First-passage-time and busy-period distributions of discrete-time Markovian queues:Geom(n)/Geom(n)/1/N

This paper gives simple explicit solutions of various first-passage-time distributions for a general class of discrete-time queueing models under arbitrary initial conditions, state-dependent transition probabilities and the finite waiting room. Explicit closed form expressions are obtained in terms of roots. These expressions are then used to get numerical as well as graphical results. Explicit closed-form expressions are also deduced for the continuous-time models including the busy-period distributions. The analysis is then extended to cover the case of two absorbing states.