Bounding superposed on - off sources - Variability ordering and majorization to the rescue by Armand M . Makowski CSHCN TR 2003 - 19 ( ISR TR 2003 - 38 )

We consider the problem of bounding the loss rate of the aggregation of independent on-off sources in a bufferless model by the loss rate resulting from the aggregation of i.i.d. on-off sources. This is done through a unified framework based on the interplay of well-known results from the theory of variability orderings with the concept of majorization ordering. In particular, we use a basic comparison result to readily derive a bound of Rasmussen et al. for heterogeneous sources and an upper bound of Mao and Habibi for homogeneous sources, and to discuss a second upper bound proposed by these authors. It is argued that this conjectured upperbound is too tight in general, and should be replaced by new and provably correct upper bound.