Bounding superposed on-off sources - variability ordering and majorization to the rescue

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. 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 a new and provably correct upper bound.