Tuesday, July 21, 2009

Gilgal logic

Whenever Gilgal gets mentioned at the Shuttle site someone always pipes up with something along the lines of "Ah it's bad drivers, they should merge" and I always respond with "They can't". The other line is that traffic shouldn't be stopping at the merge point but carrying on until a gap forms again I counter that this is illogical. I realise now I haven't explained the logic behind this, so I will lay it out now.

There are two premises I base this on:

  1. The majority of traffic wishes to use the left-hand lane.
  2. Any gap that does form will be filled by the first Vale Road car that meets it.
Both based on observation.

So the first logically step based on premise 1 is that the most likely place a gap will form is at the end of any queue formed in the left-hand lane where the traffic builds up.
If the queue doesn't reach the merger point then it will be filled by traffic from Vale Road until it does as per premise 2.
Thus given a sufficient quantities of traffic the end of the queue will always be either at or beyond the merger point.
Given the first logical step any gaps will form at the end of this queue.
Therefore if the gap remains it will be at or pass by the merger point and as per premise 2 will be filled by the first car from Vale Road it meets which will be the one waiting at the merger point.

Therefore if you decide to travel down the right-hand side you are waiting for a gap that is less likely to form than at the merger point or hoping someone will let you in which is just as likely while waiting at the merger point.

While it is possible that someone will continue down the left-hand lane and change lanes later there remains an even chance that they will do so either before or after your current position and that the gap will be closed up by the time you or it is reached.

Therefore when traffic creates a queue in Gilgal to increase your chances of joining the left-hand lane you should stop at the merger point.