Peer-to-peer (P2P) overlay networks such as BitTorrent and Avalanche are increasingly used for disseminating potentially large files from a server to many end users via the Internet. The key idea is to divide the file into many equally-sized parts and then let users download each part (or, for network coding based systems such as Avalanche, linear combinations of the parts) either from the server or from another user who has already downloaded it. However, their performance evaluation has typically been limited to comparing one system relative to another and typically been realized by means of simulation and measurements. In contrast, we provide an analytic performance analysis that is based on a new uplink-sharing version of the well-known broadcasting problem. Assuming equal upload capacities, we show that the minimal time to disseminate the file is the same as for the simultaneous send receive version of the broadcasting problem. For general upload capacities, we provide a mixed integer linear program (MILP) solution and a complementary fluid limit solution. We thus provide a lower bound which can be used as a performance benchmark for any P2P file dissemination system. We also investigate the performance of a decentralized strategy, providing evidence that the performance of necessarily decentralized P2P file dissemination systems should be close to this bound and therefore that it is useful in practice.
In this paper, we provide the scheduling background, proofs and discussion of the results in our extended abstracts @cite_16 and @cite_34 . It is essentially Chapter 2 of @cite_27 , but we have added Theorem and the part on theoretical bounds in Section . @cite_29 the authors also consider problems concerned with the service capacity of P2P networks, however, they only give a heuristic argument for the makespan with equal upload capacities when @math is of the simple form @math . @cite_26 a fluid model for BitTorrent-like networks is introduced and studied, also looking at the effect of incentive mechanisms to address free-riding. Link utilization and fairness are issues in @cite_13 . @cite_31 , also motivated by the BitTorrent protocol and file swarming systems in general, the authors consider a probabilistic model of coupon replication systems. Multi-torrent systems are discussed in @cite_17 . There is other related work in @cite_10 .
@cite_26 @cite_10 @cite_29 @cite_34 @cite_27 @cite_31 @cite_16 @cite_13 @cite_17
2010859647 2171217544 2144334146 2117047663
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 are characterised by their current collection of coupons, and leave the system once they complete their coupon collection. The system evolution is then specified by describing how users of distinct types meet, and which coupons get replicated upon such encounters.For open systems, with exogenous user arrivals, we derive necessary and sufficient stability conditions in 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 performance, captured by sojourn time, is asymptotically optimal in both systems 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 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 left-overs is of order log(log(N)).These results suggest that performance of file swarming systems does not depend critically on either altruistic user behavior, or on load balancing strategies such as rarest first. 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. A number of analytical models exists that capture various properties of the BitTorrent protocol. However, until now virtually all of these models have been based on the assumption that the peers in the system have homogeneous bandwidths. As this is highly unrealistic in real swarms, these models have very limited applicability. Most of all, these models implicitly ignore BitTorrent's most important property: peer selection based on the highest rate of reciprocity. As a result, these models are not suitable for understanding or predicting the properties of real BitTorrent networks. Furthermore, they are hardly of use in the design of realistic BitTorrent simulators and new P2P protocols. In this paper, we extend existing work by presenting a model of a swarm in BitTorrent where peers have arbitrary upload and download bandwidths. In our model we group peers with (roughly) the same bandwidth in classes, and then analyze the allocation of upload slots from peers in one class to peers in another class. We show that our model accurately predicts the bandwidth clustering phenomenon observed experimentally in other work, and we analyze the resulting data distribution in swarms. We validate our model with experiments using real BitTorrent clients. Our model captures the effects of BitTorrent's well-known ‘tit-for-tat’ mechanism in bandwidth-inhomogeneous swarms and provides an accurate mathematical description of the resulting dynamics. We study the 'service capacity' of peer to peer (P2P) file sharing applications. We begin by considering a transient regime which is key to capturing the ability of such systems to handle bursty traffic, e.g., flash crowds. In this context our models, based on age dependent branching processes, exhibit exponential growth in service capacity, and permit the study of sensitivity of this growth to system policies and parameters. Then we consider a model for such systems in steady state and show how the average delay seen by peers would scale in the offered load and rate at which peers exit the system. We find that the average delays scale well in the offered load. In particular the delays are upper bounded by some constant given any offered load and even decrease in the offered load if peers exit the system slowly. We validate many of our findings by analyzing traces obtained from a second generation P2P application called BitTorrent.