Bayesian estimation of finite buffer size in single server Markovian queuing system

For operating any new finite capacity (say K) queuing system in which customers arrive according to a Poisson process and are served by a single server under exponential service time (in Kendall’s notation M/M/1/K system), the assumption of fixing K and estimating the parameter traffic intensity \(\rho\) $\rho$ , is quite practical. But in situation of any pre-existing M/M/1/K queuing system, it is essential to determine an estimator of K to increase system efficiency for fixed value of \(\rho\) $\rho$ . This paper therefore considered the problem of estimating the parameter finite buffer (K). A Bayes estimator of K is proposed and compared it with classical estimator based on maximum likelihood principal, under the assumption that \(\rho\) $\rho$ is known. A simulation study is carried out to establish the efficacy and effectiveness of the proposed approaches. A real life situation is analyzed to illustrate the applicability of the developed algorithms.