Bayesian Estimation of M/Ek/1 Queueing Model using Bivariate Prior

Abstract

This article describes Bayes estimation of various queue characteristics such as queue parameters λ and μ, and queue performance measures like traffic intensity, expected waiting time in the queue, and expected queue size of $M/E_k/1$ model using Mckay’s bivariate gamma distribution as prior under squared error loss function as well as entropy loss function. Closed form expressions are obtained for the Bayes estimators of the queue parameters and various queue performance measures using the properties of confluent hyper geometric function and Gauss hyper geometric function. Bootstrap Bayes estimates and credible regions are computed using simulated data for different set of hyper parameter values. Also we apply Markov Chain Monte Carlo method and compute Bayes estimates and credible intervals of various queue characteristics using the same joint prior distribution and compare the values with bootstrap estimates.

KEYWORDS AND PHRASES:

• Bayes estimate
• M/E_k/1 queueing model
• McKay’s bivariate gamma distribution
• confluent hyper geometric function
• Gauss hyper geometric function
• Markov Chain Monte Carlo method