Bayesian queueing model with multiple working vacations under Gumbel distribution

Abstract

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.

Single server queueing model with Gumbel distribution using Bayesian approach

“…From the outputs of OpenBugs, the diagnostic checking plots for each model parameters are presented in Appendix. The Markov chain has converged in both informative and non-informative priors since it likely to be sampling from the stationary distribution and horizontal band, with no long upward or downward trends as shown in Figure [15,16,17,18]. Moreover, the autocorrelation is almost negligible for all the model parameters (see Figure [19,20,21,22]).…”

“…The evaluation of M/G/1 queueing model with the service time as assumed to Gumbel distribution, which has been explained by numerically and graphically based on the various combinations of the arbitrary values [20]. The extended queueing model when service time distributed according to Gumbel distribution under multiple working vacations scenario and the model parameters has been estimated based on Bayesian approaches with Gibbs sampling algorithm through Markov Chain Monte Carlo (MCMC) technique [18]. This article introduces tele-trac and insurance data and some of the unusual characteristics of these types of data which motivate some of the inter-arrival and service time model that are analyzed through heavy tailed nature, particularly in Gumbel distribution.…”