Jean-Yves Le Boudec

A class of mean field interaction models for computer and communication systems

In this presentation we review a generic mean field interaction model where N objects are evolving according to an objectpsilas individual finite state machine and the state of a global resource. We show that, in order to obtain mean field convergence for large N to an Ordinary Differential Equation (ODE), it is sufficient to assume that (1) the intensity, i.e. the number of transitions per object per time slot, vanishes and (2) the coefficient of variation of the total number of objects that do a transition in one time slot remains bounded. No independence assumption is needed anywhere. We find convergence in mean square and in probability on any finite horizon, and derive from there that, in the stationary regime, the support of the occupancy measure tends to be supported by the Birkhoff center of the ODE. We use these results to develop a critique of the fixed point method sometimes used in the analysis of communication protocols.

The age of gossip: spatial mean field regime

Disseminating a piece of information, or updates for a piece of information, has been shown to benefit greatly from simple randomized procedures, sometimes referred to as gossiping, or epidemic algorithms. Similarly, in a network where mobile nodes occasionally receive updated content from a base station, gossiping using opportunistic contacts allows for recent updates to be efficiently maintained, for a large number of nodes. In this case, however, gossiping depends on node mobility. For this reason, we introduce a new gossip model, with mobile nodes moving between different classes that can represent locations or states, which determine gossiping behavior of the nodes. Here we prove that, when the number of mobile nodes becomes large, the age of the latest updates received by mobile nodes approaches a deterministic mean-field regime. More precisely, we show that the occupancy measure of the process constructed, with the ages defined above, converges to a deterministic limit that can be entirely characterized by differential equations. This major simplification allows us to characterize how mobility, source inputs and gossiping influence the age distribution for low and high ages. It also leads to a scalable numerical evaluation of the performance of mobile update systems, which we validate (using a trace of 500 taxicabs) and use to propose infrastructure deployment.

MPTCP is not pareto-optimal: performance issues and a possible solution

Multipath TCP (MPTCP) has been proposed recently as a mechanism for transparently supporting multiple connections to the application layer. It is under discussion at the IETF. We nevertheless demonstrate that the current MPTCP suffers from two problems: P1) Upgrading some TCP users to MPTCP can reduce the throughput of others without any benefit to the upgraded users, which is a symptom of not being Pareto-optimal; and P2) MPTCP users could be excessively aggressive toward TCP users. We attribute these problems to the linked-increases algorithm (LIA) of MPTCP and, more specifically, to an excessive amount of traffic transmitted over congested paths. The design of LIA forces a tradeoff between optimal resource pooling and responsiveness. We revisit the problem and show that it is possible to provide these two properties simultaneously. We implement the resulting algorithm, called the opportunistic linked-increases algorithm (OLIA), in the Linux kernel, and we study its performance over our testbed by simulations and by theoretical analysis. We prove that OLIA is Pareto-optimal and satisfies the design goals of MPTCP. Hence, it can avoid the problems P1 and P2. Our measurements and simulations indicate that MPTCP with OLIA is as responsive and nonflappy as MPTCP with LIA and that it solves problems P1 and P2.

Energy savings for cellular network with evaluation of impact on data traffic performance

We present a concrete methodology for saving energy in future and contemporary cellular networks. It is based on re-arranging the user-cell association so as to allow shutting down under-utilized parts of the network. We consider a hypothetical static case where we have complete knowledge of stationary user locations and thus the results represent an upper bound of potential energy savings. We formulate the problem as a binary integer programming problem, thus it is NP-hard, and we present a heuristic approximation method. We simulate the methodology on an example real cellular network topology with traffic-and user distribution generated according to recently measured patterns. Further, we evaluate the energy savings, using realistic energy profiles, and the impact on the user-perceived network performance, represented by delay and throughput, at various times of day. The general findings conclude that up to 50% energy may be saved in less busy periods, while the performance effects remain limited. We conclude that practical, real-time user-cell re-allocation methodology, taking into account user mobility predictions, may thus be feasible and bring significant energy savings at acceptable performance impact.

Energy consumption comparison between macro-micro and public femto deployment in a plausible LTE network

We study the energy consumptions of two strategies that increase the capacity of an LTE network: (1) the deployment of redundant macro and micro base stations by the operator at locations where the traffic is high, and (2) the deployment of publicly accessible femto base stations by home users. Previous studies show the deployment of publicly accessible residential femto base stations is considerably more energy efficient; however, the results are proposed using an abstracted model of LTE networks, where the coverage constraint was neglected in the study, as well as some other important physical and traffic layer specifications of LTE networks. We study a realistic scenario where coverage is provided by a set of non-redundant macro-micro base stations and additional capacity is provided by redundant macro-micro base stations or by femto base stations. We quantify the energy consumption of macro-micro and femto deployment strategies by using a simulation of a plausible LTE deployment in a mid-size metropolitan area, based on data obtained from an operator and using detailed models of heterogeneous devices, traffic, and physical layers. The metrics of interest are operator-energy-consumption/total-energy-consumption per unit of network capacity. For the scenarios we studied, we observe the following: (1) There is no significant difference between operator energy consumption of femto and macro-micro deployment strategies. From the point of view of society, i.e. total energy consumption, macro-micro deployment is even more energy efficient in some cases. This differs from the previous findings, which compared the energy consumption of femto and macro-micro deployment strategies, and found that femto deployment is considerably more energy efficient. (2) The deployment of femto base stations has a positive effect on mobile-terminal energy consumption; however, it is not significant compared to the macro-micro deployment strategy. (3) The energy saving that could be obtained by making macro and micro base stations more energy proportional is much higher than that of femto deployment.

The Bounded Confidence Model Of Opinion Dynamics

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into a random set of clusters too far apart to interact, and thereafter all opinions in every cluster converge to their barycenter. We then prove a mean-field limit result, propagation of chaos: as the number of peers goes to infinity in adequately started systems and time is rescaled accordingly, the opinion processes converge to i.i.d. nonlinear Markov (or McKean-Vlasov) processes; the limit opinion processes evolves as if under the influence of opinions drawn from its own instantaneous law, which are the unique solution of a nonlinear integro-differential equation of Kac type. This implies that the (random) empirical distribution processes converges to this (deterministic) solution. We then prove that, as time goes to infinity, this solution converges to a law concentrated on isolated opinions too far apart to interact, and identify sufficient conditions for the limit not to depend on the initial condition, and to be concentrated at a single opinion. Finally, we prove that if the equation has an initial condition with a density, then its solution has a density at all times, develop a numerical scheme for the corresponding functional equation, and show numerically that bifurcations may occur.

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called “mean field limit”, or “hydrodynamic limit”). A common practice, often called the “fixed point approximation” consists in approximating the stationary behaviour of the stochastic process by the stationary points of the fluid limit. It is known that this may be incorrect in general, as the stationary behaviour of the fluid limit may not be described by its stationary points. We show however that, if the stochastic process is reversible, the fixed point approximation is indeed valid. More precisely, we assume that the stochastic process converges to the fluid limit in distribution (hence in probability) at every fixed point in time. This assumption is very weak and holds for a large family of processes, among which many mean field and other interaction models. We show that the reversibility of the stochastic process implies that any limit point of its stationary distribution is concentrated on stationary points of the fluid limit. If the fluid limit has a unique stationary point, it is an approximation of the stationary distribution of the stochastic process.

Demand response using service curves

Existing methods for demand response either assume direct control of appliances by supplier, or assume that consumers adapt their load by reacting to pricing signals. The former are intrusive and might not scale well; the latter expose consumers to price volatility and require detailed awareness of time varying prices. We propose an alternative approach, based on “service curves”, which uses the following two ingredients. (1) The rate at which a consumer may draw power from the grid may be controlled by real time signals. Typical concerned devices would be heating systems, air conditioners and e-car batteries. (2) However, consumers are guaranteed that, over any window of time t, the amount of energy that may be drawn is at least equal to b(t), where the function b() (called the service curve) is agreed upon by contract at subscription time. The contract also specifies the maximum power that may be drawn, as well as a fixed price per unit of energy. Hence users are protected from price variability, at the expense of possible, but upper bounded, delays. With a proper service curve definition, an operator may distribute small service reductions in order to alleviate the impact of massive incoming demand onto the power grid. Consumers are able to observe the past service control signals that they received and can compute optimal load schedules from this and their service curve contracts, using only local information. Thus, this provides a distributed, scalable and robust demand response mechanism.

Experimental Validation of an Explicit Power-Flow Primary Control in Microgrids

The existing approaches to control electrical grids combine frequency and voltage controls at different time-scales. When applied in microgrids with stochastic distributed generation, grid quality of service problems may occur, such as under- or overvoltages as well as congestion of lines and transformers. The COMMELEC framework proposes to solve this compelling issue by performing explicit control of power flows with two novel strategies: 1) a common abstract model is used by resources to advertise their state in real time to a grid agent; and 2) subsystems can be aggregated into virtual devices that hide their internal complexity in order to ensure scalability. While the framework has already been published in the literature, in this paper, we present the first experimental validation of a practicable explicit power-flow primary control applied in a real-scale test-bed microgrid. We demonstrate how an explicit power-flow control solves the active and reactive power sharing problem in real time, easily allowing the microgrid to be dispatchable in real time (i.e., it is able to participate in energy markets) and capable of providing frequency support, while always maintaining quality of service.

Existence and Uniqueness of Load-Flow Solutions in Three-Phase Distribution Networks

We present sufficient conditions for the existence and uniqueness of load-flow solutions in three-phase distribution networks. The conditions can be efficiently verified for real distribution systems.