Morvarid Derakhshan Andisheh Journal of Quality Engineering and Management 3134-0849 16 1 2026 05 22 An improved E2-Bayesian estimator for the efficiency parameter of an infinite-capacity multi-server queueing system An improved E2-Bayesian estimator for the efficiency parameter of an infinite-capacity multi-server queueing system 1 14 236531 10.48313/jqem.2025.553995.1579 FA Shahram Yaghoobzadeh Shahrastani Department of Statistics, Payame Noor University, Tehran, Iran. 0000-0002-8794-2222 Iman Makhdoom Department of Statistics, Payame Noor University, Tehran, Iran. 0000-0002-2768-1024 Journal Article 2025 10 18 Purpose: The study aims to develop a new Bayesian estimation approach, termed the E2-Bayesian method, for estimating the traffic intensity parameter in the multi-server M/M/c/∞ queueing system. Given the crucial role of accurate efficiency estimation in optimizing service systems, this research addresses the need for more reliable inference under uncertainty. Methodology: The M/M/c/∞ queueing model, characterized by servers, exponential interarrival times with rate parameter λ, and exponential service times with rate parameter μ, is considered. The traffic intensity parameter is estimated using Bayesian, E-Bayesian, and the newly proposed E2-Bayesian methods under the general entropy loss function. The performance of the proposed estimator is assessed through Monte Carlo simulation and validated using a real dataset. Findings: Simulation results and empirical analysis demonstrate that the proposed E2-Bayesian estimator outperforms the traditional Bayesian and E-Bayesian estimators in terms of efficiency and accuracy. The estimator that minimizes the mean waiting time of customers in the queue is identified as the optimal choice. Originality/Value: This research introduces a novel E2-Bayesian estimation approach that enhances the precision of parameter estimation in queueing models under uncertainty. The integration of the general entropy loss function provides a flexible and robust framework, contributing to the advancement of Bayesian inference in stochastic systems. Purpose: The study aims to develop a new Bayesian estimation approach, termed the E2-Bayesian method, for estimating the traffic intensity parameter in the multi-server M/M/c/∞ queueing system. Given the crucial role of accurate efficiency estimation in optimizing service systems, this research addresses the need for more reliable inference under uncertainty. Methodology: The M/M/c/∞ queueing model, characterized by servers, exponential interarrival times with rate parameter λ, and exponential service times with rate parameter μ, is considered. The traffic intensity parameter is estimated using Bayesian, E-Bayesian, and the newly proposed E2-Bayesian methods under the general entropy loss function. The performance of the proposed estimator is assessed through Monte Carlo simulation and validated using a real dataset. Findings: Simulation results and empirical analysis demonstrate that the proposed E2-Bayesian estimator outperforms the traditional Bayesian and E-Bayesian estimators in terms of efficiency and accuracy. The estimator that minimizes the mean waiting time of customers in the queue is identified as the optimal choice. Originality/Value: This research introduces a novel E2-Bayesian estimation approach that enhances the precision of parameter estimation in queueing models under uncertainty. The integration of the general entropy loss function provides a flexible and robust framework, contributing to the advancement of Bayesian inference in stochastic systems.

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