Modeling and analysis of discrete-time multiserver queues with batch arrivals: GIx/Geom/m

Multiserver queues are often encountered in telecommunication systems and have special importance in the design of asynchronous transfer mode networks. This paper analyzes a discrete-time multiserver queueing system with batch arrivals in which the interbatch and service times are, respectively, arbitrary and geometrically distributed. Using supplementary-variable and embedded-Markov-chain techniques, the queue is analyzed only for the early arrival system. Since the late arrival system can be discussed similarly, it is not considered here. In addition to developing relations among state probabilities at prearrival, arbitrary, and outside observer's observation epochs, the numerical evaluation of state probabilities is also discussed. It is also shown that, in the limiting case, the relations developed here tend to continuous-time counterparts. Further, the waiting-time distribution of a a random customer of a batch is obtained. Finally, in some cases simulation experiments have been performed to validate our results.