Moments of the queue occupancy in an ATM multiplexer loaded with on/off sources

Abstract

Matrix-analytic techniques based on the discrete-time batch Markovian arrival process (D-BMAP) modeling have been applied to the analysis of ATM multiplexers under correlated input conditions. The former results yield the multiplexer system queue occupancy using the D-BMAP/D/1 queueing system, where the aggregate of a set of homogeneous on/off sources have been modeled as a single D-BMAP. The multiplexer performance is analyzed using the first two moments of the queue distribution, which have a direct impact on the cell end-to-end delay and its variation. We express the functional equation of an infinite-capacity queueing system loaded by a set of homogeneous on/off sources and derive the first two moments of the number of cells in the system. We highlight the relationships between the source parameters, the moments and the boundary probabilities involved.<>