The Productivity of Multipurpose Seaport Terminals

This paper studies the peculiar queueing problem that arises at multipurpose port terminals serving two traffic types. Primary (liner ship) traffic obeys a schedule and has absolute priority on the use of the multipurpose facilities. Secondary (tramp) traffic, which arrives at random, can also be served elsewhere in the port. Secondary traffic is routed to the multipurpose berths only if doing so does not delay any primary ship. (The port knows a fair amount ahead of time the arrival times of these ships and the likely service times of both liners and tramps). The goal is to obtain simple analytical formulas for the multipurpose terminal's productivity, and for the resulting changes in berth utilization outside the terminal. Although the suggested strategy for routing secondary traffic leads to a queueing problem that is too complicated to yield a simple exact formula, an approximate solution for heavy tramp traffic was found. An exact numerical solution for arbitrary traffic levels, which only applies when liner operations are perfectly regular and deterministic, was also found. In this latter case, because the solution could be expressed as a function of only two parameters, it was possible to present it in graphical form and to obtain a simple analytical expression fitting the graphs.