Estimation of parameters of a single server discrete-time batch-service queue with variable service capacity

This article deals with the statistical perspective of a discrete-time batch-service queue as such systems possess relevant applications in Broadband Integrated Services Digital Networks (B-ISDN), circuit-switched time-division multiple access (TDMA) systems and IEEE 802.11n WLANs. In particular, three distinct estimation approaches, such as maximum likelihood estimation, uniformly minimum variance unbiased estimation, method of median, and Bayesian estimation for traffic intensity and average queue length have been incorporated. We also include an influence function corresponding to the sensitivity analysis of MLE. In the Bayesian framework, we evoke prior distributions as beta, incomplete inverted beta and uniform distributions in which two loss functions are also considered. In addition, we derive the predictive distribution for the model, which can be employed to forecast the number of customers in the queue. A credible interval for traffic intensity is also provided to offer insights into the uncertainty associated with the estimates. We also provide the detailed algorithm to carry out numerical results through simulations which include a real data application. Moreover, we incorporate the Markov Chain Monte Carlo method as well as a robust estimation technique.