Bandwidth Trading in Unstructured P2P Content Distribution Networks

Transcription

1 Bandwidth Trading in Unstructured P2P Content Distribution Networks Kolja Eger and Ulrich Killat Department of Communication Networks Hamburg University of Technology (TUHH) {eger, Abstract Bandwidth trading schemes give peers an incentive to provide upload bandwidth to other peers in a P2P network for fast file distribution. A popular example is the tit-fortat strategy used in the BitTorrent protocol. Although this game theoretical scheme provides an incentive to peers to contribute resources to the network it does not prevent unfairness and the performances of peers vary considerably. Therefore, we propose two new trading schemes, which are based on pricing. One uses explicit price information whereas the other scheme uses the download rates from other peers as the price. For both distributed algorithms the stable point provides a fair resource allocation as well as a Nash Equilibrium. I.e. fairness is preserved although peers behave selfishly and try to maximise their own download rates only. We compare both pricing schemes with BitTorrent in simulations of static and dynamic networks. The pricing algorithms outperform BitTorrent with respect to fairness. With explicit prices the download rates converge faster to the fair equilibrium than with implicit ones. Introduction The Peer-to-Peer (P2P) paradigm offers obvious advantages for the fast distribution of large content in the Internet. While in the client/server architecture the total load must be carried by the server(s), it is distributed across the users in a P2P network. But the cooperation of peers is not a matter of course. P2P faces the problem of free-riding [] where peers consume resources solely without contributing anything to the network. Therefore, reputation systems and/or incentive mechanisms are implemented in P2P applications frequently. A very interesting approach is the so-called swarming principle. Here, the file of interest is fragmented into blocks. When a peer completes the download of a single block, it offers it to other peers that so far have not downloaded this block. Thus, peers exchange blocks with each other although they did not finish the download of the complete file. Therefore, the resources in the P2P network are used more efficiently and the network depends not solely on the altruistic or cooperative behaviour of the peers. The swarming principle rather exploits the two-way interest of peers in different blocks, which the other one provides. Since most of the peers behave selfishly and are interested in maximising their own download rates, the mutual interest results in peers, which bargain for bandwidth with each other. Hence, the swarming principle supports also content distribution in a non-cooperative environment. A very popular example is the BitTorrent protocol [3] where a peer uploads to others from which it receives the highest download rates. This strategy is inspired by the tit-for-tat principle that is well known from game theory. Here, a player adopts the strategy, which his opponent used in the previous round. By cooperating in the first step the tit-fortat strategy proved very effective in the repeated prisoner s dilemma []. Unfortunately, simulation-based studies for BitTorrent reveal a high variability in the download rates [7] and unfairness in terms of the ratio of uploaded to downloaded data [2]. This means that some peers are better off by using the tit-for-tat strategy than the others. These results raise two questions. Firstly, from the user perspective: Does another strategy exist which outperforms BitTorrent s tit-for-tat strategy? This means with such kind of strategy a user can increase its download performance. Since the total capacity in the network is finite this happens at the expense of others. Secondly, from the angle of a protocol designer: Does a strategy exist which ensures fairness between peers although peers behave selfishly? This work tries to answer the second question. Thereby, we compare BitTorrent s titfor-tat mechanism with two bandwidth trading schemes. In both trading schemes we assume that a peer knows its upload capacity and can freely distribute this upload capacity over its connections to other peers. In the first proposed trading scheme each peer receives a (virtual) payment for

2 uploading data to others. These payments control the sending rates in the future. Peers with higher price offers will receive higher rates whereas the rate will decrease for peers with lower price offers. Furthermore, the total payments a peer can afford is limited to its own upload capacity. We will show that such an algorithm converges to a fair distribution of the available upload bandwidth in the network weighted by the upload bandwidth of a peer. In the second trading scheme peers use their download rates from other peers as the payment information. Thus, no explicit pricing must be implemented in the protocol. It should be noted that a trading scheme is only one of the building blocks of a P2P protocol. Since every peer starts with no block at the beginning a good implementation has to ensure that new peers have a decent chance to finish their first block fast. Therefore, altruistic behaviour of some peers is essential or further incentive mechanisms are needed in the network (e.g. based on the reputation of peers). Furthermore, the selection of blocks to download is important for the future exchange with other peers. The BitTorrent protocol implements a rarest-first strategy where each peer determines the rarest block of its neighbours and requests this block if available. Different papers show the efficiency of this model analytically [] or by simulation [2]. Additionally, new coding schemes resolve the block selection problem [5]. By exchanging linear combinations of all the blocks a peer stores, the probability that two peers have nothing of interest for the other one is reduced significantly. We concentrate in this work on the discussion and the detailed comparison of different trading schemes. The paper is structured as follows. Section 2 discusses the trading schemes and the Nash Equilibria of them. In Section 3 the setup of the simulation is described. The results of the simulations are presented and discussed in Section 4. Section 5 concludes the paper. 2 Trading Schemes We study bandwidth trading schemes which provide an incentive to contribute to the P2P content distribution network. Each peer tries to maximise its own download rate by appropriately allocating its upload bandwidth to other peers. The first scheme is a game theoretical approach and is used in the BitTorrent protocol. The other two schemes are based on pricing models. Thereby, both pricing algorithms use rate control at the application layer. In an real implementation this can be realised by the application putting different amounts of data into the socket buffers of the TCP connections. A more sophisticated approach is to schedule the traffic directly at the queue of the network interface card, e.g. with Linux Traffic Control [6]. 2. BitTorrent s Tit-for-Tat In BitTorrent each peer controls to whom it uploads data. This is called unchoking. A peer uploads to a fixed number of other peers (the default value is four). Thereby, a peer chooses the upload candidates from which it has the highest download rates. This tit-for-tat strategy is run every ten seconds by every peer, whereby the download rates are determined by a moving average over the last 2 seconds. To discover new peers with better performance a so-called optimistic unchoke is done additionally. Here, a peer is unchoked independently of its rate. The optimistic unchoke is changed every 3 seconds to provide enough time to be possibly unchoked by the remote peer in return. When a peer has completed the download of the file, unchoking is based on its upload rates to the connected peers. This unchoking algorithm gives peers an incentive to upload data to the network since it increases the chance to be unchoked by others with increasing upload capacity. Details about the BitTorrent protocol can be found in [3]. 2.2 Resource Pricing We proposed in [4] a distributed algorithm for a fair resource allocation. This algorithm can be applied to P2P content distribution networks whereas the upload bandwidth is the scarce resource. In our model each peer pays a virtual price for using upload bandwidth at a remote peer. The sum of all prices a peer can afford to pay is bounded by its willingness-to-pay. For P2P file-sharing this willingnessto-pay is the upload bandwidth of a peer. This model gives an incentive to contribute to the network since a peer with a high upload capacity can offer higher prices than others and therefore receives a higher download rate. The distributed algorithm is explained in the following. Assume each peer allocates an upload capacity to the P2P application which is denoted as at peer p. Furthermore, peer p can upload to a number of peers which are interested in a block which peer p offers. This set of peers is denoted as the service customers SC(p) of p. Each interested peer offers a price λ c per unit of upload bandwidth. Based on these prices peer p sets the upload rate x pc to the remote peer c. Furthermore, the price offer of an interested peer is proportional to its upload capacity. Hence, the resource pricing algorithm is the set of differential equations RESOURCE PRICING (RP) : ( d dt x pc(t) =γx pc (t) λ c (t) x ) pd(t)λ d (t) λ c (t) = () C c p SP(c) x pc(t), (2)

3 where SP(c) denotes the set of peers in which peer c is interested in. Thus, the denominator of (2) is the total download rate of peer c. (Furthermore, two exceptional cases have to be considered in a real implementation. When the total download rate of a peer is zero, we set λ c (t) =C c. And secondly, when λ c (t) > but x pc (t) = we set x pc (t +)=ɛ where ɛ is a small positive constant.) () can be interpreted as follows. Since λ c is the price per unit of bandwidth, the product x pc λ c is the total price which is payed by peer c. According to this the sum in the numerator of () represents the total revenue of peer p. Multiplying the total revenue by xpc specifies the average revenue peer p generates by allocating the rate x pc. If the total price of peer c is higher than the average price (i.e. the left term in the bracket of () is greater than the right one), then peer p increases its upload rate to c and decreases it otherwise. Further on, when we assume that two peers receive different download rates although they provide the same upload capacity to the network we see from (2) that the peer with the smaller download rate will offer a higher price per unit in the future than the other one. Hence, its download rate will increase. The equilibrium of the system (-2) can be determined by setting () to zero. Thus, the total download rate for a peer c in equilibrium is [4] y c = p SP(c) x pc = C c p P d SC C d, (3) where SC is the set of peers which currently download the file and P is the set of all peers in the network, i.e. also including the seeds, peers which stay altruistically in the network after completion of their download. It can be seen from (3) that the download rates of the peers are proportional to their upload capacity and the bandwidth allocation is fair weighted by the contribution of each peer. When no peer behaves altruistically (3) reduces to y c = C c. 2.3 Reciprocal Rate Control The resource pricing algorithm in Section 2.2 assumes the correct signalling of the price offers. Thus, an implementation must ensure that malicious users cannot forge their price offers to obtain higher download rates. When this is not possible in a specific application, an upload rate control algorithm can only be based on the download rates of the connected peers (like in BitTorrent). In the context of pricing mechanisms the download rates can be interpreted as the price a remote peer is willing to pay for the upload bandwidth allocated to it. In the resource pricing algorithm the total price paid by the remote peer is the product x pc λ c. Hence, by replacing x pc λ c with the rate x cp in () we obtain a reciprocal rate control algorithm using an implicit pricing signal RECIPROCAL RATE CONTROL (RRC) : ( d dt x pc(t) =γ x cp (t) x pc (t) x ) dp(t) In the following we prove that the proposed algorithm fully utilises the upload capacity under the assumption that in the previous step all resources are used. Therefore, we sum up over all upload rates of peer p x pc (t +) (5) = (4) ( ( x pc (t)+γ x cp (t) x pc (t) x )) dp(t) (6) = x pc (t)+γ x cp (t) x pc (t) x dp(t) = + γ (7) x cp (t) C x dp(t) p (8) = (9) This means when we start with an initial rate allocation which is efficient (e.g. by splitting the upload capacity evenly over all connections) all following rate allocations are efficient as well. Furthermore, we prove that the stable point of the distributed algorithm is efficient by setting (4) to zero = γ (x cp x x ) dp pc () x pc = x x cp () dp x pc = (2) The upload rates in equilibrium can be computed with () and (2) x cp = x x dp pc (3) x cp = x pc (4) In equilibrium a peer uses its full upload bandwidth (cp. (2)) and downloads from a specific peer with the same rate as it is uploading (cp. (4)). Thus, with (2) and (4) the total download rate over all connections is equal to the upload capacity of the peer.

4 The RRC algorithm is restricted to peers that did not complete the download already. It ensures that a peer receives at least the rate, which it provides to the network. Seeds cannot run the RRC algorithm and have to use other rules for their upload. (E.g. these peers can upload to peers, which have nothing at all.) Therefore, an advantage of explicit prices used in Section 2.2 compared to implicit prices is that fairness is preserved also over the altruistically contributed resources in the network. 2.4 Nash Equilibrium Most peers in a P2P network behave selfishly and try to maximise their performance only. Therefore, we can interpret the trading of bandwidth as a non-cooperative game and study the Nash equilibrium. In a Nash equilibrium no peer gains by only changing its strategy while all other players keep their strategy unchanged. This means a Nash equilibrium corresponds to a set of strategies where every player has found the best response to the actions of the other players []. [] studies the Nash equilibrium for the BitTorrent protocol. Thereby, each peer can choose its upload bandwidth between and its physical upload capacity. Since a higher upload bandwidth is associated with a higher cost, a peer is interested primarily in maximising its download rate while also minimising its cost at the same time. [] shows that a Nash equilibrium exists for networks consisting of groups (with a group size larger than the number of unchokes plus one) of peers where peers belonging to the same group have identical upload bandwidths. In this situation the best case for a peer is to upload to other peers in its group. The threshold to be unchoked is exactly the upload bandwidth divided by the number of unchokes (which is assumed to be equal for all peers). Therefore, a peer will be choked by the peers of its group when it reduces its upload bandwidth. This results in inferior performance. On the other hand a Nash equilibrium does not exist when peers have different upload capacities as it is demonstrated by an example in []. In the following we study the Nash equilibria for the two proposed pricing schemes in steady-state. Assume for Resource Pricing that a peer cannot forge its price offer λ. It can be seen directly from (3) that any reduction of upload capacity will result in a decrease of the download rate. When maximising the download rate has priority over minimising the upload cost every peer will upload with its physical upload capacity. Thus, the steady-state of the system (-2) is a Nash equilibrium. Similarly, the existence of the Nash equilibrium for Reciprocal Rate Control can be shown for the steady-state with (4). Since a peer receives exactly the rate, which it provides to the other peer, it gains nothing by reducing its upload bandwidth. 3 Simulation Setup Because of the computational complexity of the simulations at packet-level we restrict our analysis to the application layer. Therefore, the TCP behaviour is omitted. We assume a user sets the maximal upload bandwidth of his P2P application between zero and his physical upload capacity. Furthermore, we assume this is the bottleneck in the network. Since the utilisation in the core of the network is low [9] and access lines are often asymmetric favouring the downlink we believe this is a reasonable assumption. The bandwidth trading schemes depend highly on the number of neighbours and especially on the number of connections where both sides are interested in data blocks of the other side. Thus, the schemes depend on the topology generated by the protocol and the implemented block selection algorithm. To concentrate on the trading schemes in the simulations we omit the block selection algorithm and assume connected peers are always interested in blocks of each other. The overlay topology is constructed in our simulations according the original BitTorrent implementation [3]. Here, a peer asks a so-called tracker, a centralised component that stores information about all peers, for a list of other peers in the network. The tracker returns a random subset of length to the requesting peer. Hence, a peer opens a new connection to a remote peer based on the list returned by the tracker or when a remote peer asks for it. In our simulations we consider static and dynamic P2P networks. In the static case all N P peers are registered at the tracker. Then each peer obtains a peer list from the tracker. If we assume that all peers accept every incoming connection request, a peer p iterates through its peer list and opens connections. Furthermore, one more connection is established when a remote peer which is unknown to p, i.e. not on the peer list of p, contacts it. The probability that x peers contact p is B(x) and follows the binomial distribution ( ) NP B(x) = P x ( P ) NP x, (5) x where P is the probability that peer p is on the peer list of a peer q under the assumption that q is not on the list of p. The probability that a specific peer id is returned by the tracker is based on the hypergeometric distribution and is (N P ) 2 N ( R NP ) = N N P, (6) R when we assume a tracker does not return the id of the requesting peer. Thus, we can compute P with P = N ( R N P N P ). (7)

5 The expectation value E[N C ] of the number of connections N C of a peer is the sum of and the expectation value E[X] of the random variable X which is distributed according (5). Therefore, E[N C ]= + E[X] (8) ( = +(N P ) N ) R (9) N P N P ( = + N ) R (2) N P 2 (2) The approximation in (2) holds if N P. For the simulations with dynamics we model the peer behaviour as a Poisson process, where the interarrival times between peers and the session times of peers are exponentially distributed. The expectation value of the number of peers in the network is E[N P ]= λ µ which depends on the mean arrival rate λ and the mean service rate µ. We assume the tracker returns valid information of online peers only. Since the Poisson process is memoryless a peer which is asked to open a new connection by a remote peer has a remaining session time distributed with mean µ. Therefore, the rate of closing connections for a peer is µ. On the other hand new peers will open a connection to peer p. The probability that peer p is chosen by a new peer is given by (6) and can be estimated with E[N P ]. New peers enter with the rate of λ. Therefore, the rate of opening new N connections is λ R E[N P ]. Hence, the expectation value of the number of connections is λ E[N C ] = (E[N P ] ) µ (22) λ N λ R (23) µ µ = (24) The results of the expected number of connections in the static and the dynamic network in (2) and (24), respectively, are different and deviate by a factor of 2. This has to be taken into account for the simulations where fairness is studied for different values of. 4 Simulation Results 4. Static networks One major difference of the two pricing schemes to Bit- Torrent s tit-for-tat strategy is their convergence to a steadystate. To demonstrate the basic functionality of all algorithms we run a simulation for a small network of peers with homogeneous upload capacities of C =. The superposition of the download rates of the peers is depicted in Figure. Whereas the download rates of the peers oscillate between.4 and.6 for BitTorrent, the rates converge fast to a fair allocation for the Resource Pricing and the Reciprocal Rate Control algorithm where each peer receives exactly its upload capacity. Especially the performance of BitTorrent depends on the number of neighbours. To study the influence of the topology on the download performance simulations are run with varying parameter. The network population was peers, each peer starting with a small random offset to avoid synchronisation effects. The simulation consisted of iterations of the respective algorithm and was repeated 5 times. We set γ =. for RP and RRC and ɛ =.C/N C. The empirical cumulative distribution function (CDF) of the mean download rate over the iterations is depicted over all runs in Figure 2. To compare the three algorithms Figure 2 shows the results for download rates between 5 and.5. With BitTorrent s tit-for-tat algorithm peers receive highly different download rates while providing the same upload capacity. To see its performance in detail Figure 3 shows the CDF for download rates of.5 to 2. Tit-fortat depends on the number of neighbours. With =2a peer has on average four connections only and therefore no choice in selecting peers. This results in a poor performance where % of the peers receive half of what they provide. Download rates are distributed more equitably with increasing.for =all peers receive a mean download rate of ±2% of their upload capacity, whereas this percentage decreases to ±% for =5. Nonetheless, the distribution of download rates with BitTorrent is not as uniformly distributed as with the two proposed pricing algorithms. Nearly all peers receive download rates between 8 and.2 with both algorithms and values of > 2. Furthermore, the download rates at the end of each simulation were equal to one for every peer. This means the pricing algorithms converged. Thus, the differences of the CDFs for different values of in Figure 2(b) and 2(c) are due to differences in the rate of convergence. Because of the slight differences observed in the results we analyse the convergence properties for the case of heterogeneous peers. For the next simulation we consider heterogeneous peers with upload capacities of integers between and. The capacity is determined randomly at the start of the simulation. With a total of peers there are on average peers with the same capacity in the network. The download performance of each peer is measured by the ratio of mean download rate to upload capacity. The CDF of the download performances is depicted for BitTorrent in Figure 4. As expected the download performances of the peers vary more as compared to the simulation results with homogeneous peers. In all four curves some peers receive more

6 Download Rate Download Rate Download Rate Round Round Round (a) BitTorrent (b) Resource Pricing (c) Reciprocal Rate Control Figure. Superposition of the download rates of peers for different trading schemes =.3.2. =.3.2. = (a) BitTorrent (b) Resource Pricing (c) Reciprocal Rate Control Figure 2. for varying parameter =.2. = / Upload Capacity Upload Capacity Figure 3. CDF for BitTorrent Figure 4. CDF for BitTorrent with heterogeneous peers Figure 5. Superposition of mean download rates for Bit- Torrent ( =)

7 5 =5 5 5 Weighted Fairness Index =5 = Weighted Fairness Index =5 = N =5 R N =2 R Weighted Fairness Index N =5 R = =5 N =2 R = Iteration Iteration Iteration (a) BitTorrent (b) Resource Pricing (c) Reciprocal Rate Control Figure 6. Weighted Fairness Index in heterogeneous network than the double compared to what they provide. On the other hand the performance with =5isgood: Only around % of the peers receive a download to upload ratio of less than. This proportion rises to about 5% for =and 3% for =5. The curves of the CDFs for =and =5in Figure 4 rise very slowly for values greater than.5. This suggests that a small fraction of peers have a better performance compared to all others. By looking at Figure 5 we can identify these peers. It can be seen that for Bit- Torrent peers with a upload capacity of C =receive a mean download rate larger than one whereas the peers with C =receive mostly a rate lower than their contribution. One reason for this is the optimistic unchoke since a low capacity peer gains more than it invests compared to a high capacity peer. Another reason is the incapability to find the right match which also explains the different performances between peers with the same capacity. Because of space limitations we omitted the CDFs for the two pricing schemes. They outperform BitTorrent with respect to fairness. The ratio of the mean download rate to the upload capacity is over 8 for all peers for > 2. Only for =2fairness deteriorates and around 2% of the peers have a ratio of less than 5. Since the performances of the pricing algorithms depend on the convergence we measured a variant [4] of Jain s Fairness Index [8] extended to weighted fairness over the simulation time. The results in Figure 6 show for > 2 the convergence to a fair resource allocation for both proposed algorithms in less than 7 iterations. The convergence is better with increasing and better for Resource Pricing than with Reciprocal Rate Control. When =2we observed no convergence even for higher number of iterations. In this case some peers receive an unfair download rate because its small neighbourhood cannot raise the adequate rate with their upload capacity. The weighted fairness index of BitTorrent is below for all studied values of. (It should be noted that a fairness index of corresponds for example to an allocation where % of the peers receive nothing at all and the remaining 9% receive equal rates.) 4.2 Dynamic networks We conducted simulations also for dynamic networks where interarrival times between peers and session times of peers are negative exponentially distributed. We set = and compare the performance for two cases with the same average peer population of. We assume the respective algorithm is run per unit time. The resulting CDFs are depicted in Figure 7(a) and Figure 7(b). Compared to the static case the fairness deteriorates for dynamic networks. Nevertheless, with an arrival process of peers with a rate /λ =, i.e. on average iterations of the algorithm before a new peer enters, the two pricing schemes achieve nearly uniformly distributed download performances for heterogeneous peers. For /λ =infigure 7(b) the CDF shows higher variability in the achieved download performance for the two proposed algorithms. Thereby, the results for Reciprocal Rate Control deteriorate more than for Resource Pricing comparing it with the results in Figure 7(a). Especially for /λ =, /µ = some peers stay only a very short time in the network and merely run the trading algorithm a few times. This results in poor download performance as it can be seen from Figure 7(c). Here, the minima of the download performances of peers with similar session times are measured for time intervals of 25 time units. For all schemes the minimal download performance increases with the session times of the peers. But the increase is more pronounced for the two trading schemes. After around 5 time units the minimal download performance in the net-

8 BitTorrent Resource Pricing Reciprocal Rate Control / Upload Capacity BitTorrent Resource Pricing Reciprocal Rate Control / Upload Capacity MIN( / Upload Capacity )..7.5 BitTorrent Resource Pricing Reciprocal Rate Control Peer Session Time (a) CDF for /λ =, /µ = (b) CDF for /λ =, /µ = (c) Minimal download performance (/λ =, /µ = ) Figure 7. Results for dynamic networks work is above. This indicates that the two distributed algorithms show improved fairness between peers also in varying networks compared to BitTorrent. It should also be noted that the update interval of the pricing algorithms can be adapted to the dynamics of the network as long as the download rates can be estimated accurately. 5 Conclusion BitTorrent s tit-for-tat strategy gives peers an incentive to contribute upload bandwidth to the network. But it cannot avoid unfairness between peers with respect to the experienced download performance. Especially when peers have a small number of connections download rates vary considerably. Furthermore, peers with small upload capacities compared to others receive considerably more than what they contribute to the network. This paper presents two alternatives to improve fairness. Both use price information to control the upload rates at the application layer. We derive that the proposed distributed algorithms achieve in equilibrium a fair and efficient allocation of the total upload bandwidth contributed by the peers in the network. Furthermore, the steady-states of the two schemes provide Nash equilibria. In simulations both algorithms show good convergence and better fairness as the tit-for-tat strategy used in BitTorrent. Each of the two proposed algorithms has its advantages. Reciprocal Rate Control is robust against malicious users since it uses the download rates from other peers as the price information. These cannot be forged. On the other hand Resource Pricing, which uses explicit prices, preserves fairness also for the allocation of the altruistically contributed resources offered by the peers that completed their download already. Additionally, it shows slightly better convergence than Reciprocal Rate Control in the simulations. References [] E. Adar and B. A. Huberman. Free riding on Gnutella. First Monday, 5(), Oct. 2. [2] A. R. Bharambe, C. Herley, and V. N. Padmanabhan. Analyzing and improving BitTorrent performance. Technical Report MSR-TR-25-3, Microsoft Research, 25. [3] B. Cohen. Incentives build robustness in BitTorrent. In Proc. st Workshop on Economics of Peer-to-Peer Systems, Berkeley, June 23. [4] K. Eger and U. Killat. Fair resource allocation in Peer-to- Peer networks. In Proc. 26 International Symposium on Performance Evaluation of Computer and Telecommunication Systems (SPECTS 6), Calgary, Canada, July 26. [5] C. Gkantsidis and P. Rodriguez. Network coding for large scale content distribution. In Proc. IEEE INFOCOM, Miami, March 25. [6] B. Hubert, T. Graf, G. Maxwell, R. van Mook, M. van Oosterhout, P. Schroeder, J. Spaans, and P. Larroy. Linux Advanced Routing & Traffic Control HOWTO. Documentation from [7] M. Izal, G. Urvoy-Keller, E. W. Biersack, P. Felber, A. A. Hamra, and L. Garcés-Erice. Dissecting BitTorrent: Five months in a torrent s lifetime. In Passive and Active Mesurements, pages, April 24. [8] R. Jain. The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling. John Wiley & Sons, 99. [9] A. Odlyzko. Data networks are lightly utilized, and will stay that way. Review of Network Economics, 2(3):2 237, September 23. [] M. J. Osborne. An Introduction to Game Theory. Oxford University Press, 24. [] R. Qiu, D. Srikant. Modeling and performance analysis of BitTorrent-like peer-to-peer networks. Computer Communication Review, 34(4): , 24.