<p>Performance measures are of general interest in evaluating the performance of any queuing system. They are particularly useful in effecting design improvements. A queuing analyst often finds it difficult to estimate the performance measures of an operational queuing system because of the lack of properly designed inferential procedures. A very popular approach to obtain estimators of performance measures is the plug-in estimator, also known as substitution estimator. In this context, Zheng and Seila (Oper Res Lett 26(5):231–235, 2000) have flagged issues relating to the use of substitution estimators. In particular, they have shown that in case of the M/M/1 model, the mean square errors (MSE) do not exist. They have therefore proposed alternative estimators of performance measures that are better behaved. Taking a cue out of Zheng and Seila (Oper Res Lett 26(5):231–235, 2000), we present substitution and alternative estimators of various performance measures of M/M/c/c model. This model has wide application in hospital emergency rooms with limited beds, taxi stands with limited bays, and telephone lines with fixed numbers of channels. The performances of the estimators are compared through a variety of error measures. It is shown that alternative estimators perform better than substitution estimators when judged from the perspective of a range of error metrics. Additionally, the paper proposes a guideline for using the alternative estimators. Simulation results are presented.</p>