Change point problem for Markovian arrival queueing models: Bayes factor approach

This paper considers two Markovian arrival single server queueing models, namely M/M/1 and M/E-r/1. Under the steady state condition, we observe the number of customer present at different time points for the M/M/1 queue while in case of an M/E-r/1 queue we consider the number of arrivals during the service time of a customer. A Bayesian approach is applied to study the change point problems. Testing of hypothesis for change versus no-change is carried out using predictive distributions. Further, Bayes factors are derived for change versus no-change for both the M/M/1 and M/E-r/1 queueing models under natural conjugate beta prior distribution. At last, numerical results are provided for the illustration.