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 queuing 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 queuing model, characterized by c 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.