Bayesian‎, ‎E-Bayesian and hierarchical Bayesian estimations for optimization of traffic intensity in the M/M/m/K queue based on fuzzy index

Document Type : Original Scientific Paper

Authors

Department of Statistics‎, ‎Payame Noor University‎, ‎Tehran‎, ‎Iran

Abstract

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.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 5, Issue 2
July 2024
Pages 197-212

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History

  • Receive Date: 15 March 2025
  • Revise Date: 08 September 2025
  • Accept Date: 15 September 2025

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