Abstract The stationary distribution is the key of any queueing system; its determination is sufficient to infer the corresponding characteristics. This paper deals with the Er / M / 1 {\mathrm{Er}/M/1} queue. Bayesian inference is developed to estimate the system parameters, specially the root of the relative equation which allows the determination of the stationary distribution. A numerical study is performed with MCMC methods to support the results, and a comparison with another existing method in the literature (moments method) is provided.