Classical and Bayes Estimation of Modified Traffic Intensity of a Queueing System with Balking

November 25, 2017 Posted by admin

V.S.S.Yadavalli, V.S.Vaidyanathan and P. Chandrasekhar
Department of Industrial and Systems Engineering, University of Pretoria, Pretoria 0002, South Africa
Department of Statistics, Pondicherry University, Puducherry – 605 014, India
Department of Statistics, Loyola College, Chennai-600 034, India

(Received 23 January 2017; received in revised form 6 May 2017; accepted 8 June 2017)

Abstract
By considering a Markovian queueing model with balking, the maximum likelihood and consistent estimators of modified traffic intensity are obtained based on the number of entities present at several sampled time points. Uniform minimum variance unbiased estimator (UMVUE), consistent asymptotically normal (CAN) estimator and an asymptotic confidence interval for the expected number of entities in the system are obtained. Further, Bayes estimators of modified traffic intensity, measures of system performance, minimum posterior risk and minimum Bayes risk associated with these estimators are also derived. The behavior of maximum likelihood and Bayes estimators of modified traffic intensity is illustrated through simulation study. The results obtained from the simulation study show that as the number of sampled time points increases, the expected value of the MLE of modified traffic intensity approaches its true value. The minimum Bayes risk of the estimator of modified traffic intensity also decreases.

Keywords: Bayes estimator, consistent estimator, Markovian queue, maximum likelihood estimator, multivariate central limit theorem, Slutsky theorem.

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