bayesian‎, ‎e-bayesian and hierarchical bayesian estimations for optimization of traffic intensity in the m/m/m/k queue based on fuzzy index

This paper focuses on the m/m/m/k queuing model‎, ‎where inter-arrival and service times follow exponential distributions‎. ‎we discuss the fuzzy average degree of customer satisfaction and evaluate traffic intensity based on a fuzzy index‎, ‎using bayesian‎, ‎e-bayesian‎, ‎and hierarchical bayesian methods‎, ‎applying the general entropy loss function‎. ‎additionally‎, ‎the maximum likelihood estimation method is utilized for estimation‎. ‎to compare the performances of the proposed estimation methods‎, ‎a monte carlo simulation is conducted‎. ‎evaluation criteria‎, ‎such as the cost function and the average customer satisfaction index‎, ‎are used to select the most appropriate estimation method for the present paper‎. ‎finally‎, ‎a numerical example is provided to determine the most suitable estimator‎.