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. 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.
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