Multiserver bulk service discrete-time queue with finite buffer and renewal input

This paper analyzes a discrete-time finite-buffer multi-server bulk-service queueing system in which the interarrival- and service-times are, respectively, arbitrarily and geometrically distributed. Using the supplementary variable and the imbedded Markov-chain techniques, the queue is analyzed for the early arrival system. We obtain state probabilities at prearrival, arbitrary and outside observer’s observation epochs. Some performance measures, waiting-time distribution in the queue along with some numerical results, and special cases of the model have also been discussed. Finally, it is shown that in the limiting case the results obtained in this paper tend to the continuous-time counterpart.