Effects of the optimal port queuing pricing on arrival decisions for container ships

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' arrival times at the port will be dispersed, and the queuing situation can be decreased. In this article, an optimal step toll scheme by cost equilibrium approach is designed, and all values of equilibrium queuing cost and operating cost under the scheme are obtained. According to equilibrium results in this study, we show container ships that pay the toll to berth a queuing port are those altered their original arrival times at the port before the toll established. In addition, those ships' arrival time adjusting decisions from the nontoll to the optimal step toll cases can be well investigated before tolling a queuing port.