On the steady-state distribution of number in the queue Geom/G/1

Discrete-time queues are frequently used in telecommunication networks. Thi s paper proposes a new method which is based only on probabilistic argument s. It derives the distributions of numbers of customers in the discrete-tim e systems Geom/G/1 and Geom/G/1/M. Though the derivation does not involve u se of the transforms, the transforms may be obtained, if desired. Another a dvantage of this is that the numerical results obtained are stable as there are no negative signs involved in summations. Further, the method can be e asily used to solve more complex problems in discrete- and continuous-time queues.