Determinação de momentos do estimador de máxima verossimilhança para filas Erlang e filas markovianas de servidor único

Abstract

Queueing Theory is a research area that studies systems where customers must wait in order to be served. Among the traditional queueing models, the M/M/1 queues and their generalization, the M/Er/1 queues, are relevant. A problem of interest in these models is to estimate the traffic intensity, which represents the proportion of time on which customers are being served. This thesis analyzed the central moments (mean and variance) of the maximum likelihood estimator (MLE) of traffic intensity for M/M/1 and M/Er/1 queues. This analysis is valid for both small and large samples, representing an improvement over the asymptotic results present in the literature, which are not valid for small samples. Monte Carlo simulations were used to confirm the accuracy of the obtained analytical expressions. It was observed that the MLE of traffic intensity is biased, especially for small samples and heavily loaded systems. This behavior was not predicted by the asymptotic expressions. Finally, it was noted the efficiency of the developed analytical expression, compared to the numerical simulations that would be required to approximate the central moments of the MLE.