Specific Cost Ratio In A Port Modelling By M/E-K/1 Queue

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/E-k/1 queue, where E-k (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 E-k 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.