In this paper, shrinkage and Bayesian shrinkage estimation of the expected length (l) in a M/M/1 queue system is considered. A shrinkage estimator of l is considered when a priori about l as l_0 is available. The bias and the risk of shrinkage estimators are derived under a scale-invariant squared error loss (SISEL) function. A class of Bayes shrinkage estimators for $l$ is proposed which is a generalization of Bayes shrinkage estimator and a relative performance of proposed estimators and the maximum likelihood estimator (MLE) is performed. A simulated data is given to illustrate the proposed results. Finally, we conclude with a summary of our contributions.
