Can P2P networks be super-scalable?

Abstract

We propose a new model for peer-to-peer networking which takes the network bottlenecks into account beyond the access. This model can cope with key features of P2P networking like degree or locality constraints together with the fact that distant peers often have a smaller rate than nearby peers. Using a network model based on rate functions, we give a closed form expression of peers download performance in the system's fluid limit, as well as approximations for the other cases. Our results show the existence of realistic settings for which the average download time is a decreasing function of the load, a phenomenon that we call super-scalability.

Mutual service processes in Euclidean spaces: existence and ergodicity

“…Our main results are (i) a proof of the existence and uniqueness of a stationary regime (Theorem 7.4); (ii) a hierarchy of balance equations linking the factorial moment measures [2] of neighboring orders (Theorem 8.1) for this problem, generalizing those conjectured in [1] for discussing superscalability; (iii) a general repulsion result formalizing the Palm bias alluded to above (Theorem 8.2); (iv) a result on the exponential speed at which the initial condition is forgotten (Theorem 7.1).…”

“…This paper was initially motivated by our study of peer to peer file-sharing in spatial scenarios, where the transmission speed between two peers depends on their distance [1]. The peers 1 join as a Poisson rain in R 2 , serve each other at rates given by some decreasing function f of their distances, and leave when their individual service requirements (assumed to be exponentially distributed, i.e.…”

“…All peers present in the system at any time echange small pieces of the file on a tit for tat basis. This exchange mechanism leads to the service process described above, see [1].…”

“…In [1], assuming that an ergodic steady state of the process exists in R 2 , we derived many interesting properties and formulae related to the superscalability of such mutual service systems: the larger the arrival rate, the shorter the mean service time experienced by a peer. Proving the existence of a time and space stationary and ergodic regime turns out to be difficult because of (a) the non-monotonicity of the dynamics: when a peer leaves, it also ceases to serve the others; and (b) the fact that unbounded rate functions are necessary within this context, which prevents the use of classical approaches.…”

“…Future research directions directly related to the present paper include the relaxation of certain assumptions on f , the case of non-exponential service requirement distribution, the "fluid" and "hard-core" limit regimes considered in [1], and multi-chunk models. The paper is structured as follows.…”