Analysis of $GI^{[X]}/D$-$MSP/1/\infty$ queue using $RG$-factorization

This paper analyzes an infinite-buffer single-server queueing system wherein customers arrive in batches of random size according to a discrete-time renewal process. The are served one at time under Markovian service Based on the censoring technique, UL-type \begin{document}$ RG $\end{document}-factorization for Toeplitz type block-structured Markov chain is used obtain prearrival epoch probabilities. probabilities obtained with help classical principle based theory. system-length distributions outside observer's, intermediate and post-departure epochs by making relations among various epochs. analysis waiting-time distribution measured slots arbitrary customer arrival batch has also been investigated. In order unify results both its continuous-time counterpart, we give brief demonstration get from those ones. A variety numerical provided illustrate effect model parameters performance measures.