On the compromise between burstiness and frequency of events

Consider two situations where events occur randomly in a system with a common average rate, but with different distributions for the size of bursts of events. Assume that the performance measure of interest is the probability that less than h events occur in a given time period. Is it possible to decide which of the two situations is the best? It turns out that when the average rate varies whereas the burst distributions are fixed, the winning situation may change: there is a tradeoff between burstiness and frequency. The purpose of this paper is to investigate this tradeoff. We use two simple models for this: the discrete-time two-state Markov chain (known as the Gilbert model) and a compound Poisson process, viewed as an approximation of the Gilbert model. For each of them, we show that indeed there exists a threshold value for the event rate at which the best configuration changes. We analytically derive the asymptotic value of this threshold when the number h grows. We apply this analysis to the performance evaluation of Forward Error Correction applied to flow of packets in networks with different Queue Management schemes, namely: RED and Drop Tail. The measure of interest is the probability of losing less than h packets in a certain block. Through simulation measurements, we exhibit the same tradeoff phenomenon, and we collect statistics showing that the Gilbert model is partly adequate to represent the situation.