Single server queueing model with Gumbel distribution using Bayesian approach

Bayesian methodology is an important technique in statistics, and especially in mathematical statistics. It consists of the sample information along with the prior information available about the parameter before the sample has been observed. This paper exhibits the estimation of the parameters of queueing model with inter-arrival time and service time which follows Gumbel distribution. Bayesian procedure is applied to obtain the estimation of the model parameters and the traffic intensity of queueing model based on the informative and the non-informative prior knowledges. In this paper, the Bayesian estimates are carried out by numerically and graphically with the help of Markov Chain Monte Carlo (MCMC) simulation technique, particularly in Gibbs sampling algorithm.