Bayesian methodology is an important technique in statistics, andespecially in mathematical statistics.It consists of the sampleinformation along with the prior information available about theparameter before the sample has been observed. This paper exhibitsthe estimation of the parameters of queueing model with inter-arrivaltime and service time which follows Gumbel distribution. Bayesianprocedure is applied to obtain the estimation of the model parametersand the trac intensity of queueing model based on the informativeand the non-informative prior knowledges. In this paper, the Bayesianestimates are carried out by numerically and graphically with thehelp of Markov Chain Monte Carlo (MCMC) simulation technique,particularly in Gibbs sampling algorithm.