> By Lamia Benamara and Clémence Magnien

In a P2P system, we study the time users stay connected to the system, which we approximate by the time elapsed between the first and the last query made by a given user.

This plot shows the inverse cumulative distribution of this life-duration: the *x* axis represents the fraction of the measurement period, and the *y* axis represents the number of peers which have a life-duration greater than or equal to this value. We consider this distribution for measurement periods asting one hour, one day, and one week.

We observe that the measurement period has a strong influence on what is seen. Moreover, the plot for one hour shows clearly a peak at about one half of the measurement period; this peak is less clear in the 1-day plot and is shifted towards the right, and it tends to disappear in the 1-week plot. This is probably caused by the fact than, when the measurement period is short, many peers have a life-duration longer than the measurement period; many of those make queries at the beginning and at the end of the measurement period, therefore appearing to have a life-duration close to the measurement duration. When the measurement duration increases, this effect vanishes.

A very interesting question in this context is whether the distributions converge to a fixed distribution when we increase the measurement period further.