Bayesian inference on M/M/1 queue under asymmetric loss function using Markov Chain Monte Carlo method

Abstract

A stationary M/M/1 queueing model satisfies the equilibrium condition that the arrival rate, λ is less than or equal to the service rate, µ. In this paper, we have discussed the Bayes estimation of queue parameters λ, µ and various queue characteristics using Mckay’s bivariate gamma prior distribution for (λ, µ) for a stationary M/M/1 queue as it satisfies the equilibrium order restriction, 0 < λ < µ. Using Markov Chain Monte Carlo method, we have numerically computed the Bayes estimates of queue parameters and various queue characteristics under different asymmetric loss functions.