New Queuing Theory Applied to Port Terminals and Proposal for Practical Application in Container and Bulk Terminals

Abstract

Queueing theory has been used in port management since the early 60s as a support, among others, to determine the optimal number of berths based on the occupation rate of the berths and the expected waiting time for vessels operating in them. Depending on the type of terminal involved, different authors have provided solutions for various Ek/Ek/n systems. While the equations characterizing some of these systems can be analytically resolved, and it is possible to calculate exact solutions for them, other systems are not resolvable, and only approximate solutions are presented in the form of graphs or tables. In the present work, a simple analytical methodological scheme is presented for one of these systems with approximate solutions (M/D/n) deduced from a system in which the exact analytical solutions exist (M/M/n). This new approach is proposed to be used in private container terminals without regular services and in bulk terminals in which quasi-constant size vessels arrive.