A new optimum statistical estimation of the traffic intensity parameter for the M/M/۱/K queuing model based on fuzzy and non-fuzzy criteria

This article focuses on the M/M/ ۱ /K queuing model. In this model, the inter-arrival times ofcustomers to the system are random variables with an exponential distribution parameterized by λ , andthe service times of customers are random variables with an exponential distribution parameterized byµ . We aim to estimate the traffic intensity parameter of this model using Bayesian, E-Bayesian, andhierarchical Bayesian methods. These methods utilize the entropy loss function and an appropriate priordistribution for the independent parameters λ and µ . Additionally, we employ the shrinkage-basedmaximum likelihood estimation method to obtain the parameter estimates. To determine the desiredtraffic intensity parameter estimate, we introduce a decision criterion based on a cost function, anda fuzzy criterion called the Average Customer Satisfaction Index (ACSI). The goal is to select theestimation with a higher ACSI index. To facilitate understanding, we compare this estimation using theMonte Carlo simulation method and two numerical examples based on the ACSI index.

کلیدواژه ها:

M/M/۱/K queuing model ، traffic intensity parameter ، Cost Function ، ACSI