A New Regenerative Estimator for Effective Bandwidth Prediction

The main purpose of the effective bandwidth (EB) theory is to guarantee a required Quality of Service (QoS) (a performance guarantee) for a wide class of communication networks (for instance, ATM, Ethernet). At that performance guarantee has a loss-ratio form, being a fraction of the lost arrivals (it is so-called overflow probability). It follows from the Large Deviation Theory (LDT) that an overflow probability (rare event probability) for a wide class of the buffered systems decreases exponentially fast as buffer size increases. Moreover, the LDT describes a rate-function, which in turn allows to calculate the required exponent. Thus, calculation of EB is reduced to calculation of the scaled cumulant generating function (SCGF) of the arrival process.

In a recent research, an approximation of the SCGF (to find an overflow probability) has been developed relaying on an assumption that input data form a stationary, mixing sequence. At that, a partition of the given input sequence onto blocks of a fixed size is proposed to construct a sample mean estimate of SCGF. In other words, the batch-mean method is used for the estimation which assumes that the blocks constitute i.i.d variables, if size is large enough.

In this work, instead we present a refined EB approximation which is based on a regenerative structure of the input sequence. We consider a tandem network with two single server stations, renewal input to 1st station, and a constant service rate at the second station. It follows that the 2nd station is fed by a regenerative input (the output from 1st station) and we can construct classical regenerations of the second station which occur when an arriving customer sees totally empty network. This allows us to use partition of the input sequence on the i.i.d. blocks of random length (instead of fixed length above) which coincide with the boundaries of regenerative cycles of the input.

Using regenerative simulation we calculate the effective (constant) service rate as a function of given QoS probability and the buffer-size . It is assumed to discuss the quality of new estimator and verify the effectiveness of the two different approximations (with fixed and random block lengths, respectively) comparing results with a Crude Monte-Carlo simulation.