When arriving at a busy port, a container ship usually need to queue in anchorage waiting for a berth. If the port establishes a toll scheme, the ship may rationally adjust sailing speed and time to save the cost, otherwise she has to pay for berthing on time. Consequently container ships'...

This article establishes a series of the optimal n-step toll schemes (where n = 1, 2, 3, …) which are levied to container ships for a queuing port. Container ships' arrival times at the port will be rationally dispersed after pricing the optimal n-step toll schemes. Consequently, the queuing...

This article develops the optimal single step toll scheme which is levied to bulk ships for a queuing port. Bulk ships' arrival times at the port will be rationally dispersed after pricing this toll scheme. Consequently, the queuing time at the anchorage to all bulk ships will be rationally...