Enhancing ship arrival time adjustments in the anchorage area of the Suez Canal through optimal step tolling strategies

An optimal n-step toll scheme (n = 1, 2, 3, …) has been developed to alleviate the queuing of ships waiting to enter the Suez Canal. However, current literature has not explored how tolled ships adjust their pre-toll anchorage arrival times to maintain the same equilibrium costs as they were in the pre-toll situation. To address this gap, this paper derives a series of formulas using the point slope form, depicting how tolled ships will modify their pre-toll anchorage arrival times. It is noteworthy that with a doubling of the step toll amount, the delay duration of the anchorage arrival times for early arriving tolled ships compared to their pre-toll anchorage arrival times also doubles. Conversely, with a halving of the step toll amount, the delay duration of the anchorage arrival times for late arriving tolled ships compared to their pre-toll anchorage arrival times also halves.