Andrés Ferragut

Network resource allocation for users with multiple connections: fairness and stability

This paper studies network resource allocation between users that manage multiple connections, possibly through different routes, where each connection is subject to congestion control. We formulate a user-centric Network Utility Maximization problem that takes into account the aggregate rate a user obtains from all connections, and we propose decentralized means to achieve this fairness objective. In a first proposal, cooperative users control their number of active connections based on congestion prices from the transport layer to emulate suitable primal-dual dynamics in the aggregate rate; we show this control achieves asymptotic convergence to the optimal user-centric allocation. For the case of noncooperative users, we show that network stability and user-centric fairness can be enforced by a utility-based admission control implemented at the network edge. We also study stability and fairness issues when routing of incoming connections is enabled at the edge router. We obtain in this case a characterization of the stability region of loads that can be served with routing alone and a generalization of our admission control policy to ensure user-centric fairness when the stability condition is not met. The proposed algorithms are implemented at the packet level in ns2 and demonstrated through simulation.

Network Stability Under Alpha Fair Bandwidth Allocation With General File Size Distribution

Rate allocation among a fixed set of end-to-end connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alpha-fair bandwidth allocation. This paper studies the slower dynamics of connections themselves, that arrive randomly in the network and are served at the allocated rate. It has been shown that under the condition that the mean offered load at each link is less than its capacity, the resulting queueing system is stochastically stable, for the case of exponentially distributed file-sizes. The conjecture that the result holds for general file-size distributions has remained open, and is very relevant since heavy-tailed distributions are often the best models of Internet file sizes. In this paper, building on existing fluid models of the system, we use a partial differential equation to characterize the dynamics. The equation keeps track of residual file size and therefore is suitable for general file size distributions. For alpha fair bandwidth allocation, with any positive alpha parameter, a Lyapunov function is constructed with negative drift when the offered load is less than capacity. With this tool we answer the conjecture affirmatively in the fluid sense: we prove asymptotic convergence to zero of the fluid model for general file-size distributions of finite mean, and finite-time convergence for those of finite moment. In the stochastic sense, we build on recent work that relates fluid and stochastic stability subject to a certain light-tailed restriction. We further provide the supplementary fluid stability argument to establish the conjecture for this class that includes phase-type distributions. Results are supplemented by illustrative network simulations at the packet level.

Quality of service parameters and link operating point estimation based on effective bandwidths

This work addresses the estimation and calculation of the operating point of a networks link in a digital traffic network. The notion of operating point comes from effective bandwidth (EB) theory. The results shown are valid for a wide range of traffic types. We show that, given a good EB estimator, the operating point, i.e. the values of time and space parameters in which the EB is related with the asymptotic overflow probability, can also be accurately estimated. This means that the operating point (and other parameters) inherits the statistical properties of the EB estimation. This affirmation is not an obvious one, because operating point parameters are related with the EB through an implicit function involving extremal conditions computations. Imposing some regularity conditions, a consistent estimator and confidence regions for the operating point and Quality of Service parameters are developed. These conditions are very general, and they are met by commonly used estimators as the averaging estimator presented in [C. Courcoubetis, R. Weber, Buffer overflow asymptotics for a switch handling many traffic sources, J. Appl. Probability 33 (1996)] or the Markov Fluid model estimator presented in [J. Pechiar, G. Perera, M. Simon, Effective bandwidth estimation and testing for Markov sources, Perform. Eval. 48 (2002) 157-175]. Using a software package developed by our group that estimates the EB and other relevant parameters from traffic traces, simulation results are compared with the analytical results, showing very good fitting.

Optimizing TTL Caches under Heavy-Tailed Demands

In this paper we analyze the hit performance of cache systems that receive file requests with general arrival distributions and different popularities. We consider timer-based (TTL) policies, with differentiated timers over which we optimize. The optimal policy is shown to be related to the monotonicity of the hazard rate function of the inter-arrival distribution. In particular for decreasing hazard rates, timer policies outperform the static policy of caching the most popular contents. We provide explicit solutions for the optimal policy in the case of Pareto-distributed inter-request times and a Zipf distribution of file popularities, including a compact fluid characterization in the limit of a large number of files. We compare it through simulation with classical policies, such as least-recently-used and discuss its performance. Finally, we analyze extensions of the optimization framework to a line network of caches.

Network Bandwidth Allocation via Distributed Auctions with Time Reservations

This paper studies the problem of allocating network capacity through periodic auctions. We impose the following conditions: fully distributed solutions over an arbitrary network topology, and the requirement that resources allocated in a given auction are reserved for the entire duration of the connection, not subject to future contention. Under these conditions, we study the problem of selling capacity to optimize revenue for the operator. We first study optimal revenue for a single distributed auction in a general network. Next, the periodic auctions case is considered for a single link, modelling the optimal revenue problem as a Markov decision process (MDP); we develop a sequence of receding horizon approximations to its solution. Combining the two approaches we formulate a receding horizon optimization of revenue over a general network topology, that yields a distributed implementation. The proposal is demonstrated through simulations.

PDE models for population and residual work applied to peer-to-peer networks

This paper studies partial differential equations that have recently been proposed as fluid models for queueing networks, where both populations and residual workloads must be accounted for. After reviewing these models in general, we focus on an application to peer-to-peer networks, where the dynamics must keep track of the download progress of a population of peers as content propagates among them through file sharing. Applying control-theoretic methods to this PDE yields a series of analytical results, in particular: local stability analysis of the equilibrium is proved through a small-gain argument on an appropriate feedback loop; variability around this equilibrium in the presence of random noise is analyzed through the frequency domain; and transient studies are performed to compute completion times.

Achieving network stability and user fairness through admission control of TCP connections

This paper studies a network under TCP congestion control, in which the number of flows per user is explicitly taken into account. We present a control law for this variable that, in combination with congestion control, induces as equilibrium the maximization of social welfare measured at the level of users, rather than the level of TCP connections. We use fluid flow models to prove stability theorems on the dynamics of the overall system, combining the dynamics of flows with the dynamic rates and prices of congestion control. We then develop an admission control policy for discrete TCP flows, that emulates the continuous behavior, and is modeled as a Markov chain. We present simulation studies of the overall system, which exhibit its stability and the desired user-level fairness behavior.

Dynamics of content propagation in BitTorrent-like P2P file exchange systems

Peer to peer file exchange systems such as BitTorrent are changing the way in which content is distributed in the Internet. Service capacity for a certain content adjusts dynamically as a function of peer population, thus achieving scalability. This dynamic behavior has been the subject of recent analytical studies. In this paper, we propose a partial differential equation model for BitTorrent-like systems, in which a fluid variable represents content and its distribution in the system is taken into account. This model allows for a variety of file sharing disciplines; we identify equilibrium properties that must hold regardless of this choice, and others that depend on a notion of efficiency. The equilibrium properties of many specific disciplines are described. Through a discretized ordinary differential equation model, we also present results on the stability of the equilibrium for a particular sharing policy that is suitable to model current BitTorrent systems.

Fluid Models of Population and Download Progress in P2P Networks

This paper studies partial differential equation (PDE) models for the dynamics of peer-to-peer (P2P) file-sharing networks. Using as independent variables time and a fluid measure of residual work, our PDE model tracks the population profile of the P2P swarm, allowing for general file-size distributions. Focusing on the processor-sharing discipline, which we validate as an accurate model of homogeneous P2P networks, we provide a series of analytical results invoking tools of feedback control theory. We establish local stability of the equilibrium, analyze variability around this equilibrium, and compute transient response times, all of which are shown to match tightly with simulation results for a full packet-level implementation of the BitTorrent protocol. We also extend our model to heterogeneous bandwidth scenarios, and to the case of peers contributing to the system after they finish download.

Controlling aggregates of deferrable loads for power system regulation

This paper considers the role of a demand aggregator that manages a large number of consumer loads, with the objective of participating in the frequency regulation market. The key feature to be exploited is load deferrability in time, which enables the aggregator to adapt the consumption profile and thus reduce its own consumption of regulation, and even be a provider of regulation services to others. Rather than a microscopic model that considers individual loads and their scheduling, we consider here a macroscopic viewpoint drawn from fluid models of queueing systems. Here the state variable is the quantity of currently dispatchable loads, and the control input dictates the fraction of those which are currently active. The dynamics is a simple nonlinear ODE that allows us to design a controller with a feedforward term to track an external regulation reference, and a feedback term to reduce the impact of random load oscillations, in an agnostic way to the microscopic scheduling. The performance of this controller is evaluated by simulation using practical regulation signals.