Ml. Chaudhry et al., Modeling and analysis of discrete-time multiserver queues with batch arrivals: GI(X)/Geom/m, INFORMS J C, 13(3), 2001, pp. 172-180
Multiserver queues are often encountered in telecommunication systems and h
ave special importance in the design of ATM networks. This paper analyzes a
discrete-time multiserver queueing system with batch arrivals in which the
interbatch and service times are, respectively, arbitrarily and geometrica
lly distributed. Using supplementary-variable and embedded-Markov-chain tec
hniques, 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 prearriva
l, arbitrary, and outside observer's observation epochs, the numerical eval
uation of state probabilities is also discussed. It is also shown that, in
the limiting case, the relations developed here tend to continuous-time cou
nterparts. Further, the waiting-time distribution of a random customer of a
batch is obtained. Finally, in some cases simulation experiments have been
performed to validate our results.