Free-Riding Analysis of BitTorrent-like Peer-to-Peer Networks

Transcription

1 Free-Riding Analysis of BitTorrent-like Peer-to-Peer Networks Jiadi Yu, Minglu Li, Feng Hong, and Guangtao Xue Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 23, P.R. China {jdyu,li-ml, fenghong, Abstract BitTorrent is a very popular P2P file sharing system.it has been successful at distributing large files quickly and efficiently. Embedded in BitTorrent is a set of incentive mechanisms to encourage sharing and contribute, and prevent systematic free-riding. In this paper, a fluid model with two classes of peers is used to capture the effect of free-riding in a BitTorrent system. With the model, we explore how does free-riding influenced the BitTorrent system. From results, it is shown that BitTorrent mechanism is successful to guard against free-riding. Finally, we discuss the dying process of a BitTorrent system and the probability of system dead that is induced by free-riding.. Introduction Peer-to-Peer (P2P) applications have shown their popularity in the Internet for file sharing. Among P2P application, file sharing perhaps the most popular application,which allows users to distribute and obtain a sharing file cooperatively. In contrast to the traditional server-client model of content distribution, the P2P technology has the advantage as low cost of hardware deployment, more scalable to accommodate a large number of users and amount of content, more fault tolerance for content being shared by multiple sources, and less time required to download a given data file. Among all P2P file-sharing applications, the BitTorrent system[] becomes the most popular one, which account for 35% of all the traffic on the Internet[2]. Cooperation is the key to a peer-to-peer file sharing system that depend on voluntary contribute of service resources from the system participants. However, many P2P systems suffer from free-riding [3]. Free-riding behavior among peers will get service resources while contribute nothing to the system because of lacking rational incentive mech- This work was supported by the National Natural Science Foundation of China under Grant No and No anism. the BitTorrent system is one of file sharing systems that relate to incentive mechanism. In a BitTorrent system, a sharing file is divided into multiple small pieces. A peer can download different pieces concurrently from multiple peers, and uploads holding pieces to other peer at one time. A peer wants to maximize the gain, but at the same time it also wants to minimize the cost. BitTorrent employs the tit-for-tat peer selection strategy to prevent free-riding and promote fairness, where each peer uploads to a set of peers from which it has the highest downloading rates. In addition to the tit-for-tat strategy, Bit- Torrent uses a Optimistic Unchoking process, which allow a peer to discover better peers for share exchange. In this paper, we analyze the incentive mechanism of Bit- Torrent. Based on the results of analysis, we see that freerider can get download rate from contributor to download the sharing file. In order to capture the effect of free-riding in a BitTorrent system, we incorporates an different classes of peers idea in [6] to the fluid model in [4] that takes into account only one class of peers with equal server capacity, and we introduce dynamic resource allocation to two different class of peers: nonfree-riders and free-riders, where resources assignment criteria depend on BitTorrent mechanism completely. From model result, we find that BitTorrent mechanism is successful to guard against free-riding. Finally, we discuss the dying process of a BitTorrent system and the probability of system dead that is induced by free-riding. Although free-riding can induce system dead, system dead can be avoided as long as the system manage to keep a small quantity of copies of each piece in systems. The remainder of the paper is organized as follows.for Section 2, we analyze the incentive mechanism of BitTorrent. In Section 3, we introduce an fluid model with two classes of peers, and analyze our modeling results under the steady state. We discuss the probability of the system s death in Section 4. In Section 5, related work on BitTorrent file sharing system and free-riding are surveyed. Finally, we conclude the paper in Section /6 $2. 26

2 2. Mechanism Analysis In a BitTorrent system, BitTorrent peers are using the titfor-tat strategy to select the upload/download peers: each peer will upload to a fixed number of other peers (default is four) from which it could download at the highest downloading rates in a given time. A refusal uploading is called choking, and this algorithms is called Choking Algorithm. This mechanism is employed to encourage user to upload and guard against free-riding. In [4], they prove, using game theoretical, that there exist a Nash equilibrium point with this tit-for-tat strategy, under which each peer will upload at its maximum uploading bandwih. BitTorrent also incorporates an Optimistic Unchoking strategy, wherein each peer randomly chooses a requesting peer to upload regardless of its download rate, in addition to keep connections with those peers selected by Choking Algorithm. The purpose of Optimistic Unchoking is that a peer could upload to a peer that has better download rate than the ones being downloading currently, and the newcomer that have not any share could get bootstrapped by downloading their first piece. However, Optimistic Unchoking gives a opportunity to free-rider to download sharing file. In the rest of this sectionwe analyze the effect of Optimistic Unchoking on free-rider. Let G{p, p,..., p xn, q, q,..., q xf } be a set of peers in a BitTorrent network, where x n is the number of nonfree-riders, and x f is the number of free-riders in G. We assume all nonfree-riders have the same uploading bandwih, and let µ be the uploading bandwih of a nonfreerider. The total uploading rate of the system can be expressed as µx n. Let u be the number of uploading connections of a nonfree-rider, and the one of that is Optimistic Unchoking upload. According to the BitTorrent mechanism, each nonfree-rider will randomly select a peer that it is unused connection pees currently to upload under Optimistic Unchoking, and the upload rate of a connection is limited to µ u. The total expected download rate of free-riders in G is thus E[D f ] = = x n C k x f x n u x n ( x n + x f u )k ( x n + x f u )xn k (k µ u ) and it has been proved to be close to in [4]. The efficiency of the file sharing of free-riders is equal to zero. At k= x n x f x n + x f u µ u x nx f µ time t, the total upload bandwih of the system is µηx n (t). () x n + x f u when x n +x f u. We can see in () that, in G, free-riders x can get the download rate of nx f x n+x f µ u in spite of nothing to contribute to this system. Let ρ be the ratio of the total download rate of free-riders to the total upload rate in G. Thus, ρ = E[D f ] = µx n u x f (2) x n + x f where ρ [, ].We can see in (2) that the value of ρ increases as the ratio of the number of free-riders to the number of nonfree-riders increase in the system. But each freerider may be get much less the download rate as the number of free-riders increases. 3 modeling and analysis In [4], a fluid model, which is based on Markov chain modeling idea in [5], was developed for BitTorrent-like file sharing system. Our model is an extension of the model in [4] and follow they idea. In order to capture the effect of free-riding in a BitTorrent system, we introduce an fluid model with two classes of peers, which incorporates an freeriding classes of peers to the fluid model in [4]. 3. Modeling In our model, it has been considered that peers divide into two classes in the BitTorrent system: the nonfree-riders and the free-riders, where each nonfree-riders can provide equal server capacity, and free-riders contribute nothing to the BitTorrent system. A glossary of the model notations and parameters is listed in Table. To simplify model, we assume free-riders will depart the system immediately after they have finished their download and have all pieces of the sharing file, i.e. γ f, because they don t provide any server capacity to the system even if staying in the system. In addition, we assume nonfree-riders will leave the system at once as soon as they have downloaded the sharing file completely, i.e. γ n, so that free-riders can t get behalf from seeds. Because we are interested in the situation, where peers not willing to cooperate and provide more serve capacity. The arrival process of new nonfree-riders and free-riders is modeled as a Poisson process with an arrival rate λ n and λ f respectively, i.e new nonfree-riders and free-riders flow into nonfree-riding download state and free-riding download state respectively with the rate λ n and λ f. The parameter η is used to indicate the efficiency of the file sharing, The nonfree-rider and the free-rider share the total upload resources that is provided by nonfree-riders. Let ρ(t) be the ratio of the total download rate of free-riders to the total upload bandwih in the system at time t, which give a resources assignment criteria. Applying the expression of (2), we have ρ(t) = u x f (t) x n (t) + x f (t) where ρ(t) [, ]. Therefore, the total download rate provided to nonfree-riders is µ( ρ(t))ηx n (t), and the to- (3) /6 $2. 26

3 Table. notations and model parameters x n (t) number of nonfree-riders in the system at time t x f (t) number of free-riders in the system at time t y(t) number of seeds in the system at time t λ n the arrival rate of the new nonfree-riders λ f the arrival rate of the new free-riders µ the upload bandwih of a nonfree-rider, including the seeds c the download bandwih of a peer, including the nonfree-rider and the free-rider, c µ θ the abort rate of downloaders γ n the departure rate of seeds γ f the departure rate of free-riders after they have finished their download η the efficiency of the file sharing ρ(t) the percentage of the total download rate of free -riders to the total upload rate in system at time t tal download rate provided to free-riders is µρ(t)ηx n (t). We assume that network capacity is assumed to be unconstrained, i.e. there is no constraint on download rate. θx n (t) and θx f (t) are the rate at which nonfree-riders and free-riders depart nonfree-riding download state and freeriding download state respectively without having download the entire file. Hence, the rate of change of the number of nonfree-riders and free-riders is given by the following equations: dx n (t) dx f (t) = λ n θx n (t) µ( ρ(t))ηx n (t) = λ f θx f (t) µρ(t)ηx n (t) (4) Equations (4) define a simple description of the evolution for two states of this system dynamics. 3.2 Steady-State Performance Measures To study the system in steady-state performance, we assume that lim n x n (t), and lim n x f (t) exist. Under steady state t, we have dxn(t) = dx f (t) =. To simplify modeling, we assume that the download peer will never abort the system, i.e. θ =. Hence, steady state equations are given by where = λ n µ( ρ)η x n ) = λ f µ ρη x n (5) ρ = u x f x n + x f (6) where ρ is the equilibrium values of ρ(t) and ρ [, ]. Solving Equations (5), we have x n = λ n α, x f = λ f u α (7) where α = λ f λ n+λ f, and u > α. In (7), we see that the Equations (5) has a unique solution, and the system exists a equilibrium point ( x n, x f ). However, if u < α, the value of x f is a negative, which don t accord with realistic situation, and the free-rider has not a equilibrium value. In [4], the Little s law [7] was used to evaluate the average download time for a peer in steady state as λ θ x λ x = (λ θ x)t (T is the average download time). Similarly, in our model, the average download time of the nonfreerider and the free-rider in the system is given respectively by T n = xn λ n, and T f = x f λ f. The probability that a peer who just completes its download job is a free-rider is ρ, and the probability that it is a nonfree-rider is ( ρ). Therefore, the average download time of the system is given by T = ( ρ)t n + ρt f. So we have: T n = α, Tf = u α T = µη [ + (8) ] uα where T n and T f is the average download time of the nonfree-rider and the free-rider respectively, and T is the average download time of the system. 3.3 Model Analysis and Discussion The Average Download Time α Figure. The average download time of the nonfree-rider, the free-rider and the system with varying α The model coupled with an efficient solution method provides us with the ability to explore performance of the system, and capture the effect of free-riding in a BitTorrent system. Figure plots the average download time T n T f T /6 $2. 26

4 of nonfree-riders, free-riders and system with varying the value of α, given the number of uploading connections of a peer u as 5 []. From the modeling results, we observe that the average download time of free-riders T f is always larger than the average download time of nonfreeriders T n, and there is a sharp increase in T f as increasing of α while T n also increases but it is not dramatic and little change when α isn t very large. In addition, when α.2, i.e. u, free-riders has not the average download time, i.e. some free-riders can t download the file completely. This is because that with increasing of α, there will be less peer to contribute service resources. So free-riders don t get enough downloading rate to download the entire file, whereas nonfree-riders can always finish its download job, except that α =. It is shown that BitTorrent mechanisms are successful to guard against free-riding, and free-riding don t great influence to performance of nonfree-riders in a no seed BitTorrent system. 4. System Dead In a BitTorrent system, since all peer download a sharing file cooperatively, the number and the distribution of the sharing file play a important role in service availability. If there is no complete copy of the sharing file in the system, downloaders of the system cannot complete downloading, which is called system dead. The seed who have all pieces of the sharing file ensure the availability of the file. When all seeds leave the system, not less than a copy of all pieces of the sharing file should be hold by a certain online peer, in order to avoid system dead. However, with evolution of a BitTorrent system, more and more peers will depart the system and less and less peer will arrive the system, so there are less and less service availability in the system, and the system tend to dead. In this section, we discuss the effect of free-riding to system dead in a BitTorrent system. We assume that, in the steady state of the system, the initial seed exits the system, and the peer will depart the system immediately as soon as it has downloaded the sharing file completely, i.e. there are no seed in the system, γ. Let G n {p, p,..., p xn } and G f {q, q,..., q xf } be a set of the nonfree-rider and a set of the free-rider in the system, where x n is the number of nonfree-riders, and x f is the number of free-riders in G. We assume that a sharing file is broken into N pieces. Let M{m, m,..., m N } be a set of all pieces of the sharing file. Suppose n, n,..., n N is the number of the online peer that hold piece m, m,..., m N, i.e. piece m i is distributed in n i peers. Let M i {s, s,..., s ni } be a set of peers that hold piece m i (i =,,..., N ). Free-riders share nothing to the system. The system will be dead if there is not one copy of anyone piece m i M in all nonfree-riding peers. The probability that a peer who just finish download a piece m i is the free-rider is ρ, and the probability that anyone copy of piece m i is held by free-rider is ( ρ) ni, so the probability that at least a copy of piece m i is held by nonfreeing peers is [ ( ρ) ni ]. The probability P of system dead is given by P = P [s.t. M i (i =,,..., N ), M i G n = ] = P [s.t. M i (i =,,..., N ), M i G n ] N = P [s.t. s j M i (j =,,..., n i ), s j G n ] i= N = ( P [s.t. s j M i (j =,,..., n i ), s j G f ]) i= N = [ ( ρ) ni ] (9) i= A local rarest first policy is employed to select which piece to download in the BitTorrent system, which ensure a uniform distribution of pieces among all online peers. Hence, we assume that all pieces of the sharing file have equal copy in the steady state of the system, i.e. n = n =... = n N = n. Figure 2 plots the probability of system dead with different the value of n and ρ, given N = 5 and n [, 25]. The probability P of system dead n 5 A Figure 2. The probability P of system dead when N = 5 From the result in Figure 2, we can observe that the probability P of system dead will increase as the value of ρ increase. According as the expression (9), we know the ratio of free-riders in the system in direct proportion to ρ, so the more free-riders implies the higher the probability of system dead. This is because that, with increase the ratio of free-riders in a BitTorrent system, service availability of the total system will decrease gradually because the free-rider don t provide any service capacity to the system while it can get service resource, which induce system dead. In addition, we also find that the probability P of system dead B.2.4 ρ /6 $2. 26

5 is relate to the value of n, i.e the number of copy of each piece in the system. With increase the number of copy of each piece, the probability P of system dead will decrease sharply. From analysis in section III, we know that ρ = α, and α < u. If we set the number of uploading connections u of a peer as 5, we have ρ <.2. In Figure 2, we plot the probability of system dead with different the value of n by using a set of black solid dot, given ρ =.2. In a worst situation, when there has only a copy of every piece in the system, i.e n = n = n =... = n N =, the probability of system dead is very high which is close to, as shown point A in Figure 2. However, the probability P of system dead will decrease sharply as the value of n increase. When n = 5, the probability P of system dead is close to, as shown point B in Figure 2. From the modeling results, we find that free-riding can induce system dead. However, system dead can be avoided as long as the system manage to keep a definite small quantityof copies of each piece in the system. 5. Related Work The BitTorrent system have been analyzed as well as measurement-based. A lot studies have been performed on the measurement and modeling of BitTorrent-like network. Many Measurement studies [8][9][] based on real world applications and simulations for BitTorrent characterize the BitTorrent system. In order to understand the performance of P2P file sharing system, many models[4][5][6][][2] have been presented. Our model for BitTorrent is influenced by above models. We use a simple fluid model framework in [4] and two classes of peers idea to investigate the effect of free-riding in a BitTorrent system. Although [2] presents also two different capacity classes fluid model for BitTorrent system, but [2] adopt a static resource allocation strategy, while our model study on dynamic resource allocation, where resources assignment criteria depend on BitTorrent mechanism completely. There are some study [3][3][4][5] on free-riding in P2P file sharing system. Study [3] is the first study that point out the degree of free-riding in Gnutella. Study[3] discusses that free-riding can be sustainable in equilibrium and may even occur as part of the socially optimal outcome. Study [4] devises a simple model to study the phenomenon of free-riding and the effect of free identities on user behavior in peer-to-peer systems. In [5], the free-riding behavior in the Maze system is studied. 6 Conclusion In this paper, a fluid model of two classes peers is used to capture the effect of free-riding in a BitTorrent system. With the model, we explore how does free-riding influenced the BitTorrent system. Model results shown that BitTorrent mechanism is successful to guard against free-riding. Free-riding don t great influence to performance of nonfreeriders. Finally, we discuss the dying process of a BitTorrent system and the probability of system dead that is induced by free-riding. Although free-riding can induce system dead, system dead can be avoided as long as the system manage to keep a small quantity of copies of each piece in the system. References [] B. Cohen, Incentives Build Robustness in BitTorrent, in Proc. P2P Economics Workshop, 23. [2] A. Parker, The true picture of peer-to-peer filesharing, 24 Available at: [3] E. Adar and Bernardo A. Huberman, Free riding on Gnutella, First Monday, 5(), October 2. [4] D. Qiu and R. Srikant, Modeling and performance analysis of BitTorrent-like peer-to-peer networks, in Proc. ACM Sigcomm, Portland, OR, Aug. 24. [5] X. Yang and G. de Veciana, Service Capacity of Peer to Peer Networks, In Proc. IEEE INFOCOM, 24. [6] Z. Ge, D. R. 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