Nicolas Gast

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.

Incentives and redistribution in homogeneous bike-sharing systems with stations of finite capacity

Bike-sharing systems are becoming important for urban transportation. In these systems, users arrive at a station, pick up a bike, use it for a while, and then return it to another station of their choice. Each station has a finite capacity: it cannot host more bikes than its capacity. We propose a stochastic model of an homogeneous bike-sharing system and study the effect of the randomness of user choices on the number of problematic stations, i.e., stations that, at a given time, have no bikes available or no available spots for bikes to be returned to. We quantify the influence of the station capacities, and we compute the fleet size that is optimal in terms of minimizing the proportion of problematic stations. Even in a homogeneous city, the system exhibits a poor performance: the minimal proportion of problematic stations is of the order of the inverse of the capacity. We show that simple incentives, such as suggesting users to return to the least loaded station among two stations, improve the situation by an exponential factor. We also compute the rate at which bikes have to be redistributed by trucks for a given quality of service. This rate is of the order of the inverse of the station capacity. For all cases considered, the fleet size that corresponds to the best performance is half of the total number of spots plus a few more, the value of the few more can be computed in closed-form as a function of the system parameters. It corresponds to the average number of bikes in circulation.

Optimal Generation and Storage Scheduling in the Presence of Renewable Forecast Uncertainties

Renewable energy sources, such as wind, are characterized by non-dispatchability, high volatility, and non-perfect forecasts. These undesirable features can lead to energy loss and/or can necessitate a large reserve in the form of fast-ramping fuel-based generators. Energy storage can be used to mitigate these effects. In this paper, we are interested in the tradeoff between the use of the reserves and the energy loss. Energy loss includes energy that is either wasted, due to the inefficiency of the storage cycle and the inevitable forecasting errors, or lost when the storage capacity is insufficient. We base our analysis on an initial model proposed by Bejan, Gibbens, and Kelly. We first provide theoretical bounds on the trade-off between energy loss and the use of reserves. For a large storage capacity, we show that this bound is tight, and we develop an algorithm that computes the optimal schedule. Second, we develop a scheduling strategy that is efficient for small or moderate storage. We evaluate these policies on real data from the U.K. grid and show that they outperform existing heuristics. In addition, we provide guidelines for computing the optimal storage characteristics and the reserve size for a given penetration of wind in the energy mix.

Optimal storage policies with wind forecast uncertainties

The increase in penetration of wind in the current energy mix is hindered by its high volatility and poor predictability. These shortcomings lead to energy loss and increased deployment of fast ramping generation. The use of energy storage compensates to some extent these negative effects; it plays a buffer role between demand and production. We revisit a model of real storage proposed by Bejan et al.[1]. We study the impact on performance of energy conversion efficiency and of wind prediction quality. Specifically, we provide theoretical bounds on the trade-off between energy loss and fast ramping generation, which we show to be tight for large capacity of the available storage. Moreover, we develop strategies that outperform the proposed fixed level policies when evaluated on real data from the UK grid.

Decentralized list scheduling

Classical list scheduling is a very popular and efficient technique for scheduling jobs for parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors, the cost for managing a single centralized list becomes too prohibitive. A suitable approach to reduce the contention is to distribute the list among the computational units: each processor only has a local view of the work to execute. Thus, the scheduler is no longer greedy and standard performance guarantees are lost.The objective of this work is to study the extra cost that must be paid when the list is distributed among the computational units. We first present a general methodology for computing the expected makespan based on the analysis of an adequate potential function which represents the load imbalance between the local lists. We obtain an equation giving the evolution of the potential by computing its expected decrease in one step of the schedule. Our main theorem shows how to solve such equations to bound the makespan. Then, we apply this method to several scheduling problems, namely, for unit independent tasks, for weighted independent tasks and for tasks with precedence constraints. More precisely, we prove that the time for scheduling a global workload W composed of independent unit tasks on m processors is equal to W/m plus an additional term proportional to log2W. We provide a lower bound which shows that this is optimal up to a constant. This result is extended to the case of weighted independent tasks. In the last setting, precedence task graphs, our analysis leads to an improvement on the bound of Arora et al. (Theory Comput. Syst. 34(2):115–144, 2001). We end with some experiments using a simulator. The distribution of the makespan is shown to fit existing probability laws. Moreover, the simulations give a better insight into the additive term whose value is shown to be around 3log2W confirming the precision of our analysis.

Distributed delay-power control algorithms for bandwidth sharing in wireless networks

In this paper, we formulate a delay-power control (DPC) scheme for wireless networking, which efficiently balances delay against transmitter power on each wireless link. The DPC scheme is scalable, as each link autonomously updates its power based on the interference observed at its receiver; no cross-link communication is required. It is shown that DPC converges to a unique equilibrium power and several key properties are established, concerning the nature of channel bandwidth sharing achieved by the links. The DPC scheme is contrasted to the well-known Foschini-Miljanic (FM) formulation for transmitter power control in wireless networks, and some key advantages are established. Based on the DPC and FM schemes, two protocols are developed, which leverage adaptive tuning of DPC parameters. One of them is inspired by TCP and exhibits analogous behavior. This paper primarily focuses on the theoretical underpinnings of DPC and their practical implications for efficient protocol design. The DPC dynamics are also investigated numerically.

Are Mean-field Games the Limits of Finite Stochastic Games?

Mean-field games model the rational behavior of an infinite number of indistinguishable players in interaction. An important assumption of mean-field games is that, as the number of player is infinite, the decisions of an individual player do not affect the dynamics of the mass. Each player plays against the mass. A mean-field equilibrium corresponds to the case when the optimal decisions of a player coincide with the decisions of the mass. Many authors argue that mean-field games are a good approximation of symmetric stochastic games with a large number of players, the rationale behind this being that the impact of one player becomes negligible when the number of players goes to infinity. In this paper, we question this assertion. We show that, in general, this convergence does not hold. In fact, the “tit for tat” principle allows one to define many equilibria in repeated or stochastic games with N players. However, in mean-field games, the deviation of a single player is not visi- ble by the population and therefore the “tit for tat” principle cannot be applied. The conclusion is that, even if N-player games have many equilibria with a good social cost, this may not be the case for the limit game.

Infinite labeled trees: From rational to Sturmian trees

This paper studies infinite unordered d-ary trees with nodes labeled by {0,1}. We introduce the notions of rational and Sturmian trees along with the definitions of (strongly) balanced trees and mechanical trees, and study the relations among them. In particular, we show that (strongly) balanced trees exist and coincide with mechanical trees in the irrational case, providing an effective construction. Such trees also have a minimal factor complexity, hence are Sturmian. We also give several examples illustrating the inclusion relations between these classes of trees.

Computing absorbing times via fluid approximations

Abstract In this paper we compute the absorbing time T n of an n-dimensional discrete-time Markov chain comprising n components, each with an absorbing state and evolving in mutual exclusion. We show that the random absorbing time T n is well approximated by a deterministic time t n that is the first time when a fluid approximation of the chain approaches the absorbing state at a distance 1 / n. We provide an asymptotic expansion of t n that uses the spectral decomposition of the kernel of the chain as well as the asymptotic distribution of T n , relying on extreme values theory. We show the applicability of this approach with three different problems: the coupon collector, the erasure channel lifetime, and the coupling times of random walks in high-dimensional spaces.

Construction of Lyapunov Functions via Relative Entropy with Application to Caching

We consider a system of interacting objects that is a generalization of the model of the cache-replacement policy RAND(m) introduced in [6]. We provide a mean-field approximation of this system. We show how to use relative entropy to construct a Lyapunov function for this model. This guarantees that the mean-field model converges to its unique fixed point.