## P2PSP (Peer-to-Peer “Straightforward” Protocol)

#### 6.3 Chunk lost-rate produced by churn and unwarned-churn

Polite and warned churn should never produce a loss of chunks. On the other hand, unwarned churn can produce this lost if the buﬀer size is too small or if the splitter is congested (remind that the splitter resend those chunks that are requested at least by the half of the peers of the cluster and this could congest its upload link). Independtly of the motive, the rest of the peers of the cluster will lost those chunks that were sent to the outgoing peer while the time that the splitter were not aware of this fact. Under a reasonable network performance, the this time should be smaller than the splitter delivery period $T$ and the number of lost chunks per peer should be only one.

Leo: Juan Alvaro usa una distribucion distinta a la Poisson.

... in the continuity index (ratio of received blocks vs sent blocks by the source that is perfect when reach 1) depending on the arrival and departure rate. ... and in the start-up delay.

The user-driven dynamics of peer participation, or churn, must be taken into account in both the design and evaluation of any large scale P2P application.

Usually, peers (users) arrive and leave acording to a Poisson process with rate $\lambda$, i.e., $1∕\lambda$ is the average time a peer stay in the team). The Poison counter satisﬁes that

 (18)

and

 $\overline{dN\left(t\right)}=\lambda dt,$ (19)

P2PSP (Peer-to-Peer Straightforward Protocol) by Cristobal Medina-López, J. A. M. Naranjo, L. G. Casado and Vicente González-Ruiz