On the queueing behavior of multiple first-order autoregressive sources

It is generally believed that the queueing behavior of an arrival process is most sensitive to its first and second order statistics. In this paper, we show that this is not generally true. We consider the queueing behavior of two classes of sources. The first class is the superposition of multiple discrete autoregressive sources of order 1 (referred to as DAR(1) sources), and the second class is a single DAR(1) source having the same first and second order statistics as the superposed source. In particular, we show that in the homogeneous case, the mean queue lengths of the two models are identical, but the queue length variances of the two models are significantly different depending on the correlation of individual sources.