Complete analysis of \(M/G_r^{(a,b)}/1/N\) queue with second optional service (Q6657855)

The paper under review studies a finite buffer queueing system with group size depending bulk service queue and single server. The server renders two types of services, the first service is essential service (FES) and the second one is optional service (SoS). Customers arrive in the system according to Poisson input. A service is rendered by the server by groups following the `general bulk service' rule on first come first serve basis for FES. In this article, a part of a group is allowed to be served in FES and join SoS by a group following binomial law. The service time distribution is assumed to be generally distributed and dependent on the group size under service for both of the cases FES and SoS. The study is based on the supplementary variable technique and the embedded Markov chain technique to obtain the steady state, departure epoch and arbitrary epoch joint distributions for the number of customers in the queue and with the server states both in FES and SoS. The numerical study demonstrates the performance of the key efficiency metrics.