Sunday, March 4, 2012

how to merge

In the modern world, the proliferation of automobiles as a means of transportation has given rise for the need of a special type of technique: a technique which will allow two paths of automobiles to join together, creating a single path. Especially difficult is the situation where the two paths are of automobiles traveling at different speeds—how can they safely and efficiently be combined?

In the South, we've developed a solution to this problem we call "merging." The basic idea behind merging is that drivers on the slower path and those on the faster work together to maximize their safety and their efficiency.

Step 1: drivers on the slower road who are "merging" onto the faster road accelerate as they approach that road until their speed closely approximates that of the faster road.

Step 2: now that these drivers are traveling at roughly the same speed as the faster road, they can insert themselves smoothly in between two autos on the faster road.

Step 3: in order for this to occur smoothly, both the merging driver and drivers on the faster road must be sensitive to the vehicles to their left and right, the respective speeds of those vehicles, and, crucially, the lines of sight of those vehicles. In particular, slight tweaking up or down of the speed of either the merging car or the car on the main road may be necessary in order for merging to occur with maximum smoothness. Of course, this sensitivity and cooperation is needed anyway in order for drivers on a multi-lane highway to interact safely. So, merging requires no techniques other than those required for safe driving anyway.

The great thing about "merging" is that is both safe and efficient. These two facts follow from a basic property of the relation between speed and distance: the relative distance a car travels in a given period of time is directly proportional to its speed. More speed, more distance covered; less speed, less distance covered.

When a merging auto is close in speed to the road on which it will merge, the procedure is maximally efficient because it necessitates at worst only minor changes in the speed of autos already on that road and, at best, no changes at all. The procedure is maximally safe because it ensures that the distance on the road required for cars to tweak their relative speeds in order to converge is minimal, so there is maximal flexibility in the avoidance of accidents between merging cars and those they merge with.

Contrast this with the suboptimal solution to this coordination problem which is apparently implemented in the northeast. This solution requires the driver from the slower road and the driver from the faster road to play very different roles. The slower driver plays a role called yielding while the faster driver plays a role called being an asshole.

Yielding just means "slowing down dangerously before moving into a faster stream of traffic." Because the yielding auto increases the difference between its speed and that of cars traveling on the road it wishes to join, it increases the distance needed for either itself or for those cars to adjust their speed enough to intermingle. This means both that the process is more dangerous (since there are greater distances on the road during the process at which there is risk of a collision), and less efficient (since it creates a greater risk the auto will enter the faster road at a less than average speed, necessitating the slowing down of the faster road).

These effects are exacerbated by the role played by drivers on the faster road of being an asshole. Being an asshole just means that whenever a slight tweak up or down in speed would allow the slower auto to merge smoothly, you instead accelerate into the space the slower auto would most naturally take, necessitating that they slam on their brakes, increasing the risk of accident to all parties and, crucially, trading off a risky gain in speed for one driver against maximizing the overall average speed of the road as a whole.

Of course, there are two situations under which the yielding + being an asshole would be safer and more efficient than merging. To find these situations, we simply apply our basic rule of the relationship between speed and distance again. Since we know that the combining of two streams is efficient if autos on the faster stream apply minimal breaking when a slower stream is combined, then one way to ensure that the yielding + being an asshole is relatively efficient is if distances on average between cars on the faster road were extremely long. This would ensure lots and lots of leeway for the converging auto to increase speed without danger of accident or slow down.

A second way to ensure that yielding + being an asshole were safer and more efficient than merging would be if the yield points both a) had a very long ramp before combining with the faster stream of traffic; and b) had very good visibility behind the yielding car so its driver could actually judge the distances and speeds of cars on the faster road before ending its yield. If this situation obtained, then one could ensure all the benefits of merging without the necessity of the cars on the fast road cooperating rather than being assholes.

As a matter of fact, neither of these situations obtains in the northeast. In fact, quite the opposite: highways are in general very very crowded, and on ramps are in general very very short.

I find this situation bizarre and confusing.

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