  Discrete-time queueing models find huge applications as they are used in
modeling queueing systems arising in digital platforms like telecommunication
systems, computer networks, etc. In this paper, we analyze an infinite-buffer
queueing model with discrete Markovian arrival process. The units on arrival
are served in batches by a single server according to the general bulk-service
rule, and the service time follows general distribution with service rate
depending on the size of the batch being served. We mathematically formulate
the model using the supplementary variable technique and obtain the vector
generating function at the departure epoch. The generating function is in turn
used to extract the joint distribution of queue and server content in terms of
the roots of the characteristic equation. Further, we develop the relationship
between the distribution at the departure epoch and the distribution at
arbitrary, pre-arrival and outside observer's epoch, which is used to obtain
the latter ones. We evaluate some essential performance measures of the system
and also discuss the computing process extensively which is demonstrated by a
few numerical examples.
