On loss probabilities in presence of redundant packets and several traffic sources

We study the effect of adding redundancy to an input stream on the losses that occur due to buffer overflow. We consider several sessions that generate traffic into a finite capacity queue. Using multi-dimensional probability generating functions, we derive analytical formulas for the loss probabilities and provide asymptotic analysis (for large n and small or large ρ). Our analysis allows us to investigate when does adding redundancy decrease the loss probabilities. In many cases, redundancy is shown to degrade the performance, as the gain in adding redundancy is not sufficient to compensate the additional losses due to the increased overhead. We show, however, that it is possible to decrease loss probabilities if a sufficiently large amount of redundancy is added. Indeed, we show that for an arbitrary stationary ergodic input process, if ρ<1 then redundancy can reduce loss probabilities to an arbitrarily small value.