In this thesis, we focus on the sample size of two variants of the standard M/M/1 queueing model. The reason is that variants of the standard M/M/1 queueing model are extensively used in the real world. There are many fields in which queueing models can be utilized. In these applications, parameter plays an extremely important role. For example, the paper (Choudhury and Borthakur, 2008) studied inference for parameters of the M/M/1 queueing model. Therefore, in order to guarantee the precision of parameters estimated in these queueing models, the sample size determination is proposed in this thesis. Firstly, we show how a Bayesian approach could be applied to these models to obtain the minimal sample size required by the given precision. Then, we will illustrate in detail how to use R, a statistical software, to compute the sample size for these models.