Queuing Pricings to Bulk Carriers at the Anchorage

Abstract

This paper presents a study that develops the optimal step toll scheme to bulk carriers queuing for vacant berths at a busy port. Port arrival times of bulk carriers were rationally dispersed with this toll pricing scheme, consequently decreasing queuing time of all bulk carriers at the anchorage. This paper shows all arrived bulk carriers' equilibrium queuing costs, and equilibrium derivative costs due to queuing under the optimal step toll scheme. Based on the invariant equilibrium derivative cost principle, this paper provides a framework to predict bulk carrier owners' decisions of arrival time changes from the non-toll equilibrium to the optimal step toll scheme cases.