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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.

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