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

Abstract

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

Performance analysis of an infinite-buffer batch-size-dependent bulk service queue with server breakdown and multiple vacation

“…Utilizing both embedded Markov chain technique (EMCT) and SVT, Samanta et al [37] have discussed a discrete-time group-arrival queue with single as well as multiple vacation(s) where service is provided in accordance with (a, b) rule. Using RG -factorization for the Toeplitz type blockstructured Markov chain, Samanta and Nandi [40] have analyzed an infinite-buffer group-arrival queue where arrival occurs according to a discrete-time renewal process. The server content distribution, a key ingredient from designing perspective, was lacking in all the papers.…”