Tractable effective bandwidths for end-to-end evaluation and fractional Brownian motion traffic

Effective bandwidth is a concept that has been developed for admission control as an indicator of the traffic load given to a network. However, that concept has been discussed mainly under a single node. That's because, while there are many studies on evaluation formulas for backlog at a single node, studies on end-to-end evaluation have been almost limited to ones by network calculus. In this paper, we develop an end-to-end backlog evaluation formula for a heterogeneous tandem network with cross traffic, as an extension of the one obtained in previous papers by the authors. The formula evaluates the asymptotic tail probability of the end-to-end backlog by the total traffic load at a bottleneck node, and here the traffic load of a flow is evaluated by a kind of effective bandwidth named tractable effective bandwidths (tEBW). The tEBW has a special property that makes the formula simple and tractable, and it is applicable to various types of input flows frequently used in performance analyses. Unfortunately, however, fractional Brownian motion (fBm) flows with long range dependency do not have any tEBW. For fBm flows, we show that another new tighter end-to-end backlog evaluation formula is effective, and using it we can show that, in a homogeneous tandem network with fBm cross traffic, the asymptotic tail probability of the end-to-end backlog is the same as that in the single node.