Document Type : original

Author

• Iman Makhdoom

Payame Noor University

Abstract

This article focuses on the M/M/ 1 /K queuing model. In this model, the inter-arrival times of
customers to the system are random variables with an exponential distribution parameterized by λ , and
the service times of customers are random variables with an exponential distribution parameterized by
µ . We aim to estimate the traffic intensity parameter of this model using Bayesian, E-Bayesian, and
hierarchical Bayesian methods. These methods utilize the entropy loss function and an appropriate prior
distribution for the independent parameters λ and µ . Additionally, we employ the shrinkage-based
maximum likelihood estimation method to obtain the parameter estimates. To determine the desired
traffic intensity parameter estimate, we introduce a decision criterion based on a cost function, and
a fuzzy criterion called the Average Customer Satisfaction Index (ACSI). The goal is to select the
estimation with a higher ACSI index. To facilitate understanding, we compare this estimation using the
Monte Carlo simulation method and two numerical examples based on the ACSI index.

Keywords

• M/M/1/K queuing model
• traffic intensity parameter
• cost function
• ACSI

Main Subjects

• Bayesian Computation Statistics