-H- Problem is a problem motivated by a road configurations that constitutes a rather typical pattern of streets intersection.
The -H- configurations consists of the following intersection of streets:
. | Street 1| |Street 2|
. | | | |
———— —————————— ——————–
W Street 3 Street 4 Street 5 E
———– —————————— ——————-
. | | | |
. |Street 6| |Street 7|
The problems consists in coordinating car’s traffic simultaneously along the 7 streets of the picture in order to minimise the congestion. You must allow cars to travel from any parts of the city (North, South, West, East) to travel to any other part of the city (North, South, West, East).
This problem is far from being solved from a practical point of view.
Some long time ago I was in a bus along Street 7 going North from the south. In the configurations I was:
- Street 3, 4 and 5: W<->E
- Street 1 and 6: N->S
- Street 2 and 7: S->N
And additionally, we could turn:
- From Street 7 to Street 4 to the left.
- From Street 7 to Street 5 to the right
- From Street 5 to Street 2 to the right
- From Street 4 to Street 6 to the left
- From Street 1 to Street 3 to the right
- From Street 1 to Street 4 to the left
It was a nightmare … I waited a long time to go from Street 7 to Street 2, because:
Cars going from Street 1 to Street 6 blocked cars traveling W<->E between Street 3 and 4. As a consequence, cars traveling W<->E between Street 4 and 5 were blocking cars traveling S->N from street 7 to street 2.
In practice, the results of the current design was a stationary solutions with cars not allowed to move in any direction. Cars going S<->N were blocking and blocked by cars traveling W<->E, and cars traveling W<->E were at the same time blocking and blocked the first, traveling S<->N.
I saw at the time that was completely impossible for any driver to do anything useful as an individual, in order to travel along the wanted direction without taking any decision that would had a completely disastrous consequence for the cars going along other directions.
I guess it is sad to admit that the same problem is probably repeated every single day at exactly the same time, so an efficient solution to this apparently simple but common street configuration could have valuable impact for solving transport problems in crowded cities.