Bayesian queue modelling with likelihood binomial negative and uniform discrete

Abstract

Queues often occur in everyday life, including the queue for booking train tickets. Queue analysis has the benefit of analyzing whether a service is optimal or not. Long queues will certainly cause disappointment for prospective passengers booking train tickets. Meanwhile, many unemployed services cause losses in the provision of facilities. Queue analysis tests the distribution of the number of arrivals and the number of services following the Poisson or exponential distribution. Often the assumption test does not follow this distribution and is therefore considered a General distribution. In this study, the queue at the Tawang railway station in Semarang, Indonesia, service counter was modeled by looking for a general distribution using a Bayesian approach. The results are the likelihood distribution of the number of arrivals with a Uniform and Binomial Negative distribution. Besides, the likelihood distribution for the services has a uniform distribution. The prior used is the Poisson distribution with Jeffrey’s approach. The resulting Posterior Distributions are Beta Distribution and Uniform Distribution. This shows that even though using a Bayesian approach, the resulting distribution is still General. The queue model for arrivals and services number is (G/G/2):(GD/∞/∞).