Consider a batch Markovian arrival process (BMAP) as a counting process ove
r an underlying Markov process representing the state of environment. Such
a process is useful as a model of correlated inputs, that is, burst traffic
s made of video and voice, for example. We consider Laplace transformation
of the first and second factorial moments of the counts of the BMAP. From t
his, we get the eigenvalue expression for these moments without assuming di
stinct eigenvalues of the infinitesimal generator. In this formula, matrix
exponential functions are replaced by ordinary exponentials, and the exact
time-dependent form of the moments are also obtained. This seems to be prof
itable for model fitting. (C) 2000 Elsevier Science Ltd. All rights reserve
d.