Understanding Packet Pair Separation Beyond the Fluid Model: The Key Role of Traffic Granularity

Efficient and reliable available bandwidth measurement remains an important goal for many applications. Recently a new class of active probing techniques has emerged based on observing an increased separation of probe packets due to local saturation of the queue at the narrow link, and do not require the knowledge of link capacities along the path. In this paper 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) the introduction of 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. The model can easily be extended for the multi-hop scenario and an approximate expression for the average output spacing is derived. We show that 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.

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