Specific cost ratio in a port modelling by M/Ek/1 queue

Abstract

The notion of specific cost ratio involves different type of costs of a ship and a port modeled as a queueing system. Using the known general formula for the specific cost ratio of arbitrary port queueing system (denoted as R), here we derive the related expression for R of the M/Ek/1 queue, where Ek (k = 2,3,...) is the Erlang- k probability distribution. This expression allows us to obtain a theoretical result which can be applied for determining the optimal values of shape parameter k of Ek under given constraints on other performances of the considered port queueing system. The related numerical and the graphical results are also presented. The obtained results would be a useful tool in future research in related subject areas.

Keywords

• port
• m/ek/1 queue
• erlang- k distribution
• specific cost ratio
• traffic intensity