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> How to Merge
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> The Three-Lane Merge |
The Three-Lane Merge
Often, when two lanes merge into one, there's a third lane that just goes along for the ride … and, often, that's the correct way to think of the situation, as a two-lane merge plus a third lane. The third lane may be slowed by friction, but it will still move a lot faster than the others, so the best you can do is anticipate the merge and get yourself into the correct lane.I've wondered, though … what if we considered the situation as a whole, as a three-lane merge into two lanes? Could we find a more equitable, and possibly more efficient, solution, comparable to the classic alternating merge for two lanes? We can, of course, or I wouldn't be talking about it, and here it is.
You can think of this as the middle lane merging alternately left and right while the right lane moves over, but I prefer to imagine dividing the traffic into three-car triangles, which then merge, and that's how I drew the picture. The solution is probably too complicated to adopt, but I still thought it was worth mentioning. Maybe I'll get a chance to try it out some time.
I think the solution is unique, if we require that the period be as short as possible, and that each car either stay put or move just one lane to the left.
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@ December (2001)