Discrete-time queueing models find a large number of applications as they are used in modeling queueing
systems arising in digital platforms like telecommunication systems and computer networks. 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 epochs, where the first 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 some numerical examples.