Development of an adjustable step toll scheme in compliance with expected effects of queuing reduction for the Suez Canal

Abstract

The widening and deepening of the Suez Canal were completed in 2016, and this enabled most large-sized ships to cross the canal. Because the demand for the canal has continued to increase, the queuing problem at the entrance of the canal would be anticipated to be more serious. In the existing literature, an optimal time-varying toll scheme has been established for the Suez Canal to eliminate the queuing phenomenon that many ships wait in line for entry into the canal. However, this toll scheme might be difficult to implement because the toll rate continuously changes according to the arrival time of the ship. To find an alternative, we calculate all possible combinations of the area ratios of the optimal time-varying toll triangle to its inscribed step toll rectangles to develop an adjustable step toll scheme. The developed toll scheme could achieve all expected effects of queuing reduction that could not be accomplished by other toll schemes in the existing literature. Moreover, the regularities in values of toll amounts and the start and end charging times that we have presented under the adjustable n-step toll scheme (n = 1,2,3, ...) could be conducive to the implementation of the electronic toll collection system. Finally, we simulate the implementation of the adjustable step toll scheme for the Suez Canal and provide practical suggestions for the canal authorities.