Bayesian inference on M/M/1 queue under asymmetric loss function using Markov Chain Monte Carlo method. Issue 5 (4th July 2021)

• Record Type: Journal Article
• Authors: Deepthi, V.; Jose, Joby K.
• Is Part Of: Journal of statistics & management systems. Volume 24:Issue 5(2021)
• Page Start: 1003
• Page End: 1023
• Publication Date: 2021-07-04
• Subjects: Primary 62M05 -- Secondary 62F15; M/M/1 queue -- Mckay's bivariate gamma distribution -- Entropy loss function -- Linex loss function -- Markov Chain Monte Carlo method; Statistics -- Periodicals; Mathematical models -- Periodicals; Mathematical models; Statistics; Periodicals; 519.5
• DOI: 10.1080/09720510.2020.1794529
• Languages: English
• ISSNs: 0972-0510

Abstract

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.