Recent studies have suggested that the stability of peer-to-peer networks may rely on persistent peers, who dwell on the network after they obtain the entire file. In the absence of such peers, one piece becomes extremely rare in the network, which leads to instability. Technological developments, however, are poised to reduce the incidence of persistent peers, giving rise to a need for a protocol that guarantees stability with non-persistent peers. We propose a novel peer-to-peer protocol, the group suppression protocol, to ensure the stability of peer-to-peer networks under the scenario that all the peers adopt non-persistent behavior. Using a suitable Lyapunov potential function, the group suppression protocol is proven to be stable when the file is broken into two pieces, and detailed experiments demonstrate the stability of the protocol for arbitrary number of pieces. We define and simulate a decentralized version of this protocol for practical applications. Straightforward incorporation of the group suppression protocol into BitTorrent while retaining most of BitTorrent's core mechanisms is also presented. Subsequent simulations show that under certain assumptions, BitTorrent with the official protocol cannot escape from the missing piece syndrome, but BitTorrent with group suppression does.
Massouli 'e and Vojnovic @cite_26 proved global stability in a model with non-persistent peers if all new peers arrive into the system with one uniformly random piece of the file uploaded by the fixed seed. The fixed seed's upload rate, however, may not be large enough to allow this in practice.
@cite_26
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Motivated by the study of peer-to-peer file swarming systems a la BitTorrent, we introduce a probabilistic model of coupon replication systems. These systems consist of users aiming to complete a collection of distinct coupons. Users enter the system with an initial coupon provided by a bootstrap server, acquire other coupons from other users, and leave once they complete their coupon collection. For open systems, with exogenous user arrivals, we derive stability condition for a layered scenario, where encounters are between users holding the same number of coupons. We also consider a system where encounters are between users chosen uniformly at random from the whole population. We show that sojourn time in both systems is asymptotically optimal as the number of coupon types becomes large. We also consider closed systems with no exogenous user arrivals. In a special scenario where users have only one missing coupon, we evaluate the size of the population ultimately remaining in the system, as the initial number of users N goes to infinity. We show that this size decreases geometrically with the number of coupons K. In particular, when the ratio K log(N) is above a critical threshold, we prove that this number of leftovers is of order log(log(N)). These results suggest that, under the assumption that the bootstrap server is not a bottleneck, the performance does not depend critically on either altruistic user behavior or on load-balancing strategies such as rarest first.