We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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.

/pdf/modeling-and-performance-analysis-of-bittorrent-like-peer-to-k2h0grfstv.pdf

Modeling and performance analysis of BitTorrent-like peer-to-peer networks

Peer-to-peer (P2P) file sharing accounts for an astonishing volume of current Internet traffic. This paper probes deeply into modern P2P file sharing systems and the forces that drive them. By doing so, we seek to increase our understanding of P2P file sharing workloads and their implications for future multimedia workloads. Our research uses a three-tiered approach. First, we analyze a 200-day trace of over 20 terabytes of Kazaa P2P traffic collected at the University of Washington. Second, we develop a model of multimedia workloads that lets us isolate, vary, and explore the impact of key system parameters. Our model, which we parameterize with statistics from our trace, lets us confirm various hypotheses about file-sharing behavior observed in the trace. Third, we explore the potential impact of locality-awareness in Kazaa.Our results reveal dramatic differences between P2P file sharing and Web traffic. For example, we show how the immutability of Kazaa's multimedia objects leads clients to fetch objects at most once; in contrast, a World-Wide Web client may fetch a popular page (e.g., CNN or Google) thousands of times. Moreover, we demonstrate that: (1) this "fetch-at-most-once" behavior causes the Kazaa popularity distribution to deviate substantially from Zipf curves we see for the Web, and (2) this deviation has significant implications for the performance of multimedia file-sharing systems. Unlike the Web, whose workload is driven by document change, we demonstrate that clients' fetch-at-most-once behavior, the creation of new objects, and the addition of new clients to the system are the primary forces that drive multimedia workloads such as Kazaa. We also show that there is substantial untapped locality in the Kazaa workload. Finally, we quantify the potential bandwidth savings that locality-aware P2P file-sharing architectures would achieve.

/pdf/measurement-modeling-and-analysis-of-a-peer-to-peer-file-xvfiidz1ky.pdf

Measurement, modeling, and analysis of a peer-to-peer file-sharing workload

A super-peer is a node in a peer-to-peer network that operates both as a server to a set of clients, and as an equal in a network of super-peers. Super-peer networks strike a balance between the efficiency of centralized search, and the autonomy, load balancing and robustness to attacks provided by distributed search. Furthermore, they take advantage of the heterogeneity of capabilities (e.g., bandwidth, processing power) across peers, which recent studies have shown to be enormous. Hence, new and old P2P systems like KaZaA and Gnutella are adopting super-peers in their design. Despite their growing popularity, the behavior of super-peer networks is not well understood. For example, what are the potential drawbacks of super-peer networks? How can super-peers be made more reliable? How many clients should a super-peer take on to maximize efficiency? we examine super-peer networks in detail, gaming an understanding of their fundamental characteristics and performance tradeoffs. We also present practical guidelines and a general procedure for the design of an efficient super-peer network.

Designing an Super-Peer Network

We study a map of the Internet (at the autonomous systems level), by introducing and using the method of k-shell decomposition and the methods of percolation theory and fractal geometry, to find a model for the structure of the Internet. In particular, our analysis uses information on the connectivity of the network shells to separate, in a unique (no parameters) way, the Internet into three subcomponents: (i) a nucleus that is a small (≈100 nodes), very well connected globally distributed subgraph; (ii) a fractal subcomponent that is able to connect the bulk of the Internet without congesting the nucleus, with self-similar properties and critical exponents predicted from percolation theory; and (iii) dendrite-like structures, usually isolated nodes that are connected to the rest of the network through the nucleus only. We show that our method of decomposition is robust and provides insight into the underlying structure of the Internet and its functional consequences. Our approach of decomposing the network is general and also useful when studying other complex networks.

/pdf/a-model-of-internet-topology-using-k-shell-decomposition-14or47o11j.pdf

A model of Internet topology using k-shell decomposition.

Peer-peer networking has recently emerged as a new paradigm for building distributed networked applications. We develop simple mathematical models to explore and illustrate fundamental performance issues of peer-peer file sharing systems. The modeling framework introduced and the corresponding solution methods are flexible enough to accommodate different characteristics of such systems. Through the specification of model parameters, we apply our framework to three different peer-peer architectures: centralized indexing, distributed indexing with flooded queries, and distributed indexing with hashing directed queries. Using our model, we investigate the effects of system scaling, freeloaders, file popularity and availability on system performance. In particular, we observe that a system with distributed indexing and flooded queries cannot exploit the full capacity of peer-peer systems. We further show that peer-peer file sharing systems can tolerate a significant number of freeloaders without suffering much performance degradation. In many cases, freeloaders can benefit from the available spare capacity of peer-peer systems and increase overall system throughput. Our work shows that simple models coupled with efficient solution methods can be used to understand and answer questions related to the performance of peer-peer file sharing systems.

/pdf/modeling-peer-peer-file-sharing-systems-1hdpsg5fxp.pdf

Modeling peer-peer file sharing systems

We propose a passive measurement methodology to infer and keep track of the values of two important variables associated with a TCP connection: the sender's congestion window (cwnd) and the connection round trip time (RTT). Together, these variables provide a valuable diagnostic of end-user-perceived network performance. Our methodology is validated via both simulation and concurrent active measurements, and is shown to be able to handle various flavors of TCP. Given our passive approach and measurement points within a Tier-1 network provider, we are able to analyze more than 10 million connections, with senders located in more than 45% of the autonomous systems in today's Internet. Our results indicate that sender throughput is frequently limited by a lack of data to send, that the TCP congestion control flavor often has minimal impact on throughput, and that the vast majority of connections do not experience significant variations in RTT during their lifetime

/pdf/inferring-tcp-connection-characteristics-through-passive-4ysxrzq2w1.pdf

Inferring TCP connection characteristics through passive measurements

IEEE 802.16e WiMAX is a promising new technology for broadband access networks. Amongst the class of applications that can be supported is real time video services (such as IPTV, broadcast of live events etc.). These applications are bandwidth hungry and have stringent delay constraints. Thus, scalable support for such applications is a challenging problem. To address this challenge, we consider a combination of approaches using multicast, layer encoded video and adaptive modulation of transmissions. Using these, we develop algorithms to ensure efficient, fair and timely delivery of video in WiMAX networks. The corresponding resource allocation problem is challenging because scheduling decisions (within a WiMAX base station) are performed in real-time across two dimensions, time and frequency. Moreover, combining layered video with appropriate modulation calls for novel MAC algorithms. We model the multicast resource allocation problem in WiMAX and demonstrate this problem to be NP-hard. We present a fast greedy algorithm that is (i) provably within a constant approximation of the optimal solution (based on a metric that reflects video quality as perceived by the user), and (ii) performs within 87-95% of the optimal as demonstrated by realistic simulations. We also demonstrate that our algorithm offers a 25% improvement over a naive algorithm. Moreover, in terms of the average rate received by each user, our algorithm out-performs the naive algorithm by more than 50%.

Real-Time Video Multicast in WiMAX Networks

We present a classification methodology and a measurement study for out-of-sequence packets in TCP connections going over the Sprint IP backbone. Out-of-sequence packets can result from many events including loss, looping, reordering, or duplication in the network. It is important to quantify and understand the causes of such out-of-sequence packets since it is an indicator of the performance of a TCP connection, and the quality of its end-end path. Our study is based on passively observed packets from a point inside a large backbone network--as opposed to actively sending and measuring end-end probe traffic at the sender or receiver. A new methodology is thus required to infer the causes of a connection's out-of-sequence packets using only measurements taken in the "middle" of the connection's end-end path. We describe techniques that classify observed out-of-sequence behavior based only on the previously- and subsequently-observed packets within a connection and knowledge of how TCP behaves. We analyze numerous several-hour packet-level traces from a set of OC-12 and OC-48 links for tens of millions connections generated in nearly 7600 unique ASes. We show that using our techniques, it is possible to classify almost all out-of-sequence packets in our traces and that we can quantify the uncertainty in our classification. Our measurements show a relatively consistent rate of out-of-sequence packets of approximately 4%. We observe that a majority of out-of-sequence packets are retransmissions, with a smaller percentage resulting from in-network reordering.

Sharad Jaiswal

Papers

Modeling peer-peer file sharing systems

Inferring TCP connection characteristics through passive measurements

Real-Time Video Multicast in WiMAX Networks

Measurement and classification of out-of-sequence packets in a tier-1 IP backbone

Measurement and classification of out-of-sequence packets in a tier-1 IP backbone