According to Paxson & Floyd[8], the regular assumption of the exponential times of the inter-arrival time and service time are vanished when heavy tailed scenaro. Consider the single server queue with multiple working vacation and the regular service time which follows Gumbel distribution. This paper exhibits the estimation of the parameters of queueing model under Bayesian procedure based on gibbs sampling algorithm through Markov Chain Monte Carlo(MCMC) technique. The performances of the empirical estimates of the model parameters and traffic intensity are discussed.

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 tra c 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.

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