Abstract
A maximum likelihood estimator (MLE), a consistent asymptotically normal (CAN) estimator and asymptotic confidence limits for the expected waiting time per customer in the queues of M |M |1|∞ and M |M |1|N are obtained.
Highlights
Parametric estimation is one of the essential tools to understand the random phenomena when using stochastic models
Whenever the systems are fully observable in terms of their basic random components such as inter-arrival times and service times, standard parametric estimation techniques of statistical theory are quite appropriate
Model I (M |M |1) : (F CF S|∞|∞) queue It can be readily seen [1] that the difference-differential equations governing M |M |1 are given by p′n(t) = λpn−1(t) − (λ + μ)pn(t) + μpn+1(t), n = 1, 2, 3
Summary
Parametric estimation is one of the essential tools to understand the random phenomena when using stochastic models. Whenever the systems are fully observable in terms of their basic random components such as inter-arrival times and service times, standard parametric estimation techniques of statistical theory are quite appropriate. Bhat (2003) has provided an overview of methods available for estimation, when the information is restricted to the number of customers in the system at some discrete points in time. The MLE, CAN and asymptotic confidence limits for the expected waiting time per customer in the queues of M |M |1|∞ and M |M |1|N , are obtained in this paper. These two models and the expected waiting time per customer for each model are explained briefly
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