Comparison of Two Output Models for the BMAP/MAP/1 Departure Process

The departure process of a BMAP/MAP/1 queue can be approximated in different ways: as a Markovian arrival process (MAP) or as a matrix-exponential process (MEP).Both approximations are finite truncations (say, with n + 1block levels) of the original departure process and preserve the marginal distribution of the interdeparture times. However, for true batch arrivals, the MAP model matches one more coefficient of correlation than the MEP of corresponding size,i.e., lag correlations of the interdeparture times up to lag (n-1)- as opposed to (n - 2) for MEP models. In this paper, we compare the two families of output approximations: we analyze the related complexity with respect to both the computation of output characteristics and the use of the models in network decomposition. We also investigate the potential differences in capturing the asymptotic behavior of the autocorrelation function via an eigenvalue analysis. Numerical experiments,conducted for both output models, reveal the implications in a network decomposition of dual tandem queues.