Kim, Nam, and Sung consider a single-server fluid queueing system with a service rate of C. The input follows a fractional Brownian motion.

Let Q denote the queue length in steady state. For a given buffer threshold b, overflow probability constraint L, and mean delay constraint d, the effective bandwidth e(b, L, d) is defined as the minimum value, such that C ≥ e (b, L, d) → P(Q > b) ≤ L and E(Q) ≤ Cd.

The authors derive formulas for the effective bandwidths for single and multiple sources in a novel way. They “show that there is a scaling property among the stationary queue-length distributions of different input parameters and service rates.” This scaling factor is evaluated in the paper. The authors also show that it is essential to evaluate the distribution function of a certain random variable in order to obtain an effective bandwidth.