arXiv subjects

Jean-Yves Le Boudec

Publications and source records attributed to Jean-Yves Le Boudec.

At least 37 records · Page 2Linked to original sources

arXiv2020

Interleaved Weighted Round-Robin: A Network Calculus Analysis

Weighted Round-Robin (WRR) is often used, due to its simplicity, for scheduling packets or tasks. With WRR, a number of packets equal to the weight allocated to a flow can be served consecutively, which leads to a bursty service. Interleaved Weighted Round-Robin (IWRR) is a variant that mitigates this effect. We are interested in finding bounds on worst-case delay obtained with IWRR. To this end, we use a network calculus approach and find a strict service curve for IWRR. The result is obtained using the pseudo-inverse of a function. We show that the strict service curve is the best obtainable one, and that delay bounds derived from it are tight (i.e., worst-case) for flows of packets of constant size. Furthermore, the IWRR strict service curve dominates the strict service curve for WRR that was previously published. We provide some numerical examples to illustrate the reduction in worst-case delays caused by IWRR compared to WRR.

cs.NI↗

arXiv2019

TDOA Source-Localization Technique Robust to Timing Attacks

In this paper, we focus on the localization of a passive source from time difference of arrival (TDOA) measurements. TDOA values are computed with respect to pairs of fixed sensors that are required to be accurately time-synchronized. This constitutes a weakness as all synchronization techniques are vulnerable to delay injections. Attackers are able either to spoof the signal or to inject asymmetric delays in the communication channel. By nature, TDOA measurements are highly sensitive to time-synchronization offsets between sensors. Our first contribution is to show that timing attacks can severely affect the localization process. With a delay of a few microseconds injected on one sensor, the resulting estimate might be several kilometers away from the true location of the unknown source. We also show that residual analysis does not enable the detection and identification of timing attacks. Our second contribution is to propose a two-step TDOA-localization technique that is robust against timing attacks. It uses a known source to define a weight for each pair of sensors, reflecting the confidence in their time synchronization. Our solution then uses the weighted least-squares estimator with the newly created weights and the TDOA measurements received from the unknown source. As a result, our method either identifies the network as being too corrupt to localize, or gives a corrected estimate of the unknown position along with a confidence metric. Numerical results illustrate the performance of our technique.

eess.SY↗

arXiv2019

Improved Delay Bound for a Service Curve Element with Known Transmission Rate

Network calculus is often used to prove delay bounds in deterministic networks, using arrival and service curves. We consider a FIFO system that offers a rate-latency service curve and where packet transmission occurs at line rate without pre-emption. The existing network calculus delay bounds take advantage of the service curve guarantee but not of the fact that transmission occurs at full line rate. In this letter, we provide a novel, improved delay bound which takes advantage of these two features. Contrary to existing bounds, ours is per-packet and depends on the packet length. We prove that it is tight.

cs.NI↗

arXiv2019

Improved Credit Bounds for the Credit-Based Shaper in Time-Sensitive Networking

In Time-Sensitive Networking (TSN), it is important to formally prove per flow latency and backlog bounds. To this end, recent works apply network calculus and obtain latency bounds from service curves. The latency component of such service curves is directly derived from upper bounds on the values of the credit counters used by the Credit-Based Shaper (CBS), an essential building-block of TSN. In this paper, we derive and formally prove credit upper bounds for CBS, which improve on existing bounds.

cs.NI↗

arXiv2018

A Polynomial-Time Method for Testing Admissibility of Uncertain Power Injections in Microgrids

We study the admissibility of power injections in single-phase microgrids, where the electrical state is represented by complex nodal voltages and controlled by nodal power injections. Assume that (i) there is an initial electrical state that satisfies security constraints and the non-singularity of load-flow Jacobian, and (ii) power injections reside in some uncertainty set. We say that the uncertainty set is admissible for the initial electrical state if any continuous trajectory of the electrical state is ensured to be secured and non-singular as long as power injections remain in the uncertainty set. We use the recently proposed V-control and show two new results. First, if a complex nodal voltage set V is convex and every element in V is nonsingular, then V is a domain of uniqueness. Second, we give sufficient conditions to guarantee that every element in some power injection set S has a load-flow solution in V, based on impossibility of obtaining load-flow solutions at the boundary of V. By these results, we develop a framework for the admissibility-test method; this framework is extensible to multi-phase grids. Within the framework, we establish a polynomial-time method, using the infeasibility check of convex optimizations. The method is evaluated numerically.

math.OC↗

arXiv2018

A Theory of Traffic Regulators for Deterministic Networks with Application to Interleaved Regulators

We define the minimal interleaved regulator, which generalizes the Urgency Based Shaper that was recently proposed by Specht and Samii as a simpler alternative to per-flow reshaping in deterministic networks with aggregate scheduling. With this regulator, packets of multiple flows are processed in one FIFO queue; the packet at the head of the queue is examined against the regulation constraints of its flow; it is released at the earliest time at which this is possible without violating the constraints. Packets that are not at the head of the queue are not examined until they reach the head of the queue. This regulator thus possibly delays the packet at the head of the queue but also all following packets, which typically belong to other flows. However, we show that, when it is placed after an arbitrary FIFO system, the worst case delay of the combination is not increased. This shaping-for-free property is well-known with per-flow shapers; surprisingly, it continues to hold here. To derive this property, we introduce a new definition of traffic regulator, the minimal Pi-regulator, which extends both the greedy shaper of network calculus and Chang's max-plus regulator and also includes new types of regulators such as packet rate limiters. Incidentally, we provide a new insight on the equivalence between min-plus and max-plus formulations of regulators and shapers.

cs.NI↗

arXiv2018

Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the non-singularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.

math.OC↗

arXiv2017

An Exact Convex Formulation of Optimal Power Flow in Radial Distribution Networks Including Transverse Components

The recent literature has discussed the use of the relaxed Second Order Cone Programming (SOCP) to formulate Optimal Power Flow problems (OPF) for radial power grids. However, if the shunt parameters of the lines, composing the power grid, are considered the proposed methods do not provide sufficient conditions that can be verified ex ante for the exactness of the optimal solutions. Additionally, the same formulations have not correctly accounted for the ampacity constraint of the lines. Similar to the inclusion of upper voltage-magnitude limit, the SOCP relaxation faces difficulties when the ampacity constraints of the lines are binding. In order to overcome these limitations, we propose a convex formulation of the OPF problem applied to radial power grids for which the AC-OPF equations, including the transverse parameters, are considered. We augment the formulation with a new set of more conservative constraints to limit the lines current together with the nodal voltage-magnitudes. Sufficient conditions are provided to ensure the feasibility and optimality of the proposed OPF solution. Furthermore, the proofs of the exactness of the SOCP relaxation are provided. Using standard power grids, we show that these conditions are mild and hold for real distribution networks.

math.OC↗

arXiv2016

Real-Time Minimization of Average Error in the Presence of Uncertainty and Convexification of Feasible Sets

We consider a two-level discrete-time control framework with real-time constraints where a central controller issues setpoints to be implemented by local controllers. The local controllers implement the setpoints with some approximation and advertize a prediction of their constraints to the central controller. The local controllers might not be able to implement the setpoint exactly, due to prediction errors or because the central controller convexifies the problem for tractability. In this paper, we propose to compensate for these mismatches at the level of the local controller by using a variant of the error diffusion algorithm. We give conditions under which the minimal (convex) invariant set for the accumulated-error dynamics is bounded, and give a computational method to construct this set. This can be used to compute a bound on the accumulated error and hence establish convergence of the average error to zero. We illustrate the approach in the context of real-time control of electrical grids.

math.OC↗

arXiv2016

AC OPF in Radial Distribution Networks - Parts I,II

The optimal power-flow problem (OPF) has played a key role in the planning and operation of power systems. Due to the non-linear nature of the AC power-flow equations, the OPF problem is known to be non-convex, therefore hard to solve. Most proposed methods for solving the OPF rely on approximations that render the problem convex, but that may yield inexact solutions. Recently, Farivar and Low proposed a method that is claimed to be exact for radial distribution systems, despite no apparent approximations. In our work, we show that it is, in fact, not exact. On one hand, there is a misinterpretation of the physical network model related to the ampacity constraint of the lines' current flows. On the other hand, the proof of the exactness of the proposed relaxation requires unrealistic assumptions related to the unboundedness of specific control variables. We also show that the extension of this approach to account for exact line models might provide physically infeasible solutions. Recently, several contributions have proposed OPF algorithms that rely on the use of the alternating-direction method of multipliers (ADMM). However, as we show in this work, there are cases for which the ADMM-based solution of the non-relaxed OPF problem fails to converge. To overcome the aforementioned limitations, we propose an algorithm for the solution of a non-approximated, non-convex OPF problem in radial distribution systems that is based on the method of multipliers, and on a primal decomposition of the OPF. This work is divided in two parts. In Part I, we specifically discuss the limitations of BFM and ADMM to solve the OPF problem. In Part II, we provide a centralized version and a distributed asynchronous version of the proposed OPF algorithm and we evaluate its performances using both small-scale electrical networks, as well as a modified IEEE 13-node test feeder.

eess.SY↗

arXiv2016

Explicit Conditions on Existence and Uniqueness of Load-Flow Solutions in Distribution Networks

We present explicit sufficient conditions that guarantee the existence and uniqueness of the feasible load-flow solution for distribution networks with a generic topology (radial or meshed) modeled with positive sequence equivalents. In the problem, we also account for the presence of shunt elements. The conditions have low computational complexity and thus can be efficiently verified in a real system. Once the conditions are satisfied, the unique load-flow solution can be reached by a given fixed point iteration method of approximately linear complexity. Therefore, the proposed approach is of particular interest for modern active distribution network (ADN) setup in the context of real-time control. The theory has been confirmed through numerical experiments.

math.OC↗

arXiv2015

Design of Resource Agents with Guaranteed Tracking Properties for Real-Time Control of Electrical Grids

We target the problem of controlling electrical microgrids with little inertia in real time. We consider a central controller and a number of resources, where each resource is either a load, a generator, or a combination thereof, like a battery. The controller periodically computes power setpoints for the resources based on the estimated state of the grid and an overall objective, and subject to safety constraints. Each resource is augmented with a resource agent that a) implements the setpoint requests sent by the controller on the resource, and b) translates device-specific information about the resource into a device-independent representation and transmits this to the controller. We focus on the resource agents and their impact on the overall system's behavior. Intuitively, for the system to converge to the objective, the resource agents should be obedient to the requests from the controller, in the sense that the actually implemented setpoint should be close to the requested setpoint, at least on average. This can be important especially when a controller that performs continuous optimization is used (for the sake of performance) to control discrete resources (which have a discrete set of implementable setpoints). We formalize obedience by defining the notion of $c$-bounded accumulated-error. We then demonstrate its usefulness, by presenting theoretical results (for a simple scenario) and simulation results (for a more realistic setting) that indicate that, if all resource agents in the system have bounded accumulated-error, the closed-loop system converges on average to the objective. Finally, we show how to design resource agents that provably have bounded accumulated-error for various types of resources, such as resources with uncertainty (e.g., PV panels) and resources with a discrete set of implementable setpoints (e.g., on-off heating systems).

math.OC↗

arXiv2015

A Composable Method for Real-Time Control of Active Distribution Networks with Explicit Power Setpoints

The conventional approach for the control of distribution networks, in the presence of active generation and/or controllable loads and storage, involves a combination of both frequency and voltage regulation at different time scales. With the increased penetration of stochastic resources, distributed generation and demand response, this approach shows severe limitations in both the optimal and feasible operation of these networks, as well as in the aggregation of the network resources for upper-layer power systems. An alternative approach is to directly control the targeted grid by defining explicit and real-time setpoints for active/reactive power absorptions/injections defined by a solution of a specific optimization problem; but this quickly becomes intractable when systems get large or diverse. In this paper, we address this problem and propose a method for the explicit control of the grid status, based on a common abstract model characterized by the main property of being composable. That is to say, subsystems can be aggregated into virtual devices that hide their internal complexity. Thus the proposed method can easily cope with systems of any size or complexity. The framework is presented in this Part I, whilst in Part II we illustrate its application to a CIGRÉ low voltage benchmark microgrid. In particular, we provide implementation examples with respect to typical devices connected to distribution networks and evaluate of the performance and benefits of the proposed control framework.

eess.SY↗

arXiv2014

Prolonging the Hide-and-Seek Game: Optimal Trajectory Privacy for Location-Based Services

Human mobility is highly predictable. Individuals tend to only visit a few locations with high frequency, and to move among them in a certain sequence reflecting their habits and daily routine. This predictability has to be taken into account in the design of location privacy preserving mechanisms (LPPMs) in order to effectively protect users when they continuously expose their position to location-based services (LBSs). In this paper, we describe a method for creating LPPMs that are customized for a user's mobility profile taking into account privacy and quality of service requirements. By construction, our LPPMs take into account the sequential correlation across the user's exposed locations, providing the maximum possible trajectory privacy, i.e., privacy for the user's present location, as well as past and expected future locations. Moreover, our LPPMs are optimal against a strategic adversary, i.e., an attacker that implements the strongest inference attack knowing both the LPPM operation and the user's mobility profile. The optimality of the LPPMs in the context of trajectory privacy is a novel contribution, and it is achieved by formulating the LPPM design problem as a Bayesian Stackelberg game between the user and the adversary. An additional benefit of our formal approach is that the design parameters of the LPPM are chosen by the optimization algorithm.

cs.CR↗

arXiv2013

Stability of a Stochastic Model for Demand-Response

We study the stability of a Markovian model of electricity production and consumption that incorporates production volatility due to renewables and uncertainty about actual demand versus planned production. We assume that the energy producer targets a fixed energy reserve, subject to ramp-up and ramp-down constraints, and that appliances are subject to demand-response signals and adjust their consumption to the available production by delaying their demand. When a constant fraction of the delayed demand vanishes over time, we show that the general state Markov chain characterizing the system is positive Harris and ergodic (i.e., delayed demand is bounded with high probability). However, when delayed demand increases by a constant fraction over time, we show that the Markov chain is non-positive (i.e., there exists a non-zero probability that delayed demand becomes unbounded). We exhibit Lyapunov functions to prove our claims. In addition, we provide examples of heating appliances that, when delayed, have energy requirements corresponding to the two considered cases.

eess.SY↗

arXiv2012

Efficient Computation of Sensitivity Coefficients of Node Voltages and Line Currents in Unbalanced Radial Electrical Distribution Networks

The problem of optimal control of power distribution systems is becoming increasingly compelling due to the progressive penetration of distributed energy resources in this specific layer of the electrical infrastructure. Distribution systems are, indeed, experiencing significant changes in terms of operation philosophies that are often based on optimal control strategies relying on the computation of linearized dependencies between controlled (e.g. voltages, frequency in case of islanding operation) and control variables (e.g. power injections, transformers tap positions). As the implementation of these strategies in real-time controllers imposes stringent time constraints, the derivation of analytical dependency between controlled and control variables becomes a non-trivial task to be solved. With reference to optimal voltage and power flow controls, this paper aims at providing an analytical derivation of node voltage and line current flows as a function of the nodal power injections and transformers tap-changers positions. Compared to other approaches presented in the literature, the one proposed here is based on the use of the [Y] compound matrix of a generic multi-phase radial unbalanced network. In order to estimate the computational benefits of the proposed approach, the relevant improvements are also quantified versus traditional methods. The validation of the proposed method is carried out by using both IEEE 13 and 34 node test feeders. The paper finally shows the use of the proposed method for the problem of optimal voltage control applied to the IEEE 34 node test feeder.

eess.SY↗

arXiv2012

On the Asymptotic Validity of the Decoupling Assumption for Analyzing 802.11 MAC Protocol

Performance evaluation of the 802.11 MAC protocol is classically based on the decoupling assumption, which hypothesizes that the backoff processes at different nodes are independent. This decoupling assumption results from mean field convergence and is generally true in transient regime in the asymptotic sense (when the number of wireless nodes tends to infinity), but, contrary to widespread belief, may not necessarily hold in stationary regime. The issue is often related with the existence and uniqueness of a solution to a fixed point equation; however, it was also recently shown that this condition is not sufficient; in contrast, a sufficient condition is a global stability property of the associated ordinary differential equation. In this paper, we give a simple condition that establishes the asymptotic validity of the decoupling assumption for the homogeneous case. We also discuss the heterogeneous and the differentiated service cases and formulate a new ordinary differential equation. We show that the uniqueness of a solution to the associated fixed point equation is not sufficient; we exhibit one case where the fixed point equation has a unique solution but the decoupling assumption is not valid in the asymptotic sense in stationary regime.

cs.NI↗

arXiv2012

Comment on "Mixing beliefs among interacting agents"

We comment on the derivation of the main equation in the bounded confidence model of opinion dynamics. In the original work, the equation is derived using an ad-hoc counting method. We point that the original derivation does contain some small mistake. The mistake does not have a large qualitative impact, but it reveals the danger of the ad-hoc counting method. We show how a more systematic approach, which we call micro to macro, can avoid such mistakes, without adding any significant complexity.

nlin.AO↗