Impact of the Dropping Function on Clustering of Packet Losses

The dropping function mechanism is known to improve the performance of TCP/IP networks by reducing queueing delays and desynchronizing flows. In this paper, we study yet another positive effect caused by this mechanism, i.e., the reduction in the clustering of packet losses, measured by the burst ratio. The main contribution consists of two new formulas for the burst ratio in systems with and without the dropping function, respectively. These formulas enable the easy calculation of the burst ratio for a general, non-Poisson traffic, and for an arbitrary form of the dropping function. Having the formulas, we provide several numerical examples that demonstrate their usability. In particular, we test the effect of the dropping function's shape on the burst ratio. Several shapes of the dropping function proposed in the literature are compared in this context. We also demonstrate, how the optimal shape can be found in a parameter-depended class of functions. Finally, we investigate the impact of different system parameters on the burst ratio, including the load of the system and the variance of the service time. The most important conclusion drawn from these examples is that it is not only the dropping function that reduces the burst ratio by far; simultaneously, the more variable the traffic, the more beneficial the application of the dropping function.