Bayesian inference of a queueing system with short- or long-tailed distributions based on Hamiltonian Monte Carlo

Abstract

In this paper, we deal with a Bayesian inference method for estimating the parameters of the queueing system with short- or long-tailed distributions based on the No-U-Turn Sampler (NUTS), a recently developed Hamilton Monte Carlo (HMC). We assume inter-arrival and service times to be either the short-tailed distributions or the long-tailed distributions since they are a better fit for real-world data. We illustrate our assumption using a number of simulated data sets, generated from distributions covering a wide range of cases. Then we estimate the parameters using the Bayesian approach based on No-U-Turn Sampler. As a result of comparing the No-U-Turn Sampler with the Gibbs sampler, the most common MCMC algorithm, we demonstrate that the NUTS outperforms Gibbs sampler for estimating parameters, which is especially significant for long-tailed distribution. We also investigate the influence of the size of observation data and the prior distributions on estimating these parameters.