In Search of the Worst Case Arrivals of Independent

In a previous paper 10] we have shown numerical evidence that there are traac patterns wich generate more loss in a multiplexer than the on-oo source. In this paper we derive mathematical upper and lower bound for two loss measures (P loss , the cell loss rate and P sat , the fraction of time where the multiplexer is saturated) in a buuered multiplexer fed by homogeneous leaky bucket constrained sources. Using these bounds we prove that the on-oo source is not the worst case traac pattern. We demonstrate that the so-called sym pattern generates both higher P loss and P sat , at least in the domain of validity of the bounds. We end the paper by a discussion on the implications of this new nding, especially in respect to CAC algorithms which are based on the assumption that on oo patterns are the worst case.