Abstract
This paper develops the optimal non-queuing toll and optimal step toll schemes to container ships in a queue for multiple berths at a busy port. Container ships' queuing times at the anchorage will be decreased to half of the total queuing time after pricing the optimal step toll scheme. Furthermore, container ships' arrival time change decisions from the non-toll to the optimal step toll cases can be predicted before tolling a busy port. The above outcomes are helpful if the pricing policy to a queue of container ships at the anchorage is considered by the port authorities.
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