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

摘要

A stationary M /M/1 queueing model satisfies the equilibrium condition that the arrival rate, lambda is less than or equal to the service rate, mu. In this paper, we have discussed the Bayes estimation of queue parameters lambda, mu and various queue characteristics using Mckay's bivariate gamma prior distribution for (lambda, mu) for a stationary M /M /1 queue as it satisfies the equilibrium order restriction, 0 < lambda < mu. 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.