Evolving internet: class #7

Challenged Networks and Novel Architectures:slides, pages 24-59.

Example on calculating an average delay on scheduled contacts (for the graph on page 26:

(1)\begin{align} \textrm{avgdelay}(A, B) = \frac 1 {22} \left[ \int_0^5 (5 - t) dt + \int_7^{13} (13 - t) dt + \int _{16}^{20} (20 - t) dt \right] \end{align}

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## Power law random variables

Suppose X is a random variable of inter-meeting time. If X is exponentially distributed, then $P(X > x) = e^{-x\lambda}, P(X > y + x | X > x) = e^{-y\lamnda}$.

But for mobility, this is usually not the case, some people says that the inter-meeting time (on some time intervals) follows a Pareto distribution (but that's on debate).

A power law r.v. has a tail that follows $P(X > x) \sim x^{-\alpha}$

A Pareto r.v. follows $P(X > x) = (\frac x p)^{-\alpha}$

page revision: 9, last edited: 18 Nov 2009 20:33