Laurent Massoulié

Bandwidth sharing: objectives and algorithms

This paper concerns the design of distributed algorithms for sharing network bandwidth resources among contending flows. The classical fairness notion is the so-called max-min fairness. The alternative proportional fairness criterion has recently been introduced by Kelly; we introduce a third criterion, which is naturally interpreted in terms of the delays experienced by ongoing transfers. We prove that fixed-size window control can achieve fair bandwidth sharing according to any of these criteria, provided scheduling at each link is performed in an appropriate manner. We then consider a distributed random scheme where each traffic source varies its sending rate randomly, based on binary feedback information from the network. We show how to select the source behavior so as to achieve an equilibrium distribution concentrated around the considered fair rate allocations. This stochastic analysis is then used to assess the asymptotic behavior of deterministic rate adaption procedures.

The effect of network topology on the spread of epidemics

Many network phenomena are well modeled as spreads of epidemics through a network. Prominent examples include the spread of worms and email viruses, and, more generally, faults. Many types of information dissemination can also be modeled as spreads of epidemics. In this paper we address the question of what makes an epidemic either weak or potent. More precisely, we identify topological properties of the graph that determine the persistence of epidemics. In particular, we show that if the ratio of cure to infection rates is larger than the spectral radius of the graph, then the mean epidemic lifetime is of order log n, where n is the number of nodes. Conversely, if this ratio is smaller than a generalization of the isoperimetric constant of the graph, then the mean epidemic lifetime is of order e/sup na/, for a positive constant a. We apply these results to several network topologies including the hypercube, which is a representative connectivity graph for a distributed hash table, the complete graph, which is an important connectivity graph for BGP, and the power law graph, of which the AS-level Internet graph is a prime example. We also study the star topology and the Erdos-Renyi graph as their epidemic spreading behaviors determine the spreading behavior of power law graphs.

Peer-to-peer membership management for gossip-based protocols

Gossip-based protocols for group communication have attractive scalability and reliability properties. The probabilistic gossip schemes studied so far typically assume that each group member has full knowledge of the global membership and chooses gossip targets uniformly at random. The requirement of global knowledge impairs their applicability to very large-scale groups. In this paper, we present SCAMP (Scalable Membership protocol), a novel peer-to-peer membership protocol which operates in a fully decentralized manner and provides each member with a partial view of the group membership. Our protocol is self-organizing in the sense that the size of partial views naturally converges to the value required to support a gossip algorithm reliably. This value is a function of the group size, but is achieved without any node knowing the group size. We propose additional mechanisms to achieve balanced view sizes even with highly unbalanced subscription patterns. We present the design, theoretical analysis, and a detailed evaluation of the basic protocol and its refinements. Simulation results show that the reliability guarantees provided by SCAMP are comparable to previous schemes based on global knowledge. The scale of the experiments attests to the scalability of the protocol.

Epidemic information dissemination in distributed systems

Easy to deploy, robust, and highly resilient to failures, epidemic algorithms are a potentially effective mechanism for propagating information in large peer-to-peer systems deployed on Internet or ad hoc networks. It is possible to adjust the parameters of epidemic algorithm to achieve high reliability despite process crashes and disconnections, packet losses, and a dynamic network topology. Although researchers have used epidemic algorithms in applications such as failure detection, data aggregation, resource discovery and monitoring, and database replication, their general applicability to practical, Internet-wide systems remains open to question. We describe four key problems: membership maintenance, network awareness, buffer management, and message filtering, and suggest some preliminary approaches to address them.

Probabilistic reliable dissemination in large-scale systems

The growth of the Internet raises new challenges for the design of distributed systems and applications. In the context of group communication protocols, gossip-based schemes have attracted interest as they are scalable, easy to deploy, and resilient to network and process failures. However, traditional gossip-based protocols have two major drawbacks: 1) they rely on each peer having knowledge of the global membership; and 2) being oblivious to the network topology, they can impose a high load on network links when applied to wide-area settings. In this paper, we provide a theoretical analysis of gossip-based protocols which relates their reliability to key system parameters (the system size, failure rates, and number of gossip targets). The results provide guidelines for the design of practical protocols. In particular, they show how reliability can be maintained while alleviating drawback by: 1) providing each peer with only a small subset of the total membership information and drawback; and 2) organizing members into a hierarchical structure that reflects their proximity according to some network-related metric. We validate the analytical results by simulations and verify that the hierarchical gossip protocol considerably reduces the load on the network compared to the original, non-hierarchical protocol.

Bandwidth sharing and admission control for elastic traffic

We consider the performance of a network like the Internet handling so‐called elastic traffic where the rate of flows adjusts to fill available bandwidth. Realized throughput depends both on the way bandwidth is shared and on the random nature of traffic. We assume traffic consists of point to point transfers of individual documents of finite size arriving according to a Poisson process. Notable results are that weighted sharing has limited impact on perceived quality of service and that discrimination in favour of short documents leads to considerably better performance than fair sharing. In a linear network, max–min fairness is preferable to proportional fairness under random traffic while the converse is true under the assumption of a static configuration of persistent flows. Admission control is advocated as a necessary means to maintain goodput in case of traffic overload.

Greening the internet with nano data centers

Motivated by increased concern over energy consumption in modern data centers, we propose a new, distributed computing platform called Nano Data Centers (NaDa). NaDa uses ISP-controlled home gateways to provide computing and storage services and adopts a managed peer-to-peer model to form a distributed data center infrastructure. To evaluate the potential for energy savings in NaDa platform we pick Video-on-Demand (VoD) services. We develop an energy consumption model for VoD in traditional and in NaDa data centers and evaluate this model using a large set of empirical VoD access data. We find that even under the most pessimistic scenarios, NaDa saves at least 20% to 30% of the energy compared to traditional data centers. These savings stem from energy-preserving properties inherent to NaDa such as the reuse of already committed baseline power on underutilized gateways, the avoidance of cooling costs, and the reduction of network energy consumption as a result of demand and service co-localization in NaDa.

Stability of distributed congestion control with heterogeneous feedback delays

We investigate how congestion control can achieve efficient usage of network resources in the presence of heterogeneous communication delays between network users and resources. To this end, we consider a fluid flow model of network behavior. We study the stability of the systems behavior under small perturbations around the target equilibrium point (local stability). We establish several criteria for stability of certain linear delay-differential equations, via a technique which essentially reduces the question to studying stability of ordinary differential equations. These results are then used to derive sufficient conditions for local stability of the network congestion control problem. The same issue has been studied by Johari et al. (2001), where the authors propose a conjecture according to which local stability can be ensured in a distributed way. The correctness of the conjecture was established by Johari et al., only in degenerate cases where feedback delays coincide. Our results show that a modified form of the conjecture holds true for arbitrary feedback delays.

Epidemic live streaming: optimal performance trade-offs

Several peer-to-peer systems for live streaming have been recently deployed (e.g. CoolStreaming, PPLive, SopCast). These all rely on distributed, epidemic-style dissemination mechanisms. Despite their popularity, the fundamental performance trade-offs of such mechanisms are still poorly understood. In this paper we propose several results that contribute to the understanding of such trade-offs. Specifically, we prove that the so-called random peer, latest useful chunk mechanism can achieve dissemination at an optimal rate and within an optimal delay, up to an additive constant term. This qualitative result suggests that epidemic live streaming algorithms can achieve near-unbeatable rates and delays. Using mean-field approximations, we also derive recursive formulas for the diffusion function of two schemes referred to as latest blind chunk, random peer and latest blind chunk, random useful peer. Finally, we provide simulation results that validate the above theoretical results and allow us to compare the performance of various practically interesting diffusion schemes terms of delay, rate, and control overhead. In particular, we identify several peer/chunk selection algorithms that achieve near-optimal performance trade-offs. Moreover, we show that the control overhead needed to implement these algorithms may be reduced by restricting the neighborhood of each peer without substantial performance degradation.

A queueing analysis of max-min fairness, proportional fairness and balanced fairness

We compare the performance of three usual allocations, namely max-min fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processor-sharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.