Journal of Quality Engineering and Management

Abstract 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.

Abstract Purpose: This study aims to determine the optimal model within the family of queueing models, where interarrival times follow an exponential distribution and service times follow an Erlang distribution, under a finite stopping time TTT. The significance of this research lies in its application to optimizing the performance of service systems using queueing theory.
Methodology: To select the optimal model, a cost function and a performance metric, namely the average customer satisfaction level, are first defined. Subsequently, a new index, named ORS, is introduced based on the cost function, average customer satisfaction, and the system's stability probability. The optimal model is identified as the one with the highest ORS value. Numerical analysis is employed to demonstrate the procedure for determining the optimal model.
Findings: The numerical results indicate that the ORS index is an effective criterion for evaluating and comparing different queueing models, enabling optimal model selection by incorporating multiple performance aspects.
Originality/Value: The main contribution of this research is the introduction of the ORS index as a novel and comprehensive measure for optimal model selection in queueing systems. This approach can enhance service system design and improve customer satisfaction levels in practical applications.

Abstract In this article, a queuing system with finite capacity, referred to as M/M/m/K, is analyzed for m ≥ 2, where K represents the system's capacity and m indicates the number of servers. Initially, a function known as the system cost function is introduced. This function is based on the number of customers present in the queue and the number of servers available. The main objective is to identify the optimal number of servers, termed mOpt, that minimizes the system cost function. This optimal configuration, denoted as M/M/mOpt/K, is termed the optimal system. To illustrate the concept, a numerical example is provided, showcasing various values of K to determine the optimal systems. The analysis covers key performance metrics such as the average number of customers in the queue and the entire system, the average waiting time of the customers both in the queue and the system, and a metric referred to as the average degree of customer satisfaction within these queuing systems. Through this comprehensive approach, the study aims to provide valuable insights into optimizing queuing systems for better efficiency and customer satisfaction.