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
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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 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. One of the main reasons of the recent success of peer to peer (P2P)file sharing systems such as BitTorrent is their built-in tit-for-tat mechanism. In this paper, we model the bandwidth allocation in a P2P system as an exchange economy and study a tit-for-tat dynamics, namely the proportional response dynamics, in this economy. In aproportional response dynamics each player distributes its good to its neighbors proportional to the utility it received from them in thelast period. We show that this dynamics not only converges but converges to a market equilibrium, a standard economic characterization of efficient exchanges in a competitive market. In addition, for some classes of utility functions we consider, it converges much faster than the classical tat process and any existingalgorithms for computing market equilibria. As a part of our proof we study the double normalization of a matrix, an operation that linearly scales the rows of a matrix sothat each row sums to a prescribed positive number, followed by a similar scaling of the columns. We show that the iterative double normalization process of any non-negative matrix always converges. This complements the previous studies in matrix scaling that has focused on the convergence condition of the process when the row and column normalizations are considered as separate steps. In this paper, a simple mathematical model is presented for studying the performance of the BitTorrent (1) file sharing system. We are especially interested in the distribution of the peers with different states of the download job completedness. With the model we find that in the stable state the distribution of the download peers follows a U-shaped curve, and the parameters such as the departure rate of the seeds and the abort rate of the download peers will influence the peer distribution in different ways notably. We also analyze the file availability and the dying process of the BitTorrent file sharing system. We find that the system's stability deteriorates with the clustering of the peers, and BitTorrent's built-in "tit-for-tat" unchoking strategy could not help to preserve the integrity of the file among the download peers when the size of the community is small. An innovative peer selection strategy which enables more peers to finish the download job and prolongs the system's lifetime is proposed, in which the peers cooperate to improve the stability of the system by making a tradeoff between the current download rate and the future service availability. Finally, experimental results are presented to validate our analysis and findings. In this paper we propose the following approach to the dimensioning of the radio part of the downlink in OFDMA networks. First, we use information theory to characterize the bit-rate in the channel from a base station to its mobile. It depends on the power and bandwidth allocated to this mobile. Then, we describe the resource (power and bandwidth) allocation problem and characterise feasible configurations of bit-rates of all users. As the key element, we propose some particular sufficient condition (in a multi-Erlang form) for a given configuration of bit-rates to be feasible. Finally, we consider an Erlang's loss model, in which streaming arrivals whose admission would lead to the violation of this sufficient condition are blocked and lost. In this model, the blocking probabilities can be calculated using Kaufman-Roberts algorithm. We propose it to evaluate the minimal density of base stations assuring acceptable blocking probabilities for a streaming traffic of a given load per surface unit. We validate this approach by comparison of the blocking probabilities to these simulated in the similar model in which the admission control is based on the original feasibility property (instead of its sufficient condition). Our sufficient bit-rate feasibility condition can also be used to dimension the network with respect to the elastic traffic. We study a fingerprinting game in which the number of colluders and the collusion channel are unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value of a sequence of maximin games with mutual information as their payoff functions. However, these games generally do not admit saddle-point solutions and are very hard to solve numerically. Here under the so-called Boneh-Shaw marking assumption, we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point solution. If the maximal coalition size is k and the fingerprinting alphabet is binary, we show that capacity decays quadratically with k. Furthermore, we prove rigorously that the asymptotic capacity is 1 (k221n2) and we confirm our earlier conjecture that Tardos' choice of the arcsine distribution asymptotically maximizes the mutual information payoff function while the interleaving attack minimizes it. Along with the asymptotics, numerical solutions to the game for small k are also presented. We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. Recent work on BitTorrent swarms has demonstrated that a bandwidth bottleneck at the seed can lead to the underutilization of the aggregate swarm capacity. Bandwidth underutilization also occurs naturally in mobile peer-to-peer swarms, as a mobile peer may not always be within the range of peers storing the content it desires. We argue in this paper that, in both cases, idle bandwidth can be exploited to allow content sharing across multiple swarms, thereby forming a universal swarm system. We propose a model for universal swarms that applies to a variety of peer-to-peer environments, both mobile and online. Through a fluid limit analysis, we demonstrate that universal swarms have significantly improved stability properties compared to individually autonomous swarms. In addition, by studying a swarm's stationary behavior, we identify content replication ratios across different swarms that minimize the average sojourn time in the system. We then propose a content exchange scheme between peers that leads to these optimal replication ratios, and study its convergence numerically. Existing studies on BitTorrent systems are single-torrent based, while more than 85 of all peers participate in multiple torrents according to our trace analysis. In addition, these studies are not sufficiently insightful and accurate even for single-torrent models, due to some unrealistic assumptions. Our analysis of representative Bit-Torrent traffic provides several new findings regarding the limitations of BitTorrent systems: (1) Due to the exponentially decreasing peer arrival rate in reality, service availability in such systems becomes poor quickly, after which it is difficult for the file to be located and downloaded. (2) Client performance in the BitTorrent-like systems is unstable, and fluctuates widely with the peer population. (3) Existing systems could provide unfair services to peers, where peers with high downloading speed tend to download more and upload less. In this paper, we study these limitations on torrent evolution in realistic environments. Motivated by the analysis and modeling results, we further build a graph based multi-torrent model to study inter-torrent collaboration. Our model quantitatively provides strong motivation for inter-torrent collaboration instead of directly stimulating seeds to stay longer. We also discuss a system design to show the feasibility of multi-torrent collaboration. We consider the canonical shared link caching network formed by a source node, hosting a library of @math information messages (files), connected via a noiseless multicast link to @math user nodes, each equipped with a cache of size @math files. Users request files independently at random according to an a-priori known demand distribution q. A coding scheme for this network consists of two phases: cache placement and delivery. The cache placement is a mapping of the library files onto the user caches that can be optimized as a function of the demand statistics, but is agnostic of the actual demand realization. After the user demands are revealed, during the delivery phase the source sends a codeword (function of the library files, cache placement, and demands) to the users, such that each user retrieves its requested file with arbitrarily high probability. The goal is to minimize the average transmission length of the delivery phase, referred to as rate (expressed in channel symbols per file). In the case of deterministic demands, the optimal min-max rate has been characterized within a constant multiplicative factor, independent of the network parameters. The case of random demands was previously addressed by applying the order-optimal min-max scheme separately within groups of files requested with similar probability. However, no complete characterization of order-optimality was previously provided for random demands under the average rate performance criterion. In this paper, we consider the random demand setting and, for the special yet relevant case of a Zipf demand distribution, we provide a comprehensive characterization of the order-optimal rate for all regimes of the system parameters, as well as an explicit placement and delivery scheme achieving order-optimal rates. We present also numerical results that confirm the superiority of our scheme with respect to previously proposed schemes for the same setting. BitTorrent, the immensely popular file swarming system, suffers a fundamental problem: unavailability. Although swarming scales well to tolerate flash crowds for popular content, it is less useful for unpopular or rare files as peers arriving after the initial rush find the content unavailable. Our primary contribution is a model to quantify content availability in swarming systems. We use the model to analyze the availability and the performance implications of bundling, a strategy commonly adopted by many BitTorrent publishers today. We find that even a limited amount of bundling exponentially reduces content unavailability. Furthermore, for swarms with highly unavailable publishers, the availability gain of bundling can result in a net improvement in download time, i.e., peers obtain more content in less time. We empirically confirm the model's conclusions through experiments on PlanetLab using the mainline BitTorrent client. In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server because of the routing protocol used. The goal is to minimize the total cost of these assignments—cost of each is proportional to the distance between the client and the server as well as the request size—while the load on each server is kept below its bandwidth limit. When each server also has a setup cost, this is an unsplittable hard-capacitated facility location problem. As much attention as facility location problems have received, there has been no nontrivial approximation algorithm when we have hard capacities (i.e., there can only be one copy of each facility whose capacity cannot be violated) and demands are unsplittable (i.e., all the demand from a client has to be assigned to a single facility). We observe it is NP-hard to approximate the cost to within any bounded factor in this case. Thus, for an arbitrary constant e>0, we relax the capacities to a 1+e factor. For the case where capacities are almost uniform, we give a bicriteria O(log n, 1+e)-approximation algorithm for general metrics and a (1+e, 1+e)-approximation algorithm for tree metrics. A bicriteria (α,β)-approximation algorithm produces a solution of cost at most α times the optimum, while violating the capacities by no more than a β factor. We can get the same guarantees for nonuniform capacities if we allow quasipolynomial running time. In our algorithm, some clients guess the facility they are assigned to, and facilities decide the size of the clients they serve. A straightforward approach results in exponential running time. When costs do not satisfy metricity, we show that a 1.5 violation of capacities is necessary to obtain any approximation. It is worth noting that our results generalize bin packing (zero connection costs and facility costs equal to one), knapsack (single facility with all costs being zero), minimum makespan scheduling for related machines (all connection costs being zero), and some facility location problems. In this paper, we develop simple models to study the performance of BitTorrent, a second generation peer-to-peer (P2P) application. We first present a simple fluid model and study the scalability, performance and efficiency of such a file-sharing mechanism. We then consider the built-in incentive mechanism of BitTorrent and study its effect on network performance. We also provide numerical results based on both simulations and real traces obtained from the Internet. In this paper, we study the problem of reducing the delay of downloading data from cloud storage systems by leveraging multiple parallel threads, assuming that the data has been encoded and stored in the clouds using fixed rate forward error correction (FEC) codes with parameters (n, k). That is, each file is divided into k equal-sized chunks, which are then expanded into n chunks such that any k chunks out of the n are sufficient to successfully restore the original file. The model can be depicted as a multiple-server queue with arrivals of data retrieving requests and a server corresponding to a thread. However, this is not a typical queueing model because a server can terminate its operation, depending on when other servers complete their service (due to the redundancy that is spread across the threads). Hence, to the best of our knowledge, the analysis of this queueing model remains quite uncharted. Recent traces from Amazon S3 show that the time to retrieve a fixed size chunk is random and can be approximated as a constant delay plus an i.i.d. exponentially distributed random variable. For the tractability of the theoretical analysis, we assume that the chunk downloading time is i.i.d. exponentially distributed. Under this assumption, we show that any work-conserving scheme is delay-optimal among all on-line scheduling schemes when k = 1. When k > 1, we find that a simple greedy scheme, which allocates all available threads to the head of line request, is delay optimal among all on-line scheduling schemes. We also provide some numerical results that point to the limitations of the exponential assumption, and suggest further research directions. The BitTorrent file distribution system uses tit-fortat as a method of seeking pareto efficiency. It achieves a higher level of robustness and resource utilization than any currently known cooperative technique. We explain what BitTorrent does, and how economic methods are used to achieve that goal. 1 What BitTorrent Does When a file is made available using HTTP, all upload cost is placed on the hosting machine. With BitTorrent, when multiple people are downloading the same file at the same time, they upload pieces of the file to each other. This redistributes the cost of upload to downloaders, (where it is often not even metered), thus making hosting a file with a potentially unlimited number of downloaders affordable. Researchers have attempted to find practical techniqes to do this before[3]. It has not been previously deployed on a large scale because the logistical and robustness problems are quite difficult. Simply figuring out which peers have what parts of the file and where they should be sent is difficult to do without incurring a huge overhead. In addition, real deployments experience very high churn rates. Peers rarely connect for more than a few hours, and frequently for only a few minutes [4]. Finally, there is a general problem of fairness [1]. The total download rate across all downloaders must, of mathematical necessity, be equal to the total upload rate. The strategy for allocating upload which seems most likely to make peers happy with their download rates is to make each peer’s download rate be proportional to their upload rate. In practice it’s very difficult to keep peer download rates from sometimes dropping to zero by chance, much less make upload and download rates be correlated. We will explain how BitTorrent solves all of these problems well. 1.1 BitTorrent Interface BitTorrent’s interface is almost the simplest possible. Users launch it by clicking on a hyperlink to the file they wish to download, and are given a standard “Save As” dialog, followed by a download progress dialog which is mostly notable for having an upload rate in addition to a download rate. This extreme ease of use has contributed greatly to BitTorrent’s adoption, and may even be more important than, although it certainly complements, the performance and cost redistribution features which are described in this paper. In recent years, BitTorrent has emerged as a very scalable peer-to-peer file distribution mechanism. While early measurement and analytical studies have verified BitTorrent’s performance, they have also raised questions about various metrics (upload utilization, fairness, etc.), particularly in settings other than those measured. In this paper, we present a simulationbased study of BitTorrent. Our goal is to deconstruct the system and evaluate the impact of its core mechanisms, both individually and in combination, on overall system performance under a variety of workloads. Our evaluation focuses on several important metrics, including peer link utilization, file download time, and fairness amongst peers in terms of volume of content served. Our results confirm that BitTorrent performs near-optimally in terms of uplink bandwidth utilization, and download time except under certain extreme conditions. We also show that low bandwidth peers can download more than they upload to the network when high bandwidth peers are present. We find that the rate-based tit-for-tat policy is not effective in preventing unfairness. We show how simple changes to the tracker and a stricter, block-based tit-for-tat policy, greatly improves fairness. This paper studies the problem of constructing a minimum-weight spanning tree (MST) in a distributed network. This is one of the most important problems in the area of distributed computing. There is a long line of gradually improving protocols for this problem, and the state of the art today is a protocol with running time O(Λ(G)+n⋅log∗n) due to Kutten and Peleg [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27], where Λ(G) denotes the diameter of the graph G. Peleg and Rubinovich [D. Peleg, V. Rubinovich, A near-tight lower bound on the time complexity of distributed MST construction, in: Proc. 40th IEEE Symp. on Foundations of Computer Science, 1999, pp. 253–261] have shown that Ω˜(n) time is required for constructing MST even on graphs of small diameter, and claimed that their result “establishes the asymptotic near-optimality” of the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27]. In this paper we refine this claim, and devise a protocol that constructs the MST in Ω˜(μ(G,ω)+n) rounds, where μ(G,ω) is the MST-radius of the graph. The ratio between the diameter and the MST-radius may be as large as Θ(n), and, consequently, on some inputs our protocol is faster than the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27] by a factor of Ω˜(n). Also, on every input, the running time of our protocol is never greater than twice the running time of the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27]. As part of our protocol for constructing an MST, we develop a protocol for constructing neighborhood covers with a drastically improved running time. The latter result may be of independent interest. Peer-to-peer protocols play an increasingly instrumental role in Internet content distribution. It is therefore important to gain a complete understanding of how these protocols behave in practice and how their operating parameters affect overall system performance. This paper presents the first detailed experimental investigation of the peer selection strategy in the popular BitTorrent protocol. By observing more than 40 nodes in instrumented private torrents, we validate three protocol properties that, though believed to hold, have not been previously demonstrated experimentally: the clustering of similar-bandwidth peers, the effectiveness of BitTorrent's sharing incentives, and the peers' high uplink utilization. In addition, we observe that BitTorrent's modified choking algorithmin seed state provides uniform service to all peers, and that an underprovisioned initial seed leads to absence of peer clustering and less effective sharing incentives. Based on our results, we provide guidelines for seed provisioning by content providers, and discuss a tracker protocol extension that addresses an identified limitation of the protocol.