Granular model of packet pair separation in Poissonian traffic

We introduce a theoretical model of packet pair separation based on a transient solution of the Takács integro-differential equation. We show that in addition to the parameters of the fluid approximation (physical bandwidth and the average cross traffic rate) a new parameter characterizing the granularity of the cross traffic is necessary. These three parameters determine the dynamics of the queue in the diffusive approximation and all important distributions and averages of the packet separation even in multi-hop scenarios (assuming independent cross traffic on different hops). The model describes correctly the data collected in simulations, laboratory and Internet experiments. The adjustable model parameters are the physical bandwidth, the available bandwidth and the weighted average of the packet size of the cross traffic. We show that an implementation of the theoretical results can be used to estimate such parameters in packet chirp type measurements and can be a good candidate for improved available bandwidth estimation.