Economics on the optimal port queuing pricing to bulk ships

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 decreased. This article shows bulk ships' equilibrium arrival rate distributions during the queuing period before and after establishing the optimal single step toll scheme. This article also shows bulk ship owners' decisions of arrival time adjustments under the optimal single step toll scheme. Based on these results, we find some bulk ships that paid no toll under the optimal single step toll scheme to maintain the same arrival times at the anchorage as they did in the original nontoll equilibrium situation. New arrival times at the anchorage for other bulk ships that paid the toll are postponed when compared with their original arrival times in the nontoll equilibrium situation.