As the insufficiency of watercourses and the limitation of breadth are leading to long queues at Panama Canal, the plan of canal expansion is undertaken by the authorities to increase the service capacity. In order to avoid ships queuing at the entrance of the canal, this research establishes an...

Compared with the liner container ships, the tramp bulk carriers often have to queue for vacant berths at a busy port. In order to solve this problem, this paper develops the optimal n-step toll schemes (n=1, 2, 3, …) to bulk carriers in a queue for multiple berths. Bulk carriers' queuing...