In many everyday situations in which a queue is formed, queueing models may play a key role. By using such models, which are idealizations of reality, accurate performance measures can be determined, such as traffic intensity (ρ), which is defined as the ratio between the arrival rate and the service rate. An intermediate step in the process includes the statistical estimation of the parameters of the proper model. In this study, we are interested in investigating the finite-sample behavior of some well-known methods for the estimation of ρ for single-server finite Markovian queues or, in Kendall notation, M/M/1/K queues, namely, the maximum likelihood estimator, Bayesian methods, and bootstrap corrections. We performed extensive simulations to verify the quality of the estimators for samples up to 200. The computational results show that accurate estimates in terms of the lowest mean squared errors can be obtained for a broad range of values in the parametric space by using the Jeffreys’ prior. A numerical example is analyzed in detail, the limitations of the results are discussed, and notable topics to be further developed in this research area are presented.

Dealing with uncertain data requires effective methods to properly describe their real meaning in terms of a trade-off between interpretability and generality on the process of knowledge formation based on data abstraction. This paper proposes an online granulation process based on Evolving Ellipsoidal Fuzzy Information Granules (EEFIG) and the Principle of Justifiable Granularity (PJG) for data streams parameterization. The granulation process consists in the information granule development taking into consideration the data stream with a simplified optimal granularity allocation. In the sequel, an evolving Takagi-Sugeno fuzzy model based on the ellipsoidal granules is proposed for data reconstruction and one-step ahead prediction from past data numerical evidence. Experimental studies concerning clustering, data granulation, and time-series forecasting are performed to illustrate the effectiveness of the proposed method.