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A discrete-time batch service queue with batch renewal input and randomserving capacity rule under the late arrival delayed access system (LAS-DA),has recently appeared in the literature [2]. In this paper, we consider thesame model under the early arrival system (EAS), since it is more applicable intelecommunication systems where an arriving batch of packets needs to betransmitted in the same slot in which it has arrived. In doing so, we derivethe steady-state queue length distributions at various epochs and show that inlimiting case the result gets converted to the continuous-time queue [1]. Wediscuss a few numerical results as well.

A discrete-time GI^X/Geo^Y/1 queue with early arrival system