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 2090459604 2145080738 2119200834 2083594366 2136340918
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.