  This paper considers a BMAP/M/$\infty$ queue with a batch Markovian arrival
process (BMAP) and an exponential service time distribution. We first prove
that the BMAP/M/$\infty$ queue is stable if and only if the expectation of the
logarithm of the batch-size distribution is finite. Using this result, we also
present the stability condition for an infinite-server queue with a multiclass
batch Markovian arrival process and class-dependent exponential service times.
