In high-speed communication networks it is common to have requirements
of very small cell loss probabilities due to buffer overflow. Losses are measured to verify that the cell loss requirements are being met, but it is not
clear how to interpret such measurements. We propose methods for determining whether or not cell loss requirements are being met. A key idea is
to look at the stream of losses as successive clusters of losses. Often clusters of losses, rather than individual losses, should be regarded as the important loss events. Thus we propose modeling the cell loss process by a
batch Poisson stochastic process. Successive clusters of losses are assumed
to arrive according to a Poisson process. Within each cluster, cell losses
do not occur at a single time, but the distance between losses within a cluster should be negligible compared to the distance between clusters. Thus,
for the purpose of estimating the cell loss probability, we ignore the spaces
between successive cell losses in a cluster of losses. Asymptotic theory
suggests that the counting process of losses initiating clusters often should
be approximately a Poisson process even though the cell arrival process is
not nearly Poisson. The batch Poisson model is relatively easy to test statistically and fit; e.g., the batch-size distribution and the batch arrival rate
can readily be estimated from cell loss data. Since batch (cluster) sizes
may be highly variable, it may be useful to focus on the number of
batches instead of the number of cells in a measurement interval. We also
propose a method for approximately determining the parameters of a special batch Poisson cell loss with geometric batch-size distribution from a
queueing model of the buffer content. For this step, we use a reflected
Brownian motion (RBM) approximation of a G/D/1/C queueing model.
We also use the RBM model to estimate the input burstiness given the cell
loss rate. In addition, we use the RBM model to determine whether the
presence of losses should significantly affect the estimation of server utilization when both losses and utilizations are estimated from data. Overall,
our analysis can serve as a basis for determining required observation intervals in order to reach conclusions with a solid statistical basis. Thus our
analysis can help plan simulations as well as computer system measurements.
Service Rate Optimization of Finite Population Queueing Model with State Dependent Arrival and Service Rates
