More on selfish merge and jams
I wrote earlier this week about selfish merging and traffic jams and this prompted some to ask if the selfish merge is really selfish. Update: There is more and new thinking in this later post on selfish merge being not so selfish.
There are two forms in which it is selfish. At its most basic, it is barging into line. A series of cars is traveling the road, and one car, who is behind all the others, waits for them to merge out of the vanishing lane, then zooms ahead of all of them, and get somebody up front to let them in where the merge has made things stop-and-go. 100 people behind the merger are delayed 5 seconds each, and he gains 500 seconds compared to joining the back of the line. That's if you presume it's a zero sum situation.
However, I believe it is worse than zero-sum, for a couple of reasons. A typical highway lane can handle 2,000 cars/hour, but only about 1,000 if traffic slows to a crawl. Cars that merge while traffic is still flowing are less likely to cause the collapse than those who attempt to merge from a stopped position at the end of the vanishing lane. It starts when somebody slows to let them in, or they barge in forcing somebody to brake.
Now if two lanes able to carry 2,000 cars/hour merge to one, we can only have smooth flow if there are in fact only 1,000 cars per hour (or fewer, since heavy merging reduces capacity to about 1,500 cars/hour) in each lane. If input is within the output capacity of the continuing lane, we can do fine. However, if slowing to stop and go reduces the chokepoint to 1,000 cars per hour, we can only handle 500/cars/hour/lane or the jam backs up for a long distance. Once input exceeds the output capacity we must take more dramatic steps to stop a long traffic jam.
This is the theory that supports metering lights on highways. As long as the highway flows at good speed, its capacity is high and sufficient for the traffic. If it gets a burst of high-demand, it collapses into a traffic jam. Thus, for people waiting at metering lights, while they are annoyed at waiting, in fact because everybody is being metered they will get there faster than if they don't wait. For the car at the "tipping point" it can be the case that if they wait, they will join a smooth traffic flow, but if they rush into traffic, they will be the straw that breaks the camel's back and slows everybody, including themselves.
My proposal is similar to metering lights, except for a merge. Merging reduces lane capacity as cars must increase spacing to allow safe merging. Or they must stop entirely in a jam. If demand starts to exceed capacity, my proposal is to prohibit merging well down the highway. The cars in the continuing lane zoom through without merging using the full capacity of the lane. However, from time to time they must stop (creating a waiting line) to let the cars in the vanishing lane through, also at full speed without merging. The volume of cars through the chokepoint is what matters here, and if we can increase that to 2,000 cars/hour instead of 1,000 cars/hour, we will have a far shorter jam when there is no choice but to have a jam (ie. more than 2,000 cars/hour coming in.) And by encouraging cars to merge early, we can avoid a jam when we have less than 1,500 cars/hour coming in. When we have something in between, we introduce a hopefully short single pause but maintain a little under 2,000 in output capacity. We would need experimentation to learn what the output capacity is with metered stopping.