We consider stationary discrete-time single-server
queues fed by independent heterogeneous Markovian sources
with geometrically distributed idle periods. While being
active, each source generates some cells depending on
the state of the underlying Markov chain. The purpose
of this paper is twofold. One is the derivation of the
explicit formula for the mean buffer contents when the
underlying Markov chain of each source has finite state
space. The other is the derivation of the explicit
formula for the mean buffer contents in a queue fed by
Markovian autoregressive sources, each of which is
characterized completely by the marginal distribution
of cells arriving in a slot and its correlation
coefficients.