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

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