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

• Authors: Qi Zhang;Armin Heindl;Evgenia Smirni;Andreas Stathopoulos
• Venue: QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
• Year: 2009

The departure process of a BMAP/MAP/1 queuecan be approximated in different ways: as a Markovian arrivalprocess (MAP) or as a matrix-exponential process (MEP).Both approximations are finite truncations (say, with n + 1block levels) of the original departure process and preservethe marginal distribution of the interdeparture times. However,for true batch arrivals, the MAP model matches one morecoefficient 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, wecompare the two families of output approximations: we analyzethe related complexity with respect to both the computation ofoutput characteristics and the use of the models in networkdecomposition. We also investigate the potential differencesin capturing the asymptotic behavior of the autocorrelationfunction via an eigenvalue analysis. Numerical experiments,conducted for both output models, reveal the implications in anetwork decomposition of dual tandem queues.