Computing waiting-time probabilities in the discrete-time queue: GIX/G/1

In this paper, we consider the discrete-time bulk-arrival GIX/G/1 queue and propose a simple procedure for computing waiting-time probabilities of the first and the random customers. As can be seen from our analysis that even analytic procedure is simpler than the one discussed by Murata and Miyahara [Perf. Eval. 13 (1991) 87]. Further, the procedure discussed here works for both finite and specialized infinite support interarrival-/service-time distributions such as geometric and negative binomial.