This thesis gives simple explicit solutions of idle and busy period distributions for discrete-time queueing models with Bernoulli arrivals, geometrically distributed service times and finite waiting room. In this paper, the old definition of idle and busy period is replaced with the new one, which well represents the characteristics of discrete-time queue. The analysis of busy period is based on the absorbing Markov chain approach. This approach is useful in obtaining the probability generating function of busy period as the solution of first-passage-time from busy to idle states. The P.G.F. obtained can be easily inverted to the convolution form of geometric distributions.
The explicit solutions in this paper are focused on the queues that have a jump in state transition, especially on multi-server queues and bulk service queues. Applications for these queues and simple numerical examples are provided in the last section.
