TrebleCast Notes and Analysis

 

TrebleCast is a new structured P2P overlay supported by an unstructured substrate. TrebleCast's design philosophy is intended to take advantage of specific P2P properties.

The structured overlay is designed to accommodate extremely heterogeneous nodes. Previous research in P2P indicate that available up and down bandwidth, link latency and availability of nodes vary widely between 3 to 5 orders of magnitude [1]. Early literature in P2P measurement and analysis often used an exponentially distribution to model the length of time that a node spends in the network. The exponential distribution is memoryless, however recent studies have shown that this is very likely not the case. The expected time that a node spends in the network is directly dependent on how long the node has been in the network [2]. In [2], the authors find that a Pareto distribution which belongs to the UBNE class of distributions best models the behaviour of nodes in the network. The Pareto distribution is a power law probability distribution. Power law distributions have the scale invariance property. This property effectively means that in a log-log plot, the distribution looks like a straight-line. The concept of scale invariance is very similar to the concept of self-similarity. This is exactly the property that we want to look at.

TrebleCast attempts to take advantage of the property that if node A has been in the network longer than node B, then node A has a higher probability of remaining in the network than node B.

The Pareto distribution has the pdf:

x = - b ± b 2 - 4 ⁢ a ⁢ c 2 ⁢ a