Studying various models in queueing theory is essential for improving the efficiency of queueing systems. In this paper, from the family of models {E_r/M/c; r,c in N}, the E_r/M/3 model is introduced, and quantities such as the distribution of the number of customers in the system, the average number of customers in the queue and in the system, and the average waiting time in the queue and in the system for a single customer are obtained. Given the crucial role of the traffic intensity parameter in performance evaluation criteria of queueing systems, this parameter is estimated using Bayesian, E‑Bayesian, and hierarchical Bayesian methods under the general entropy loss function and based on the system’s stopping time. Furthermore, based on the E‑Bayesian estimator, a new estimator for the traffic intensity parameter is proposed, referred to in this paper as the E^2‑Bayesian estimator. Accordingly, among the Bayesian, E‑Bayesian, hierarchical Bayesian, and the new estimator, the one that minimizes the average waiting time in the customer queue is considered the optimal estimator for the traffic intensity parameter in this paper. Finally, through Monte Carlo simulation and using a real dataset, the superiority of the proposed estimator over the other mentioned estimators is demonstrated.

In this paper, a first-order integer-valued autoregressive process with non-negative integer values is introduced, based on the binomial thinning operator and driven by Poisson-Komal distributed noise. To estimate the parameters of the proposed model, two estimation methods are investigated: Conditional Maximum Likelihood Estimation and the Yule–Walker Method. Furthermore, the performance of these estimation techniques is evaluated through a simulation study. In addition, the practical applicability of the proposed model is demonstrated using two real-world datasets from the field of veterinary sciences.

In this paper, we present a comprehensive review and comparative analysis of estimation methods for periodic autoregressive (PAR) models driven by scale mixture of skew-normal (SMSN) innovations, a flexible class suitable for modeling both symmetric and asymmetric data. Expectation-conditional maximization algorithms are employed to develop maximum likelihood, maximum a posteriori, and Bayesian estimation procedures. A thorough evaluation of these methods is conducted using simulation studies, with particular attention to asymptotic properties and robustness against outliers, high peaks, and heavy tails. To demonstrate their practical utility, these methods are applied to monthly Google stock price data.