Performance analysis of a GI [ X ] / Geo / m / N queue with partial- and total-batch rejection
This paper analyzes a discrete-time multiserver finite-buffer queueing system with batch renewal arrivals in which inter-batch time of batches and service times of customers are, respectively, arbitrarily and geometrically distributed. Each customer gets service from only one server. Using the supplementary variable and the imbedded Markov chain techniques, we obtain the state probabilities at prearrival, arbitrary and outside observers observation epochs for partial- and total-batch rejection policies. The blocking probability of the first-, an arbitrary- and the last-customer in a batch, and other performance measures along with some numerical results have been discussed. The analysis of actual waiting-time distributions measured in slots of the first-, an arbitrary- and the last-customer in an accepted batch has also been investigated. Finally, it is shown that in the limiting case the results obtained in this paper tend to the continuous-time counterpart.
total-batch rejection discrete-time multiserver finite-buffer queue partial-batch rejection