Printed in the U.S.A. ()1998 by North Atlantic Science Publishing Company 319

• Main Authors: Kerry W. Fendick, Ward Whitt
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 1998
• Subjects: North Atlantic
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.587.3789; http://emis.math.tifr.res.in/journals/HOA/JAMSA/11/3319.pdf

In high-speed communication networks it is common to have requirements of very small cell loss probabilities due to buffer overflow. Losses are mea-sured to verify that the cell loss requirements are being met, but it is not clear how to interpret such measurements. We propose methods for deter-mining 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 clus-ters of losses, rather than individual losses, should be regarded as the im-portant "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 clus-ter 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 stat-istically 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 spe-