Just have to disagree with the ‘only saves five minutes’ argument that was made earlier - and here’s why:
On Wednesday this last week I had to get to work via a specific route - one of only two available. Unfortunately, the backup started AFTER the point where that choice could be made, so I was stuck. I was also in the CORRECT lane for the merge already. I sat there for 15 minutes to get through the approximately ONE mile backup, while watching others zip past me in the open lane (once I’m in the correct lane, I’m not going to jump to the empty lane - that can be dangerous - you never know when a car two behind you has had the same idea and >>>CRUNCH<<<)
Fast forward two hours - I had to run an errand which required me to go out and return by the same route, so I decided to stay in the INCORRECT lane until I had to merge. Got past the backup (which was about the same size it was earlier) in three minutes.
lawoot, your experience is perfectly consistent with my analysis.
Where the traffic merges too early, the traffic density in the one lane into which everyone has merged shoots up, lowering speed, often to the point of congestion. On the other hand, the other lane is nearly empty, so traffic there can move quickly.
By travelling on the empty lane you’re not slowing down the overall traffic, because the critical capacity is the ability of the one-lane segment of road to absorb the traffic (whichever lane it originally comes in on).
If the traffic were to stay in both lanes until as late as they can while still safely and efficiently merging, the average travel time and length of backup could be reduced. The capacity of the two lane roadway would be used to the greatest extent possible.
I’m not advocating waiting until the very last possible moment where you have to merge or you’ll hit the construction barrier. Obviously that’s problematic. However, using the highway’s full capacity for as long as reasonably possible is the most efficient way.
The issue raised by the OP is really: “Who’s the asshole?” Unsurprisingly, this question is not covered in the traffic engineering manuals I’ve run across.
lawoot’s adventures last Wednesday show the results of the two possible strategies, merge immediately or stay in the lane that will be dropped. (lawoot correctly concluded that once you’re in a congested lane, it can be quited dangerous to try to jump out into free-flowing traffic.)
The “asshole” question turns on whether it’s wrong to bypass the queuing traffic to take an opportunity to help yourself. In my view, it’s not an asshole thing to do, because it ultimately helps traffic and average travel time. If half the traffic were to be “assholes” by staying in the lane that will ultimately be dropped, traffic flow would be optimized.
The former certainly is a subset of the latter, but the latter includes much more than the former.
Now, Billdo, here’s another attempt to explain what’s wrong with your analysis.
You said that at 20 m/h, the throughput is 1000 c/h. (1000c/h)/(20m/h)= 50 c/m. Similary, (1000c/h)/(60 m/h)=16.6… c/m. (And 8.3…c/m in each lane.)
So say I’m at the beginning of this stretch of highway, and everyone merges at the beginning. That’s 3 miles of 50 c/m or 150 cars that are in front of me.
Now, the number of cars in front of me isn’t going to change just because they’re proceeding at a different speed. So in the second situation, there are still 150 cars in front of me. There are 50 in the first mile (50 c/m * 1m), which leaves 100 cars at 16.6… c/m. (100 c)/( 16.6 c/m)=6 miles. So that’s 1 mile at 20 mph (3 minutes) and 6 miles at 60 mph (6 minutes). What’s the total? 9 minutes, exactly the same as if everyone had merged at the beginning. The difference in travel time that you calculated was simply due to creative accounting, not to any time savings in the real world.