Effective bandwidths for a class of non Markovian fluid sources

This paper proves the existence of and explicitly determines effective bandwidths for a class of non Markovian fluid source models, featuring multiple data-transmission rates and arbitrary distributions for the times these rates are sustained. The investigated models cover considerably more traffic profiles than the usual Markovian counterparts and have reduced state-space requirements. The effective bandwidth, as a function of the asymptotic loss probability decay rate, is implicitly derivable by the requirement that the spectral radius of an appropriate nonnegative matrix be equal to unity. The effective bandwidth function is shown to be, either strictly increasing, or constant and equal to the mean rate. Sources of the second kind, which are characterized, generalize the notion of 'CBR' traffic. Furthermore, a study for the limiting effective bandwidth, towards a loss-less environment, is undertaken; it is shown that the limiting value may, under some fully identified restrictions on the source behavior, be less than the source's peak rate. Under those restrictions, a source may have reduced bandwidth requirements, even if it features a large peak rate.