The Entropy of Cell Streams as aTra c Descriptor in ATM

We examine the properties of a promising new traac descriptor for ATM networks, namely the entropy of cell streams. The entropy is a measure of the disorganization among cells within a traac stream; alternatively we can say that entropy captures the amount of randomness in cell scattering. We study the entropy of ON-OFF sources with respect to the typical queue parameters of interest: average queue size, queue variance and equivalent buuers. The equivalent buuer is deened as the minimum buuer size needed to achieve a speciic loss probability. We demonstrate that the average queue size and the variance of queue size are monotonically decreasing with increasing entropy in streams with the same xed load. We nd that the inverse of the entropy is closely linear, to within a good approximation, to the equivalent buuer. This simple relation demonstrates the appeal of the entropy estimator. In addition to a measure of cell scattering, our results suggest another interpretation of entropy as a measure of smoothness. Traac streams with higher entropy (i.e. smoother) have less buuering needs in terms of average, variance and equivalent buuers. Based on this observation we introduce a traac shaping mechanism whose goal is to boost the entropy of a stream.