Mode-Suppression: A Simple and Provably Stable Chunk-Sharing Algorithm for P2P Networks

Abstract

The ability of a P2P network to scale its throughput up in proportion to the arrival rate of peers has recently been shown to be crucially dependent on the chunk sharing policy employed. Some policies can result in low frequencies of a particular chunk, known as the missing chunk syndrome, which can dramatically reduce throughput and lead to instability of the system. For instance, commonly used policies that nominally "boost" the sharing of infrequent chunks such as the wellknown rarest-first algorithm have been shown to be unstable. Recent efforts have largely focused on the careful design of boosting policies to mitigate this issue. We take a complementary viewpoint, and instead consider a policy that simply prevents the sharing of the most frequent chunk(s). Following terminology from statistics wherein the most frequent value in a data set is called the mode, we refer to this policy as mode-suppression. We also consider a more general version that suppresses the mode only if the mode frequency is larger than the lowest frequency by a fixed threshold. We prove the stability of mode-suppression using Lyapunov techniques, and use a Kingman bound argument to show that the total download time does not increase with peer arrival rate. We then design versions of mode-suppression that sample a small number of peers at each time, and construct noisy mode estimates by aggregating these samples over time.We show numerically that the variants of mode-suppression yield near-optimal download times, and outperform all other recently proposed chunk sharing algorithms.

Mode-Suppression: A Simple, Stable and Scalable Chunk-Sharing Algorithm for P2P Networks

“…A preliminary version of this work was presented in [34], which only considered the stability of a basic version of modesuppression. The current work derives a stability result for a generalized version of mode-suppression that has a frequency difference threshold, empirically determines the right threshold, and develops a Kingman-bound-based sojourn time scaling result.…”

Rarest-First with Probabilistic-Mode-Suppression

“…The protocol was proved to be stable for a two-chunk file-sharing system and its stability for multi-chunk systems was left as a conjecture. ‚ Reddyvari, Parag and Shakkottai [11] took a chunklevel viewpoint and proposed the Mode-Suppression (MS) protocol. Here, the transfer of pieces in the mode (present with the most number of peers) is prohibited, except when all pieces are in the mode, and a random-novel piece not in the mode (if any) is sent.…”

“…The notation used in this paper is a combination of related notations in [8] and [11]. We classify peers into types according to the swarm they belong to, and the set of pieces in their cache.…”

“…Suppose that at time t ě 0, a pV, T q-peer has push-contacted its ally-peer, say a pW, Sq-peer (W P W V ), with revealed cache-profile p T . To describe Swarm-based RFwPMS, some definitions (a'la [11]- [13]) are needed.…”

“…DISCUSSION A. Sharing vs Suppression Trade-off for Non-Rare Pieces Note that with α W P p0, 1s sufficiently small, if we take the limit β W Ñ 8, swarm-based RFwPMS converges to a swarmbased version of RF (which is unstable in high arrival-rate regime), whereas if we take the limit β W Ñ 0, swarm-based RFwPMS converges to a swarm-based version of MS [11]. Thus, our expectation is that by choosing α W sufficiently small, and β W appropriately, an appropriate trade-off between the sharing and suppression of the non-rare pieces can be found.…”