In the Suez Canal Problem we consider the real-world, multi-million dollar question of traffic flow through the Suez Canal.
The region of the Suez Canal available for ship passage is 160 NORTH Mediterranean Sea kilometers long, 169 meters wide, and 21 meters deep. The number Port Said of ships desiring passage through the canal is essentially the same in both directions in each 24-hour period. Since the shipping region is not wide enough to allow simultaneous travel in both directions, the ships must travel in convoys either North-South or South-North.
As shown in the figure to the left, the only positions along the canal which allow for ships to pass are at the Ballah Bypass and the Bitter Lakes. The Ballah Bypass is 10 kilometers in length, stretching Ballah Bypass Capacity: 17 ships from the 50 to 60 kilometer mark south of Port Said. The Bitter Lakes extend for 20 kilometers, from 100 to 120 kilometers south of Port Said. In order for ships to pass, one convoy must pull to the side and dock at floating moorings. The movement of ships in the opposite direction makes unmoored ships too unstable and likely to run aground. Unfortunately, the Ballah Bypass has room for only 17 ships to moor. The Bitter Lakes can accommodate up to 36 ships at a time. Traditionally, the convoy which moves South to North (SN) Bitter Lakes never stops. The Convoys which move North to South (NS) pull aside Capacity: 36 ships at the Ballah Bypass and the Bitter Lakes to allow the convoy moving SN to pass. The timing is important, so that the convoys will meet each other at the proper places.
The average speed of ships traversing the canal is 14km/hr with a 10-minute separation between ships. The schedule for canal passage must repeat every 24 hours.
Determine the maximum number of ships that can traverse the SOUTH Red Sea canal on a 24-hour schedule traveling at an average speed of Port Tewfik 14km/h with a separation time of 10 minutes.
Generalize your model. Determine the maximum number of ships that can traverse the canal on a 24-hour schedule traveling at an average speed of S with a separation time of T.
If the Ballah bypass could be lengthened to hold more ships, how much would this affect the capacity of the canal? Would it be better to enlarge the Bitter Lakes.