exupero's blog

# Speeding and stop lights

In the previous post I discussed the hypothetical time gains produced by speeding, but I ignored trickier questions like stop lights and traffic. As a conservative driver I've occasionally had a someone speed by, only to then catch up to them waiting at a red light. Anecdotally, red lights seem to negate some of the gains of speeding.

Let's check this intuition with a graph of two choices of speed. Here's a scenario with two drivers and no impediments, a hypothetical best-case scenario:

Now let's introduce some random stop lights:

The faster driver initially has a hard time gaining a lead on the slower driver. They both get green lights at the first two intersections, but the faster driver ends up stopped at the third as the slower driver catches up. Both get stopped at the fourth, fifth and sixth intersections, effectively restarting their race each time. Not until the seventh intersection does the faster driver start gaining ground, as he slips through just before a red light that catches the slower driver. After that, luck is on the faster driver's side, and he gets greens at the next three intersections while the slower driver gets delayed at a couple reds. In the end, the faster driver seems to arrive about as much before the slower driver as he would without stop lights.

While this simulation does reproduce the anecdote of a slower driver catching up to a speedy driver at red lights, it also shows that the effect of stop lights cancels out over time. Not only do slow drivers sometimes cruise through just after red lights, but fast drivers sometimes slip through just before red lights.

Another interesting effect is visible when we look at a range of speeds:

Though speeds fan out across a continuous range at the start, arrival times at the top of the graph are fragmented into buckets. To arrive sooner, it may not be enough to drive slightly faster. A driver needs to speed enough to jump to a bucket that arrives earlier.

That may explain one commute I used to have where it felt like I could never time it just right to arrive at work at a particular time. I would either arrive a little too late or a little too early. It was also the commute with the most stop lights, so I now realize that the bucketing illustrated above was probably somewhat to blame.

Of course, this is a very loose simulation. It assumes constant driving speeds and uses random stop lights instead of planned timings or lights that change according to traffic conditions. But it does hint that speeding may sometimes be just racing from stop light to stop light, as appears to be the case for the fastest driver shown above. For me, that would only feed whatever exasperation is making me speed in the first place.

We'll take a look at moving obstacles in the next post.