5$. Then, for $n \to \infty$, $T_n$ diverges, and you have as much time as you may ever need until the light turns green again. Even if your traffic light was indeed a permanent red, you don't have to worry since you will not reach it in finite time.
If you have an estimate (say, as a very conservative one, the longest time $T^*$ you ever experienced a traffic light to stay red), then you can fit $a$ by roughly setting $T^* =  \frac{d}{v} \frac{1}{1 - 1/(2a)}$. You my adapt this to actual knowledge of the phase time. 
What's rather difficult is to adapt it to the true remaining "red" time, unless you take other factors into account, e.g. how many cars are standing waiting at the red light, which at this time of a normal day means that the light is red already for time $t$ ... this is very unreliable information.
Lastly, if your plan is to "arrive" at some braking distance $d^*$ from the traffic light with some remaining speed $v^*$ (which would allow you to brake), then you should have, after $n$ segments, $d^* = 0.5^n d$ and $v^* = a^n v$, hence set $$a = (\frac{v^*}{v})^{1/(\log(d^*/d) / \log(0.5))}$$ and better have a processor to do this for you on site... 
