The Susceptible-Infected-Susceptible (SIS) model is a widely used model for the spread of information and infectious diseases, particularly non-immunizing ones, on a graph. Given a highly contagious disease, a natural question is how to best vaccinate individuals to minimize the disease's extinction time. While previous works showed that the problem of optimal vaccination is closely linked to the NP-hard *Spectral Radius Minimization* (SRM) problem, they assumed that the graph is known, which is often not the case in practice. In this work, we consider the problem of minimizing the extinction time of an outbreak modeled by an SIS model where the graph on which the disease spreads is unknown and only the infection states of the vertices are observed. To this end, we split the problem into two: learning the graph and determining effective vaccination strategies. We propose a novel inclusion-exclusion-based learning algorithm and, unlike previous approaches, establish its sample complexity for graph recovery. We then detail an optimal algorithm for the SRM problem and prove that its running time is polynomial in the number of vertices for graphs with bounded treewidth. This is complemented by an efficient and effective polynomial-time greedy heuristic for any graph. Finally, we present experiments on synthetic and real-world data that numerically validate our learning and vaccination algorithms.

This paper establishes the theoretical limits of graph clustering under the Popularity-Adjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex degrees, and to the Degree-Corrected Block Model (DCBM), which applies uniform degree corrections across clusters, PABM introduces separate popularity parameters for intra- and inter-cluster connections. Our main contribution is the characterization of the optimal error rate for clustering under PABM, which provides novel insights on clustering hardness: we demonstrate that unlike SBM and DCBM, cluster recovery remains possible in PABM even when traditional edge-density signals vanish, provided intra- and inter-cluster popularity coefficients differ. This highlights a dimension of degree heterogeneity captured by PABM but overlooked by DCBM: local differences in connectivity patterns can enhance cluster separability independently of global edge densities. Finally, because PABM exhibits a richer structure, its expected adjacency matrix has rank between $k$ and $k^2$, where $k$ is the number of clusters. As a result, spectral embeddings based on the top $k$ eigenvectors may fail to capture important structural information. Our numerical experiments on both synthetic and real datasets confirm that spectral clustering algorithms incorporating $k^2$ eigenvectors outperform traditional spectral approaches.

Clustering is a pivotal challenge in unsupervised machine learning and is often investigated through the lens of mixture models. The optimal error rate for recovering cluster labels in Gaussian and sub-Gaussian mixture models involves ad hoc signal-to-noise ratios. Simple iterative algorithms, such as Lloyd’s algorithm, attain this optimal error rate. In this paper, we first establish a universal lower bound for the error rate in clustering any mixture model, expressed through Chernoff information, a more versatile measure of model information than signal-to-noise ratios. We then demonstrate that iterative algorithms attain this lower bound in mixture models with sub-exponential tails, notably emphasizing location-scale mixtures featuring Laplace-distributed errors. Additionally, for datasets better modelled by Poisson or Negative Binomial mixtures, we study mixture models whose distributions belong to an exponential family. In such mixtures, we establish that Bregman hard clustering, a variant of Lloyd’s algorithm employing a Bregman divergence, is rate optimal.

Bayesian Optimization (BO) is typically used to optimize an unknown function $f$ that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for $f$. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of $f$ without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of $f$ comprises high-dimensional factors.

Bayesian Optimization (BO) has proven to be very successful at optimizing a static, noisy, costly-to-evaluate black-box function $f : \mathcal{S} \to \mathbb{R}$. However, optimizing a black-box which is also a function of time (*i.e.*, a *dynamic* function) $f : \mathcal{S} \times \mathcal{T} \to \mathbb{R}$ remains a challenge, since a dynamic Bayesian Optimization (DBO) algorithm has to keep track of the optimum over time. This changes the nature of the optimization problem in at least three aspects: (i) querying an arbitrary point in $\mathcal{S} \times \mathcal{T}$ is impossible, (ii) past observations become less and less relevant for keeping track of the optimum as time goes by and (iii) the DBO algorithm must have a high sampling frequency so it can collect enough relevant observations to keep track of the optimum through time. In this paper, we design a Wasserstein distance-based criterion able to quantify the relevancy of an observation with respect to future predictions. Then, we leverage this criterion to build W-DBO, a DBO algorithm able to remove irrelevant observations from its dataset on the fly, thus maintaining simultaneously a good predictive performance and a high sampling frequency, even in continuous-time optimization tasks with unknown horizon. Numerical experiments establish the superiority of W-DBO, which outperforms state-of-the-art methods by a comfortable margin.

The metric backbone of a weighted graph is the union of all-pairs shortest paths. It is obtained by removing all edges $(u,v)$ that are not the shortest path between $u$ and $v$. In networks with well-separated communities, the metric backbone tends to preserve many inter-community edges, because these edges serve as bridges connecting two communities, but tends to delete many intra-community edges because the communities are dense. This suggests that the metric backbone would dilute or destroy the community structure of the network. However, this is not borne out by prior empirical work, which instead showed that the metric backbone of real networks preserves the community structure of the original network well. In this work, we analyze the metric backbone of a broad class of weighted random graphs with communities, and we formally prove the robustness of the community structure with respect to the deletion of all the edges that are not in the metric backbone. An empirical comparison of several graph sparsification techniques confirms our theoretical finding and shows that the metric backbone is an efficient sparsifier in the presence of communities.

Identifying causal effects is a key problem of interest across many disciplines. The two long-standing approaches to estimate causal effects are observational and experimental (randomized) studies. Observational studies can suffer from unmeasured confounding, which may render the causal effects unidentifiable. On the other hand, direct experiments on the target variable may be too costly or even infeasible to conduct. A middle ground between these two approaches is to estimate the causal effect of interest through proxy experiments, which are conducted on variables with a lower cost to intervene on compared to the main target. In an earlier work, we studied this setting and demonstrated that the problem of designing the optimal (minimum-cost) experiment for causal effect identification is NP-complete and provided a naive algorithm that may require solving exponentially many NP-hard problems as a sub-routine in the worst case. In this work, we provide a few reformulations of the problem that allow for designing significantly more efficient algorithms to solve it as witnessed by our extensive simulations. Additionally, we study the closely-related problem of designing experiments that enable us to identify a given effect through valid adjustments sets.

Extracting noisy or incorrectly labeled samples from a labeled dataset with hard/difficult samples is an important, and yet under-explored topic. Current methods focus in general either on noisy labels, or on hard samples, but not jointly on both. When the two types of data are both present, these methods often fail to distinguish them, which results in a decline in the overall performance of the model. We propose a systematic empirical study that provides insights into the similarities and more importantly the differences between hard and noisy samples. The method consists of designing synthetic datasets customized with different hardness and noisiness levels for different samples. These controlled experiments pave the way for the evaluation and development of methods that distinguish between hard and noisy samples. We evaluate how various data-partitioning methods are able to remove noisy samples while retaining hard samples. Our study highlights the advantages of using a metric in data partitioning that we propose and call static centroid distance. The resulting data-partitioning method outperforms others: It leads to a high test accuracy on models trained on the filtered datasets, as shown both for datasets with synthetic label noise and for datasets with real-world label noise. It also significantly outperforms other methods when employed within a semi-supervised learning framework.

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with $1\le\alpha\le2$ which holds in a wide range of applications in machine learning and signal processing. This condition ensures that any first-order stationary point is a global optimum. We prove that the total sample complexity of SCRN in achieving $\epsilon$-global optimum is $\mathcal{O}(\epsilon^{-7/(2\alpha)+1})$ for $1\le\alpha< 3/2$ and $\mathcal{\tilde{O}}(\epsilon^{-2/(\alpha)})$ for $3/2\le\alpha\le 2$. SCRN improves the best-known sample complexity of stochastic gradient descent. Even under a weak version of gradient dominance property, which is applicable to policy-based reinforcement learning (RL), SCRN achieves the same improvement over stochastic policy gradient methods. Additionally, we show that the average sample complexity of SCRN can be reduced to ${\mathcal{O}}(\epsilon^{-2})$ for $\alpha=1$ using a variance reduction method with time-varying batch sizes. Experimental results in various RL settings showcase the remarkable performance of SCRN compared to first-order methods.

The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to the graph. The extra edge can either be selected adversarially, in which case we are interested in the largest possible value that the MD can take, or uniformly at random, in which case we are interested in the distribution of the MD. The adversarial setting has already been studied by Eroh et al., (2015) for general graphs, who found an example where the MD doubles on adding a single edge. By constructing a different example, we show that this increase can be as large as exponential. However, we believe that such a large increase can occur only in specially constructed graphs, and that in most interesting graph families, the MD at most doubles on adding a single edge. We prove this for d-dimensional grid graphs, by showing that 2d appropriately chosen corners and the endpoints of the extra edge can distinguish every pair of nodes, no matter where the edge is added. For the special case of d=2, we show that it suffices to choose the four corners as landmarks. Finally, when the extra edge is sampled uniformly at random, we conjecture that the MD of 2-dimensional grids converges in probability to 3+Ber(8/27), and we give an almost complete proof.

We study the problem of identifying the source of a stochastic diffusion process spreading on a graph based on the arrival times of the diffusion at a few queried nodes. In a graph G=(V,E), an unknown source node v⁎∈V is drawn uniformly at random, and unknown edge weights w(e) for e∈E, representing the propagation delays along the edges, are drawn independently from a Gaussian distribution of mean 1 and variance σ2. An algorithm then attempts to identify v⁎ by querying nodes q∈V and being told the length of the shortest path between q and v⁎ in graph G weighted by w. We consider two settings: non-adaptive, in which all query nodes must be decided in advance, and adaptive, in which each query can depend on the results of the previous ones. Both settings are motivated by an application of the problem to epidemic processes (where the source is called patient zero), which we discuss in detail. We characterize the query complexity when G is an n-node path. In the non-adaptive setting, Θ(nσ2) queries are needed for σ2≤1, and Θ(n) for σ2≥1. In the adaptive setting, somewhat surprisingly, only Θ(log⁡log1/σ⁡n) are needed when σ2≤1/2, and Θ(log⁡log⁡n)+Oσ(1) when σ2≥1/2. This is the first mathematical study of source identification with time queries in a non-deterministic diffusion process.

Temporal point-processes are often used for mathematical modeling of sequences of discrete events with asynchronous timestamps. We focus on a class of temporal point-process models called multivariate Wold processes (MWP). These processes are well suited to model real-world communication dynamics. Statistical inference on such processes often requires learning their corresponding parameters using a set of observed timestamps. In this work, we relax some of the restrictive modeling assumptions made in the state-of-the-art and introduce a Bayesian approach for inferring the parameters of MWP. We develop a computationally efficient variational inference algorithm that allows scaling up the approach to high-dimensional processes and long sequences of observations. Our experimental results on both synthetic and real-world datasets show that our proposed algorithm outperforms existing methods.

Multivariate Hawkes processes (MHPs) are widely used in a variety of fields to model the occurrence of causally related discrete events in continuous time. Most state-of-the-art approaches address the problem of learning MHPs from perfect traces without noise. In practice, the process through which events are collected might introduce noise in the timestamps. In this work, we address the problem of learning the causal structure of MHPs when the observed timestamps of events are subject to random and unknown shifts, also known as random translations. We prove that the cumulants of MHPs are invariant to random translations, and therefore can be used to learn their underlying causal structure. Furthermore, we empirically characterize the effect of random translations on state-of-the-art learning methods. We show that maximum likelihood-based estimators are brittle, while cumulant-based estimators remain stable even in the presence of significant time shifts.

Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. We shed light on this matter by linking the loss function to the output's sensitivity to its input. We find a rather strong empirical relation between the output sensitivity and the variance in the bias-variance decomposition of the loss function, which hints on using sensitivity as a metric for comparing the generalization performance of networks, without requiring labeled data. We find that sensitivity is decreased by applying popular methods which improve the generalization performance of the model, such as (1) using a deep network rather than a wide one, (2) adding convolutional layers to baseline classifiers instead of adding fully-connected layers, (3) using batch normalization, dropout and max-pooling, and (4) applying parameter initialization techniques.

We address the problem of predicting aggregate vote outcomes (e.g., national) from partial outcomes (e.g., regional) that are revealed sequentially. We combine matrix factorization techniques and generalized linear models (GLMs) to obtain a flexible, efficient, and accurate algorithm. This algorithm works in two stages: First, it learns representations of the regions from high-dimensional historical data. Second, it uses these representations to fit a GLM to the partially observed results and to predict unobserved results. We show experimentally that our algorithm is able to accurately predict the outcomes of Swiss referenda, U.S. presidential elections, and German legislative elections. We also explore the regional representations in terms of ideological and cultural patterns. Finally, we deploy an online Web platform (www.predikon.ch) to provide real-time vote predictions in Switzerland and a data visualization tool to explore voting behavior. A by-product is a dataset of sequential vote results for 330 referenda and 2196 Swiss municipalities.

A body of law is an example of a dynamic corpus of text documents that are jointly maintained by a group of editors who compete and collaborate in complex constellations. Our goal is to develop predictive models for this process, thereby shedding light on the competitive dynamics of parliamentarians who make laws. For this purpose, we curated a dataset of 450000 legislative edits introduced by European parliamentarians over the last ten years. An edit modifies the status quo of a law, and could be in competition with another edit if it modifies the same part of that law. We propose a model for predicting the success of such edits, in the face of both the inertia of the status quo and the competition between overlapping edits. The parameters of this model can be interpreted in terms of the influence of parliamentarians and of the controversy of laws.

Abstract Anonymous communication tools, such as Tor, are extensively employed by users who want to keep their web activity private. But recent works have shown that when a local, passive adversary observes nothing more than the timestamp, size and direction (incoming or outgoing) of the packets, it can still identify with high accuracy the website accessed by a user. Several defenses against these website fingerprinting attacks have been proposed but they come at the cost of a significant overhead in traffic and/or website loading time. We propose a defense against website fingerprinting which exploits multihoming, where a user can access the Internet by sending the traffic through multiple networks. With multihoming, it is possible to protect against website fingerprinting by splitting traffic among the networks, i.e., by removing packets from one network and sending them through another, whereas current defenses can only add packets. This enables us to design a defense with no traffic overhead that, as we show through extensive experimentation against state-of-the-art attacks, reaches the same level of privacy as the best existing practical defenses. We describe and evaluate a proof-ofconcept implementation of our defense and show that is does not add significant loading-time overhead. Our solution is compatible with other state-of-the-art defenses, and we show that combining it with another defense further improves privacy.

Multivariate Hawkes processes (MHP) are widely used in a variety of fields to model the occurrence of discrete events. Prior work on learning MHPs has only focused on inference in the presence of perfect traces without noise. We address the problem of learning the causal structure of MHPs when observations are subject to an unknown delay. In particular, we introduce the so-called synchronization noise, where the stream of events generated by each dimension is subject to a random and unknown time shift. We characterize the robustness of the classic maximum likelihood estimator to synchronization noise, and we introduce a new approach for learning the causal structure in the presence of noise. Our experimental results show that our approach accurately recovers the causal structure of MHPs for a wide range of noise levels, and significantly outperforms classic estimation methods.

Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences. However, when only short sequences are available, the lack of data amplifies the risk of overfitting and regularization becomes critical. Due to the challenges of hyper-parameter tuning, state-of-the-art methods only parameterize regularizers by a single shared hyper-parameter, hence limiting the power of representation of the model. To solve both issues, we develop in this work an efficient algorithm based on variational expectation-maximization. Our approach is able to optimize over an extended set of hyper-parameters. It is also able to take into account the uncertainty in the model parameters by learning a posterior distribution over them. Experimental results on both synthetic and real datasets show that our approach significantly outperforms state-of-the-art methods under short observation sequences.

In all networks, link or route capacities fluctuate for multiple reasons, e.g., fading and multi-path effects on wireless channels, interference and contending users on a shared medium, varying loads in WAN routers, impedance changes on power-line channels. These fluctuations severely impact packet delays. In this paper, we study delays in time-varying networks. Intuitively, we expect that for a given average service rate, an increased service rate variability yields larger delays. We find that this is not always the case. Using a queuing model that includes time-varying service rates, we show that for certain arrival rates, a queue with larger service rate variance offers smaller average delays than a queue with the same average service rate and lower service rate variance. We also verify these findings on a wireless testbed. We then study the conditions under which using simultaneously two independent paths helps in terms of delays, for example, in hybrid networks where the two paths use different physical layer technologies. We show that using two paths is not always better, in particular for low arrival rates. We also show that the optimal traffic splitting between the two paths depends on the arrival rate.

Coordinate descent methods minimize a cost function by updating a single decision variable (corresponding to one coordinate) at a time. Ideally, we would update the decision variable that yields the largest marginal decrease in the cost function. However, finding this coordinate would require checking all of them, which is not computationally practical. Therefore, we propose a new adaptive method for coordinate descent. First, we define a lower bound on the decrease of the cost function when a coordinate is updated and, instead of calculating this lower bound for all coordinates, we use a multi-armed bandit algorithm to learn which coordinates result in the largest marginal decrease and simultaneously perform coordinate descent. We show that our approach improves the convergence of the coordinate methods both theoretically and experimentally.

In recent years, multipath routing, i.e., employing several paths simultaneously, has emerged as an efficient way to provide significant throughput gains in local networks. This has been observed both with technologies that are not subject to interference, such as Ethernet, and with technologies that are, such as WiFi, power-line communications (PLC) and LTE. With technologies that are subject to interference, adding more paths is not always beneficial. We investigate the number of simultaneous paths necessary to reach maximal throughput when using multipath routing in multi-hop mesh networks with several self-interfering technologies. We show analytically, numerically and experimentally that the optimal number of paths M optis tightly linked with the number of technologies K. For certain classes of networks (in particular, for typical home networks), we prove analytically that Mopt =K, and our analytical findings are verified both with simulations and with experiments on a testbed composed of PLC and two orthogonal WiFi channels. In general networks, our numerical and experimental results show that the throughput loss caused by using at most K simultaneous paths is very small: The relative loss is smaller than 0.05 in 97 % of the networks and smaller than 0.1 in 99% of the networks.

We propose a new statistical dictionary learning algorithm for sparse signals that is based on an $\alpha$-stable innovation model. The parameters of the underlying model—that is, the atoms of the dictionary, the sparsity index $\alpha$ and the dispersion of the transform-domain coefficients—are recovered using a new type of probability distribution tomography. Specifically, we drive our estimator with a series of random projections of the data, which results in an efficient algorithm. Moreover, since the projections are achieved using linear combinations, we can invoke the generalized central limit theorem to justify the use of our method for sparse signals that are not necessarily $\alpha$-stable. We evaluate our algorithm by performing two types of experiments: image in-painting and image denoising. In both cases, we find that our approach is competitive with state-of-the-art dictionary learning techniques. Beyond the algorithm itself, two aspects of this study are interesting in their own right. The first is our statistical formulation of the problem, which unifies the topics of dictionary learning and independent component analysis. The second is a generalization of a classical theorem about isometries of $\ell_p$-norms that constitutes the foundation of our approach.

Source localization, the act of finding the originator of a disease or rumor in a network, has become an important problem in sociology and epidemiology. The localization is done using the infection state and time of infection of a few designated sensor nodes; however, maintaining sensors can be very costly in practice.

Power-line communications (PLC) are becoming a key component in home networking, because they provide easy and high-throughput connectivity. The dominant MAC protocol for high data-rate PLC, the IEEE 1901, employs a CSMA/CA mechanism similar to the backoff process of 802.11. Existing performance evaluation studies of this protocol assume that the backoff processes of the stations are independent (the so-called decoupling assumption). However, in contrast to 802.11, 1901 stations can change their state after sensing the medium busy, which is regulated by the so-called deferral counter. This mechanism introduces strong coupling between the stations and, as a result, makes existing analyses inaccurate. In this paper, we propose a performance model for 1901, which does not rely on the decoupling assumption. We prove that our model admits a unique solution for a wide range of configurations and confirm the accuracy of the model using simulations. Our results show that we outperform current models based on the decoupling assumption. In addition to evaluating the performance in steady state, we further study the transient dynamics of 1901, which is also affected by the deferral counter.

Several technologies, such as WiFi, Ethernet and power-line communications (PLC), can be used to build residential and enterprise networks. These technologies often co-exist; most networks use WiFi, and buildings are readily equipped with electrical wires that can offer a capacity up to 1 Gbps with PLC. Yet, current networks do not exploit this rich diversity and often operate far below the available capacity.

We consider online predictions of vote results, where regions across a country vote on an issue under discussion. Such online predictions before and during the day of the vote are useful to media agencies, polling institutes, and political parties, e.g., to identify regions that are crucial in determining the national outcome of a vote. We analyze a unique dataset from Switzerland. The dataset contains 281 votes from 2352 regions over a period of 34 years. We make several contributions towards improving online predictions. First, we show that these votes exhibit a bi-clustering of the vote results, i.e., regions that are spatially close tend to vote similarly, and issues that discuss similar topics show similar global voting patterns. Second, we develop models that can exploit this bi-clustering, as well as the features associated with the votes and regions. Third, we show that, when combining vote results and features together, Bayesian methods are essential to obtaining good performance. Our results show that Bayesian methods give better estimates of the hyperparameters than non-Bayesian methods such as cross-validation. The resulting models generalize well to many different tasks, produce robust predictions, and are easily interpretable.

Many biological systems exhibit collective behaviors that strengthen their adaptability to their environment, compared to more solitary species. Describing these behaviors is challenging yet necessary in order to understand these biological systems. We propose a probabilistic model that enables us to uncover the collective behaviors observed in a colony of ants. This model is based on the assumption that the behavior of an individual ant is a time-dependent mixture of latent behaviors that are specific to the whole colony. We apply this model to a large-scale dataset obtained by observing the mobility of nearly 1000 Camponotus fellah ants from six different colonies. Our results indicate that a colony typically exhibits three classes of behaviors, each characterized by a specific spatial distribution and a level of activity. Moreover, these spatial distributions, which are uncovered automatically by our model, match well with the ground truth as manually annotated by domain experts. We further explore the evolution of the behavior of individual ants and show that it is well captured by a second order Markov chain that encodes the fact that the future behavior of an ant depends not only on its current behavior but also on its preceding one.

Power-line communications are employed in home networking to provide easy and high-throughput connectivity. The IEEE 1901, the MAC protocol for power-line networks, employs a CSMA/CA protocol similar to that of 802.11, but is substantially more complex, which probably explains why little is known about its performance. One of the key differences between the two protocols is that whereas 802.11 only reacts upon collisions, 1901 also reacts upon several consecutive transmissions and thus can potentially achieve better performance by avoiding unnecessary collisions. In this paper, we propose a model for the 1901 MAC. Our analysis reveals that the default configuration of 1901 does not fully exploit its potential and that its performance degrades with the number of stations. Based on analytical reasoning, we derive a configuration for the parameters of 1901 that drastically improves throughput and achieves optimal performance without requiring the knowledge of the number of stations in the network. In contrast, 802.11 requires knowing the number of contending stations to provide a similar performance, which is unfeasible for realistic traffic patterns. We confirm our results and enhancement with testbed measurements, by implementing the 1901 MAC protocol on WiFi hardware.

Most users of online services have unique behavioral or usage patterns. These behavioral patterns can be exploited to identify and track users by using only the observed patterns in the behavior. We study the task of identifying users from statistics of their behavioral patterns. In particular, we focus on the setting in which we are given histograms of users' data collected during two different experiments. We assume that, in the first data set, the users' identities are anonymized or hidden and that, in the second data set, their identities are known. We study the task of identifying the users by matching the histograms of their data in the first data set with the histograms from the second data set. In recent works, the optimal algorithm for this user identification task is introduced. In this paper, we evaluate the effectiveness of this method on three different types of data sets with up to 50 000 users, and in multiple scenarios. Using data sets such as call data records, web browsing histories, and GPS trajectories, we demonstrate that a large fraction of users can be easily identified given only histograms of their data; hence, these histograms can act as users' fingerprints. We also verify that simultaneous identification of users achieves better performance compared with one-by-one user identification. Furthermore, we show that using the optimal method for identification indeed gives higher identification accuracy than the heuristics-based approaches in the practical scenarios. The accuracy obtained under this optimal method can thus be used to quantify the maximum level of user identification that is possible in such settings. We show that the key factors affecting the accuracy of the optimal identification algorithm are the duration of the data collection, the number of users in the anonymized data set, and the resolution of the data set. We also analyze the effectiveness of k-anonymization in resisting user identification attacks on these data sets.

We are interested in inferring the set of waypoints (or intermediate destinations) of a mobility trajectory in the absence of timing information. We find that, by mining a dataset of real mobility traces, computing the entropy of conditional Markov trajectory enables us to uncover waypoints, even though no timing information nor absolute geographic location is provided. We build on this observation and design an efficient algorithm for trajectory segmentation. Our empirical evaluation demonstrates that the entropy-based heuristic used by our segmentation algorithm outperforms alternative approaches as it is 43% more accurate than a geometric approach and 20% more accurate than path-stretch based approach. We further explore the link between trajectory entropy, mobility predictability and the nature of intermediate locations using a route choice model on real city maps.

It has recently been shown that "flexible channelization", whereby wireless stations adapt their spectrum bands on a per-frame basis, is feasible in practice. In this paper, we propose TF-CSMA/CA, an algorithm for flexible channelization that schedules packets in time and frequency domains. TF-CSMA/CA is a simple extension of the CSMA/CA protocol used by IEEE 802.11. Contrary to existing channelization schemes, it is entirely distributed and it reacts only to packet collisions, successful transmissions and carrier sensing. With TF-CSMA/CA, when a station is involved in a collision, it performs backoff in both time and frequency domains. Backing off also in the frequency domain allows the transmitters to be much more efficient and aggressive in the time domain, which significantly reduces the severe overheads present with recent 802.11 PHY layers. The main challenge, however, is that the stations need some level of self-organization in order to find spectrum bands of variable widths that minimize interference, while still efficiently using the available spectrum. Using analysis and simulations, we show that such an extension of CSMA/CA to the frequency domain drastically improves both throughput and fairness. Notably, it enables the stations to find interference-free spectrum bands of appropriate size using no communication -- relying only on collisions and successes as implicit signals.

Power-line communication (PLC) is widely used as it offers high data-rates and forms a network over electrical wiring, an existing and ubiquitous infrastructure. PLC is increasingly being deployed in hybrid networks that combine multiple technologies, the most popular among which is WiFi. However, so far, it is not clear to which extent PLC can boost network performance or how hybrid implementations can exploit to the fullest this technology. We compare the spatial and temporal variations of WiFi and PLC.

Energy efficiency of wireless sensor networks (WSNs) can be improved by moving base stations (BSs), as this scheme evenly distributes the communication load in the network. However, physically moving the BSs is complicated and costly. In this paper, we propose a new scheme: virtually moving the BSs. We deploy an excessive number of BSs and adaptively re-select a subset of active BSs so as to emulate the physical movement. Beyond achieving high energy-efficiency, this scheme obviates the difficulties associated with physically moving the BSs.

In wireless sensor networks (WSNs), the base station (BS) is a critical sensor node whose failure causes severe data losses. Deploying multiple fixed BSs improves the robustness, yet requires all BSs to be installed with large batteries and large energy-harvesting devices due to the high energy consumption of BSs. In this paper, we propose a scheme to coordinate the multiple deployed BSs such that the energy supplies required by individual BSs can be substantially reduced. In this scheme, only one BS is selected to be active at a time and the other BSs act as regular sensor nodes. We first present the basic architecture of our system, including how we keep the network running with only one active BS and how we manage the handover of the role of the active BS. Then, we propose an algorithm for adaptively selecting the active BS under the spatial and temporal variations of energy resources. This algorithm is simple to implement but is also asymptotically optimal under mild conditions. Finally, by running simulations and real experiments on an outdoor testbed, we verify that the proposed scheme is energy-efficient, has low communication overhead and reacts rapidly to network changes.

Consider a set of probes, called “agents”, who sample, based on opportunistic contacts, a population moving between a set of discrete locations. An example of such agents are Bluetooth probes that sample the visible Bluetooth devices in a population. Based on the obtained measurements, we construct a parametric statistical model to jointly estimate the total population size (e.g., the number of visible Bluetooth devices) and their spatial density. We evaluate the performance of our estimators by using Bluetooth traces obtained during an open-air event and Wi-Fi traces obtained on a university campus.

Power-line communications are employed in home networking to provide easy and high-throughput connectivity. IEEE 1901, the MAC protocol for power-line networks, employs a CSMA/CA protocol similar to that of 802.11, but is substantially more complex, which probably explains why little is known about its performance. One of the key differences between the two protocols is that whereas 802.11 only reacts upon collisions, 1901 also reacts upon several consecutive transmissions and thus can potentially achieve better performance by avoiding unnecessary collisions.

We study the problem of privacy-preserving computation of functions of data that belong to users in a social network under the assumption that users are willing to share their private data with trusted friends in the network. We demonstrate that such trust relationships can be exploited to significantly improve the tradeoff between the privacy of users' data and the accuracy of the computation. Under a one-hop trust model we design an algorithm for partitioning the users into circles of trust and develop a differentially private scheme for computing the global function using results of local computations within each circle. We quantify the improvement in the privacy-accuracy tradeoff of our scheme with respect to other mechanisms that do not exploit inter-user trust. We verify the efficiency of our algorithm by implementing it on social networks with up to one million nodes. Applications of our method include surveys, elections, and recommendation systems.

Power-line communications are becoming a key component in home networking. The dominant MAC protocol for high data-rate power-line communications, IEEE 1901, employs a CSMA/CA mechanism similar to the back off process of 802.11. Existing performance evaluation studies of this protocol assume that the back off processes of the stations are independent (the so-called decoupling assumption). However, in contrast to 802.11, 1901 stations can change their state after sensing the medium busy, which introduces strong coupling between the stations and, as a result, makes existing analyses inaccurate. In this paper, we propose a new performance model for 1901, which does not rely on the decoupling assumption. We prove that our model admits a unique solution. We confirm the accuracy of our model using both test bed experiments and simulations, and we show that it surpasses current models based on the decoupling assumption. Furthermore, we study the trade off between delay and throughput existing with 1901. We show that this protocol can be configured to accommodate different throughput and jitter requirements, and we give systematic guidelines for its configuration.

We investigate the IEEE 1901 MAC protocol, the dominant protocol for high data rate power-line communications. 1901 employs a CSMA/CA mechanism similar to - but much more complex than - the backoff mechanism of 802.11. Because of this extra complexity, and although this mechanism is the only widely used MAC layer for power-line networks, there are few analytical results on its performance. We propose a model for the 1901 MAC that comes in the form of a single fixed-point equation for the collision probability. We prove that this equation admits a unique solution, and we evaluate the accuracy of our model by using simulations.

We consider the problem of jointly allocating channel center frequencies and bandwidths for IEEE 802.11 wireless LANs (WLANs). The bandwidth used on a link affects significantly both the capacity experienced on this link and the interference produced on neighboring links. Therefore, when jointly assigning both center frequencies and channel widths, there is a trade-off between interference mitigation and the potential capacity offered on each link. We study this tradeoff and we present SAW (spectrum assignment for WLANs), a decentralized algorithm that finds efficient configurations. SAW is tailored for 802.11 home networks. It is distributed, online and transparent. It does not require a central coordinator and it constantly adapts the spectrum usage without disrupting network traffic. A key feature of SAW is that the access points (APs) need only a few out-of-band measurements in order to make spectrum allocation decisions. Despite being completely decentralized, the algorithm is self-organizing and provably converges towards efficient spectrum allocations. We evaluate SAW using both simulation and a deployment on an indoor testbed composed of off-the-shelf 802.11 hardware. We observe that it dramatically increases the overall network efficiency and fairness.

Wireless multi-hop local area networks use in general scheduling schemes that assume the network capacity to be known. Indeed in most of the throughput-optimal algorithms the sources are assumed to send at a rate within the capacity region. However, measurements made on real deployments show that the network capacity is usually difficult to characterize and also time-varying. It is therefore important to understand how the network behaves when the sources attempt to transmit at a rate above capacity. Toward this goal, we show 3-phase regime in the effect of the input rate λ on the end-to-end throughput μ of a multi-hop network. First, when λ is smaller than a threshold λ1, μ is an increasing function of λ. Second, when λ is larger than another threshold λ2> λ1, μ is independent of λ. Third, when λ12, μ decreases with λ. To understand this phenomenon, we capture the relation between the end-to-end throughput and the queue stability with a mathematical model that allows us to explain and derive the exact values of the transition points λi. We then validate experimentally our simulation results with measurements on a testbed composed of five wireless routers.

To quantify the randomness of Markov trajectories with fixed initial and final states, Ekroot and Cover proposed a closed-form expression for the entropy of trajectories of an irreducible finite state Markov chain. Numerous applications, including the study of random walks on graphs, require the computation of the entropy of Markov trajectories conditional on a set of intermediate states. However, the expression of Ekroot and Cover does not allow for computing this quantity. In this paper, we propose a method to compute the entropy of conditional Markov trajectories through a transformation of the original Markov chain into a Markov chain that exhibits the desired conditional distribution of trajectories. Moreover, we express the entropy of Markov trajectories-a global quantity-as a linear combination of local entropies associated with the Markov chain states.

Boolean Inference makes it possible to observe the congestion status of end-to-end paths and infer, from that, the congestion status of individual network links. In principle, this can be a powerful monitoring tool, in scenarios where we want to monitor a network without having direct access to its links. We consider one such real scenario: a Tier-1 ISP operator wants to monitor the congestion status of its peers. We show that, in this scenario, Boolean Inference cannot be solved with enough accuracy to be useful; we do not attribute this to the limitations of particular algorithms, but to the fundamental difficulty of the Inference problem. Instead, we argue that the "right" problem to solve, in this context, is compute the probability that each set of links is congested (as opposed to try to infer which particular links were congested when). Even though solving this problem yields less information than provided by Boolean Inference, we show that this information is more useful in practice, because it can be obtained accurately under weaker assumptions than typically required by Inference algorithms and more challenging network conditions (link correlations, non-stationary network dynamics, sparse topologies).

We present PIE, a scalable routing scheme that achieves 100% packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual coordinates in a space of concise dimensionality, which enables greedy routing based only on local knowledge. PIE is a general routing scheme, meaning that it works on any graph. We focus however on the Internet, where routing scalability is an urgent concern. We show analytically and by using simulation that the scheme scales extremely well on Internet-like graphs. In addition, its geometric nature allows it to react efficiently to topological changes or failures by finding new paths in the network at no cost, yielding better delivery ratios than standard algorithms. The proposed routing scheme needs an amount of memory polylogarithmic in the size of the network and requires only local communication between the nodes. Although each node constructs its coordinates and routes packets locally, the path stretch remains extremely low, even lower than for centralized or less scalable state-of-the-art algorithms: PIE always finds short paths and often enough finds the shortest paths.

We conduct an experiment where ten attendees of an open-air music festival are acting as Bluetooth probes. We then construct a parametric statistical model to estimate the total number of visible Bluetooth devices in the festival area. By comparing our estimate with ground truth information provided by probes at the entrances of the festival, we show that the total population can be estimated with a surprisingly low error (1.26% in our experiment), given the small number of agents compared to the area of the festival and the fact that they are regular attendees who move randomly. Also, our statistical model can easily be adapted to obtain more detailed estimates, such as the evolution of the population size over time.

The goal of jointly providing efficiency and fairness in wireless networks can be seen as the problem of maximizing a given utility function. In contrast with wired networks, the capacity of wireless networks is typically time-varying and not known explicitly. Hence, as the capacity region is impossible to know or measure exactly, existing scheduling schemes either under-estimate it and are too conservative, or they over-estimate it and suffer from congestion collapse. We propose a new adaptive algorithm, called Enhance & Explore (E&E). It maximizes the utility of the network without requiring any explicit characterization of the capacity region. E&E works above the MAC layer and it does not demand any modification to the existing networking stack. We first evaluate our algorithm theoretically and we prove that it converges to a state of optimal utility. We then evaluate the performance of the algorithm in a WLAN setting, using both simulations and real measurements on a testbed composed of IEEE 802.11 wireless routers.

Breadth First Search (BFS) is a widely used approach for sampling large graphs. However, it has been empirically observed that BFS sampling is biased toward high-degree nodes, which may strongly affect the measurement results. In this paper, we quantify and correct the degree bias of BFS. First, we consider a random graph RG(pk) with an arbitrary degree distribution pk. For this model, we calculate the node degree distribution expected to be observed by BFS as a function of the fraction f of covered nodes. We also show that, for RG(pk), all commonly used graph traversal techniques (BFS, DFS, Forest Fire, Snowball Sampling, RDS) have exactly the same bias. Next, we propose a practical BFS-bias correction procedure that takes as input a collected BFS sample together with the fraction f. Our correction technique is exact (i.e., leads to unbiased estimation) for RG(pk). Furthermore, it performs well when applied to a broad range of Internet topologies and to two large BFS samples of Facebook and Orkut networks.

We investigate, both theoretically and experimentally, the stability of CSMA-based wireless mesh networks, where a network is said to be stable if and only if the queue of each relay node remains (almost surely) finite. We identify two key factors that impact stability: the network size and the so-called “stealing effect,” a consequence of the hidden-node problem and nonzero transmission delays. We consider the case of a greedy source and prove, by using Foster's theorem, that three-hop networks are stable, but only if the stealing effect is accounted for. We also prove that four-hop networks are, on the contrary, always unstable (even with the stealing effect) and show by simulations that instability extends to more complex linear and nonlinear topologies. To tackle this instability problem, we propose and evaluate a novel, distributed flow-control mechanism called EZ-flow. EZ-flow is fully compatible with the IEEE 802.11 standard (i.e., it does not modify headers in packets), can be implemented using off-the-shelf hardware, and does not entail any communication overhead. EZ-flow operates by adapting the minimum congestion window parameter at each relay node, based on an estimation of the buffer occupancy at its successor node in the mesh. We show how such an estimation can be conducted passively by taking advantage of the broadcast nature of the wireless channel. Real experiments, run on a nine-node test-bed deployed over four different buildings, show that EZ-flow effectively smooths traffic and improves delay, throughput, and fairness performance.

Network tomography establishes linear relationships between the characteristics of individual links and those of end-to-end paths. It has been proved that these relationships can be used to infer the characteristics of links from end-to-end measurements, provided that links are not correlated, i.e., the status of one link is independent from the status of other links.

We present Netscope, a tomographic technique that infers the loss rates of network links from unicast end-to-end measurements. Netscope uses a novel combination of first- and second-order moments of end-to-end measurements to identify and characterize the links that cannot be (accurately) characterized through existing practical tomographic techniques. Using both analytical and experimental tools, we show that Netscope enables scalable, accurate link-loss inference: in a simulation scenario involving 4000 links, 20% of them lossy, Netscope correctly identifies 94% of the lossy links with a false positive rate of 16%-a significant improvement over the existing alternatives. Netscope is robust in the sense that it requires no parameter tuning, moreover its advantage over the alternatives widens when the number of lossy links increases. We also validate Netscope's performance on an "Internet tomographer" that we deployed on an overlay of 400 PlanetLab nodes.

This paper presents a general class of gossip-based averaging algorithms, which are inspired from Uniform Gossip. While Uniform Gossip works synchronously on complete graphs, weighted gossip algorithms allow asynchronous rounds and converge on any connected, directed or undirected graph. Unlike most previous gossip algorithms, Weighted Gossip admits stochastic update matrices which need not be doubly stochastic. Double-stochasticity being very restrictive in a distributed setting, this novel degree of freedom is essential and it opens the perspective of designing a large number of new gossip-based algorithms. To give an example, we present one of these algorithms, which we call One-Way Averaging. It is based on random geographic routing, just like Path Averaging, except that routes are one way instead of round trip. Hence in this example, getting rid of double stochasticity allows us to add robustness to Path Averaging.

We show that CSMA is able to spontaneously synchronize transmissions in a wireless network with constant-size packets, and that this property can be used to devise efficient synchronized CSMA scheduling mechanisms without message passing. Using tools from queuing theory, we prove that for any connected wireless networks with arbitrary interference constraints, it is possible to implement self-synchronizing TDMA schedules without any explicit message passing or clock synchronization besides transmitting the original data packets, and the interaction can be fully local in that each node decides when to transmit next only by overhearing its neighbors' transmissions. We also provide a necessary and sufficient condition on the emergence of self-synchronization for a given TDMA schedule, and prove that such conditions for self-synchronization can be checked in a finite number of steps for a finite network topology.

Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust message-passing schemes for distributed information processing over networks. However, for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges as slowly as flooding (O(n2) messages). A recently proposed algorithm called geographic gossip improves gossip efficiency by a √n factor, by exploiting geographic information to enable multihop long-distance communications. This paper proves that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional √n factor, and is order optimal (O(n) messages) for grids and random geometric graphs with high probability. We develop a general technique (travel agency method) based on Markov chain mixing time inequalities which can give bounds on the performance of randomized message-passing algorithms operating over various graph topologies.

Recent analytical and experimental work demonstrate that IEEE 802.11-based wireless mesh networks are prone to turbulence. Manifestations of such turbulence take the form of large buffer build-up at relay nodes, end-to-end delay fluctuations, and traffic congestion. In this paper, we propose and evaluate a novel, distributed flow-control mechanism to address this problem, called EZ-flow. EZ-flow is fully compatible with the IEEE 802.11 standard (i.e., it does not modify headers in packets), can be implemented using off-the-shelf hardware, and does not entail any communication overhead. EZ-flow operates by adapting the minimum congestion window parameter at each relay node, based on an estimation of the buffer occupancy at its successor node in the mesh. We show how such an estimation can be conducted passively by taking advantage of the broadcast nature of the wireless channel. Real experiments, run on a 9-node testbed deployed over 4 different buildings, show that EZ-flow effectively smoothes traffic and improves delay, throughput, and fairness performance. We further corroborate these results with a mathematical stability analysis and extensive ns-2 simulations run for different traffic workloads and network topologies.

We design distributed and quantized average consensus algorithms on arbitrary connected networks. By construction, quantized algorithms cannot produce a real, analog average. Instead, our algorithm reaches consensus on the quantized interval that contains the average. We prove that this consensus in reached in finite time almost surely. As a by-product of this convergence result, we show that the majority voting problem is solvable with only 2 bits of memory per agent.

The automatic detection of failures in IP paths is an essential step for operators to perform diagnosis or for overlays to adapt. We study a scenario where a set of monitors send probes toward a set of target end-hosts to detect failures in a given set of IP interfaces. Unfortunately, there is a large probing cost to monitor paths between all monitors and targets at a very high frequency. We make two major contributions to reduce this probing cost. First, we propose a formulation of the probe optimization problem which, in contrast to the established formulation, is not NP complete. Second, we propose two linear programming algorithms to minimize probing cost. Our algorithms combine low frequency per-path probing to detect per-interface failures at a higher frequency. We analyze our solutions both analytically and experimentally. Our theoretical results show that the probing cost increases linearly with the number of interfaces in a random power-law graph. We confirm this linear increase in Internet graphs measured from PlanetLab and RON. Hence, Internet graphs belong to the most costly class of graph to probe.

We investigate both theoretically and experimentally the stability of CSMA-based wireless mesh networks, where a network is said to be stable if and only if the queue of each relay node remains (almost surely) finite. We identify two key factors that impact stability: the network size and the so-called "stealing effect", a consequence of the hidden node problem and non-zero propagation delays. We consider the case of a greedy source and prove, by using Foster's theorem, that 3-hop networks are stable, but only if the stealing effect is accounted for. On the other hand, we prove that 4-hop networks are always unstable (even with the stealing effect) and show by simulations that instability extends to more complex linear and non-linear topologies. We devise a stabilization strategy that throttles the source and prove that there exists a finite, non-zero rate at which the source can transmit while keeping the system stable. We run real experiments on a testbed composed of IEEE 802.11 nodes, which show the contrasting behavior of 3-hop and 4-hop networks and the effectiveness of our stabilization strategy.

We characterize the fairness of decentralized medium access control protocols based on CSMA/CA, in large multi-hop wireless networks. In particular, we show that the widely observed unfairness of these protocols in small network topologies does not always persist in large topologies. In regular networks, this unfairness is essentially due to the unfair advantage of nodes at the border of the network, which have a restricted neighborhood and thus a higher probability to access the communication channel. In large 1D lattice networks these border effects do not propagate inside the network, and nodes sufficiently far away from the border have equal access to the channel; as a result the protocol is long-term fair. In 2D lattice networks, we observe a phase transition. If the access intensity of the protocol is small, the border effects remain local and the protocol behaves similarly as in one-dimensional networks. However, if the access intensity of the protocol is large enough, the border effects persist independently of the size of the network and the protocol is strongly unfair. In irregular networks, the topology is inherently unfair. This unfairness increases with the access intensity of the protocol, but in a much smoother way than in regular two-dimensional networks. Finally, in situations where the protocol is long-term fair, we provide a characterization of its short-term fairness.

Decentralized medium access control schemes for wireless networks based on CSMA/CA, such as the IEEE 802.11 protocol, are known to be unfair. In multihop networks, they can even favor some links to such an extent that the others suffer from virtually complete starvation. This observation has been reported in quite a few works, but the factors causing it are still not well understood. We find that the capture effect and the relative values of the receive and carrier sensing ranges play a crucial role in the performance of these protocols. Using a simple Markovian model, we show that an idealized CSMA/CA protocol suffers from starvation when the receiving and sensing ranges are equal, but quite surprisingly that this unfairness is reduced or even disappears when these two ranges are sufficiently different. We also show that starvation has a positive counterpart, namely organization. When its access intensity is large the protocol organizes the transmissions in space in such a way that it maximizes the number of concurrent successful transmissions. We obtain exact formula for the so-called spatial reuse of the protocol on large line networks.

Average consensus and gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. Inspired by heat diffusion, they compute the average of sensor networks measurements by iterating local averages until a desired level of convergence. Confronted with the diversity of these algorithms, the engineer may be puzzled in his choice for one of them. As an answer to his/her need, we develop precise mathematical metrics, easy to use in practice, to characterize the convergence speed and the cost (time, message passing, energy...) of each of the algorithms. In contrast to other works focusing on time-invariant scenarios, we evaluate these metrics for ergodictime-varyingnetworks. Our study is based on Oseledec's theorem, which gives an almost- sure description of the convergence speed of the algorithms of interest. We further provide upper bounds on the convergence speed. Finally, we use these tools to make some experimental observations illustrating the behavior of the convergence speed with respect to network topology and reliability in both average consensus and gossip algorithms.

We characterize the fairness of decentralized medium access control protocols based on CSMA/CA, such as IEEE 802.11, in large multi-hop wireless networks. In particular, we show that the widely observed unfairness of the protocol in small network topologies does not always persist in large topologies. This unfairness is essentially due to the unfair advantage of nodes at the border of the network, which have a restricted neighborhood and thus a higher probability to access the communication channel. In large one-dimensional networks these border effects do not propagate inside the network, and nodes sufficiently far away from the border have equal access to the channel; as a result the protocol is long-term fair. In two-dimensional networks, we observe a phase transition. If the access intensity of the protocol is small, the border effects remain local and the protocol behaves similarly as in one- dimensional networks. However, if the access intensity of the protocol is large enough, the border effects persist independently of the size of the network and the protocol is strongly unfair. Finally, in situations where the protocol is long-term fair, we provide a characterization of its short-term fairness.

Due to the increased usage of NAT boxes and firewalls, it has become harder for applications to establish direct connections seamlessly among two end-hosts. A recently adopted proposal to mitigate this problem is to use relay nodes, end-hosts that act as intermediary points to bridge connections. Efficiently selecting a relay node is not a trivial problem, specially in a large-scale unstructured overlay system where end-hosts are heterogeneous. In such environment, heterogeneity among the relay nodes comes from the inherent differences in their capacities and from the way overlay networks are constructed. Despite this fact, good relay selection algorithms should effectively balance the aggregate load across the set of relay nodes. We address this problem using algorithms based on the two random choices method. We first prove that the classic load-based algorithm can effectively balance the load even when relays are heterogeneous, and that its performance depends directly on relay heterogeneity. Second, we propose an utilization-based random choice algorithm to distribute load in order to balance relay utilization. Numerical evaluations through simulations illustrate the effectiveness of this algorithm, indicating that it might also yield provable performance (which we conjecture). Finally, we support our theoretical findings through simulations of various large-scale scenarios, with realistic relay heterogeneity.

Wireless Mesh Networks (WMNs) are based on packet forwarding and therefore require efficient multi-hop protocols for their deployment. Toward this objective, we study the flow of packets through the network and using an analogy with fluid physics we classify them as being either laminar in the case of a smooth propagation or turbulent otherwise. Following this terminology, we present the tendency of current 802.11 to generate turbulent flows, i.e. to queue packets at the intermediate nodes for a non-deterministic time. However numerous applications such as VoIP, TCP and streaming are very delay sensitive and therefore laminar behavior is desirable. We model existing 802.11 multi-hop networks and identify the exponential backoff policy as a main parameter in the transition between laminar and turbulent behavior.

We address the problem of calculating link loss rates from end-to-end measurements. Contrary to existing works that use only the average end-to-end loss rates or strict temporal correlations between probes, we exploit second-order moments of end-to-end flows. We first prove that the variances of link loss rates can be uniquely calculated from the covariances of the measured end-to-end loss rates in any realistic topology. After calculating the link variances, we remove the un-congested links with small variances from the first-order moment equations to obtain a full rank linear system of equations, from which we can calculate precisely the loss rates of the remaining congested links. This operation is possible because losses due to congestion occur in bursts and hence the loss rates of congested links have high variances. On the contrary, most links on the Internet are un-congested, and hence the averages and variances of their loss rates are virtually zero. Our proposed solution uses only regular unicast probes and thus is applicable in today's Internet. It is accurate and scalable, as shown in our simulations and experiments on PlanetLab.

Decentralized medium access control schemes for wireless networks based on CSMA/CA, such as the 802.11 protocol, are known to be unfair. In multi-hop networks, they can even favor some connections to such an extent that the others suffer from virtually complete starvation. This observation has been reported in quite a few works, but the factors causing it are still not well understood. We find that the capture effect and the relative values of the receiving and carrier sensing ranges play a crucial role in the unfairness of these protocols. We show that an idealized 802.11 protocol does suffer from starvation when the receiving and sensing ranges are equal, but quite surprisingly this unfairness is reduced or even disappears when these two ranges are sufficiently different. Using a Markovian model, we explain why apparently benign variations in these ranges have such a dramatic impact on the 802.11 protocol performance.

Like other problems in network tomography or traffic matrix estimation, the location of congested IP links from end-to-end measurements requires solving a system of equations that relate the measurement outcomes with the variables representing the status of the IP links. In most networks, this system of equations does not have a unique solution. To overcome this critical problem, current methods use the unrealistic assumption that all IP links have the same prior probability of being congested. We find that this assumption is not needed, because these probabilities can be uniquely identified from a small set of measurements by using properties of Boolean algebra. We can then use the learnt probabilities as priors to find rapidly the congested links at any time, with an order of magnitude gain in accuracy over existing algorithms. We validate our results both by simulation and real implementation in the PlanetLab network.

We propose a mechanism for reliable broadcasting in wireless networks, that consists of two components: a method for bandwidth efficient acknowledgment collection, and a coding scheme that uses acknowledgments. Our approach combines ideas from network coding and distributed space time coding.

In this paper we study the capacity of wireless ad hoc networks with infrastructure support of an overlay of wired base stations. Such a network architecture is often referred to as hybrid wireless network or multihop cellular network. Previous studies on this topic are all focused on the twodimensional disk model proposed by Gupta and Kumar in their original work on the capacity of wireless ad hoc networks. We further consider a one-dimensional network model and a two-dimensional strip model to investigate the impact of network dimensionality and geometry on the capacity of such networks. Our results show that different network dimensions lead to significantly different capacity scaling laws. Specifically, for a one-dimensional network of n nodes and b base stations, even with a small number of base stations, the gain in capacity is substantial, increasing linearly with the number of base stations as long as b log b ≤ n. However, a two-dimensional square (or disk) network requires a large number of base stations b = Ω ( √ n) before we see such a capacity increase. For a 2-dimensional strip network, if the width of the strip is at least on the order of the logarithmic of its length, the capacity follows the same scaling law as in the 2-dimensional square case. Otherwise the capacity exhibits the same scaling behavior as in the 1-dimensional network. We find that the different capacity scaling behaviors are attributed to the percolation properties of the respective network models.

Failure restoration at the IP layer in IP-over-WDM networks requires to map the IP topology on the WDM topology in such a way that a failure at the WDM layer leaves the IP topology connected. Such a mapping is called survivable. Finding a survivable mapping is known to be NP-complete, making it impossible in practice to assess the existence or absence of such a mapping for large networks, (i) we first introduce a new concept of piecewise survivability, which makes the problem much easier in practice (although still NP-complete), and allows us to formally prove that a given survivable mapping does or does not exist, (ii) secondly, we show how to trace the vulnerable areas in the topology, and how to strengthen them to enable a survivable mapping, (iii) thirdly, we give an efficient and scalable algorithm that finds a survivable mapping. In contrast to the heuristics proposed in the literature to date, our algorithm exhibits a number of provable properties (e.g., it guarantees the piecewise survivability) that are crucial for (i) and (ii)

An achievable bit rate per source-destination pair in a wireless network of n randomly located nodes is determined adopting the scaling limit approach of statistical physics. It is shown that randomly scattered nodes can achieve, with high probability, the same 1/radicn transmission rate of arbitrarily located nodes. This contrasts with previous results suggesting that a 1/radicnlogn reduced rate is the price to pay for the randomness due to the location of the nodes. The network operation strategy to achieve the result corresponds to the transition region between order and disorder of an underlying percolation model. If nodes are allowed to transmit over large distances, then paths of connected nodes that cross the entire network area can be easily found, but these generate excessive interference. If nodes transmit over short distances, then such crossing paths do not exist. Percolation theory ensures that crossing paths form in the transition region between these two extreme scenarios. Nodes along these paths are used as a backbone, relaying data for other nodes, and can transport the total amount of information generated by all the sources. A lower bound on the achievable bit rate is then obtained by performing pairwise coding and decoding at each hop along the paths, and using a time division multiple access scheme

Confronted with the generalization of monitoring in operational networks, researchers have proposed placement algorithms that can help ISPs deploy their monitoring infrastructure in a cost effective way, while maximizing the benefits of their infrastructure. However, a static placement of monitors cannot be optimal given the short-term and long-term variations in traffic due to re-routing events, anomalies and the normal network evolution. In addition, most ISPs already deploy router embedded monitoring functionalities. Despite some limitations (inherent to being part of a router), these monitoring tools give greater visibility on the network traffic but raise the question on how to configure a network-wide monitoring infrastructure that may contain hundreds of monitoring points.We reformulate the placement problem as follows. Given a network where all links can be monitored, which monitors should be activated and which sampling rate should be set on these monitors in order to achieve a given measurement task with high accuracy and low resource consumption? We provide a formulation of the problem, an optimal algorithm to solve it, and we study its performance on a real backbone network.

Abstract — In multi-hop ad hoc networks, the efficiency of a medium access control protocol under heavy traffic load depends mainly on its ability to schedule a large number of simultaneous non-interfering transmissions. However, as each node has only a local view of the network, it is difficult to globally synchronize transmission times over the whole network. How does the lack of global coordination affect spatial reuse in multi-hop wireless networks? We show that in a de-centralized network the spatial reuse does not benefit from global clock synchronization. On the contrary, we demonstrate that non-slotted protocols using collision avoidance mechanisms can achieve a higher spatial reuse than the corresponding slotted protocols. By means of a simple backoff mechanism, one can thus favor the spontaneous emergence of spatially dense transmission schedules. I.

Abstract — Compared to wired networks, sensor networks pose two additional challenges for monitoring functions: they support much less probing traffic, and they change their routing topologies much more frequently. We propose therefore to use only endto-end application traffic to infer performance of internal network links. End-to-end data do not provide sufficient information to calculate link loss rates exactly but enough to identify poorly performing (lossy) links. We introduce inference techniques based on Maximum likelihood and Bayesian principles, that handle well noisy measurements and routing changes. We evaluate the performance of both inference algorithms in simulation and on real network traces. We find that these techniques achieve high detection and low false positive rates. I.

So far, performance and reliability of circuits have been determined by worst-case characterization of silicon and environmental noise. As new deep sub-micron technologies exacerbate process variations and reduce noise margins, worst-case design will eventually fail to meet an aggressive combination of objectives in performance, reliability, and power. In order to circumvent these difficulties, researchers have recently proposed a new design paradigm: self-calibrating circuits. Design parameters (e.g., operating points) of self-calibrating circuits are set by monitoring correctness of their operation, thus enabling to dynamically trade reliability for power or performance, depending on actual silicon capabilities and noise conditions. In this paper, we study the problem of detecting errors caused by self-calibration of the supply voltage and frequency of an on-chip link. These errors are caused by operation at sub-critical voltage and may be numerous. We attack the problem with a coding technique. We also discuss an alternative approach using double sampling flip-flops. We stress the complementarily of the two approaches and show how they can be combined. Finally, we consider extending our work to computation. We give preliminary research directions on the detection of errors induced by self-calibration for an adder

In this paper we consider sensor networks for intrusion detection, such that node deployment, node failures and node behavior result in coverage gaps and a fraction of disconnected nodes in an otherwise dense and well-connected network. We focus on the time delay for a mobile intruder to be detected by a sensor with a connected path to the sink, in contrast to existing results for the detection time by a sensor with arbitrary connectivity. We model our network using a supercritical percolation model on the plane, implying the existence of a unique unbounded connected component, and we assume that the sink belongs to this component. We analyze the distribution of the distance traveled by a moving target until it comes within sensing range of a node in the giant component, providing analytical bounds for linear intruder mobility and thorough simulation results for other mobility models. We show that the probability that the intruder proceeds undetected exhibits non-memoryless behavior over shorter distances and an exponentially decreasing tail. We also show that the time of contact with the giant component incurs considerably more delay than the time of first contact with any node, in networks with less than 10% of nodes without a path to the sink, which means that even a small percentage of node failures may have a drastic impact on the performance of intrusion detection by a wireless sensor networ.

The ability of the IEEE 802.11 medium access control (MAC) protocol to perform well in multi-hop ad hoc networks has been recently questioned. We observe levels of spatial reuse that are 30% to 50% away from the theoretical limit. The goal of this paper is to answer the following question: what prevents the IEEE 802.11 MAC protocol from operating at the limit determined by its physical layer? We identify three problems in the contention resolution mechanism of the IEEE 802.11 MAC protocol, and we show that they account for most of the gap separating the actual and optimal performances of the protocol. For each of the problems, we propose a solution that, once implemented, allows us to quantify the impact of the problem on the performance of the IEEE 802.11 MAC protocol. The resulting protocol operates 10% to 15% away from the theoretical limit. Finally, we show that reducing the overhead of the protocol to some negligible quantity brings the spatial reuse of the protocol to the theoretical limits. It also makes apparent the powerful organizing capacity of the IEEE 802.11 MAC protocol

The throughput of wireless networks is known to scale poorly when the number of users grows. The rate at which an arbitrary pair of nodes can communicate must decrease to zero as the number of users tends to infinity, under various assumptions. One of them is the requirement that the network is fully connected: the computed rate must hold for any pair of nodes of the network. We show that this requirement can be responsible for the lack of throughput scalability. We consider a two-dimensional (2-D) network of extending area with only one active source-destination pair at any given time, and all remaining nodes acting only as possible relays. Allowing an arbitrary small fraction of the nodes to be disconnected, we show that the per-node throughput remains constant as the network size increases. As a converse bound, we show that communications occurring at a fixed nonzero rate imply a fraction of the nodes to be disconnected. Our results are of information theoretic flavor, as they hold without assumptions on the communication strategies employed by the network nodes.

The throughput of wireless networks is known to scale poorly when the number of users grows. The rate at which an arbitrary pair of nodes can communicate must decrease to zero as the number of users tends to infinity, under various assumptions. One of them is the requirement that the network is fully connected: the computed rate must hold for any pair of nodes of the network. We show that this requirement can be responsible for the lack of throughput scalability. We consider a two-dimensional network of extending area with only one active source-destination pair at any given time, and all remaining nodes acting only as possible relays. Allowing an arbitrary small fraction of the nodes to be disconnected, we show that the per-node throughput remains constant as the network size increases. This result relies on percolation theory arguments and does not hold for one-dimensional networks, where a non-vanishing rate is impossible even if we allow an arbitrary large fraction of nodes to be disconnected. A converse bound is obtained using an ergodic property of shot noises. We show that communications occurring at a fixed nonzero rate imply a fraction of the nodes to be disconnected. Our results are of information theoretic flavor, as they hold without assumptions on the communication strategies employed by the network nodes.

We present a new scheme that mimics pattern formation in biological systems to create transmission patterns in multi-hop ad hoc networks. Our scheme is decentralized and relies exclusively on local interactions between the network nodes to create global transmission patterns. A transmission inhibits other transmissions in its immediate surrounding and encourages nodes located further away to transmit. The transmission patterns created by our medium access control scheme combine the efficiency of allocation-based schemes at high traffic loads and the flexibility of random access schemes. Moreover, we show that with appropriately chosen parameters our scheme converges to collision free transmission patterns that guarantee some degree of spatial reuse.

Failure restoration at the IP layer in IP-over-WDM networks requires to map the IP topology on the WDM topology in such a way that a failure at the WDM layer leaves the IP topology connected. Such a mapping is called survivable. Finding a survivable mapping is known to be NP-complete E. Modiano et al., (2002), making it impossible in practice to assess the existence or absence of such a mapping for large networks, (i) We first introduce a new concept of piecewise survivability, which makes the problem much easier, and allows us to formally prove that a given survivable mapping does or does not exist, (ii) Secondly, we show how to trace the vulnerable areas in the topology, and how to strengthen them to enable a survivable mapping, (iii) Thirdly, we give an efficient and scalable algorithm that finds a survivable mapping. In contrast to the heuristics proposed in the literature to date, our algorithm exhibits a number of provable properties that are crucial for (i) and (ii). We consider both link and node failures at the physical layer.

We study the impact of interferences on the connectivity of large-scale ad hoc networks, using percolation theory. We assume that a bi-directional connection can be set up between two nodes if the signal to noise ratio at the receiver is larger than some threshold. The noise is the sum of the contribution of interferences from all other nodes, weighted by a coefficient /spl gamma/, and of a background noise. We find that there is a critical value of /spl gamma/ above which the network is made of disconnected clusters of nodes. We also prove that if /spl gamma/ is nonzero but small enough, there exist node spatial densities for which the network contains a large (theoretically infinite) cluster of nodes, enabling distant nodes to communicate in multiple hops. Since small values of /spl gamma/ cannot be achieved without efficient CDMA codes, we investigate the use of a very simple TDMA scheme, where nodes can emit only every nth time slot. We show that it achieves connectivity similar to the previous system with a parameter /spl gamma//n.

Systems-on-Chip (SoC) design involves several challenges, stemming from the extreme miniaturization of the physical features and from the large number of devices and wires on a chip. Since most SoCs are used within embedded systems, specific concerns are increasingly related to correct, reliable, and robust operation. We believe that in the future most SoCs will be assembled by using large-scale macro-cells and interconnected by means of on-chip networks. We examine some physical properties of on-chip interconnect busses, with the goal of achieving fast, reliable, and low-energy communication. These objectives are reached by dynamically scaling down the voltage swing, while ensuring data integrity-in spite of the decreased signal to noise ratio-by means of encoding and retransmission schemes. In particular, we describe a closed-loop voltage swing controller that samples the error retransmission rate to determine the operational voltage swing. We present a control policy which achieves our goals with minimal complexity; such simplicity is demonstrated by implementing the policy in a synthesizable controller. Such a controller is an embodiment of a self-calibrating circuit that compensates for significant manufacturing parameter deviations and environmental variations. Experimental results show that energy savings amount up to 42%, while at the same time meeting performance requirements.

We develop a fast and efficient algorithm that finds a survivable (i.e., robust to single fiber failures) mapping of IP topology on the mesh of fibers in IP-over-WDM networks; we call it SMART. A number of algorithms solving this problem can be found in the literature. Since ILP solutions are highly complex, many heuristics were proposed. They usually start with some initial mapping and then try to gradually improve it. This involves the evaluation of the entire topology at each iteration, which is costly for large topologies. We propose a different approach. The SMART algorithm breaks down the task into a set of independent and very simple subtasks. The combination of solutions of these subtasks is a survivable mapping. This is why SMART is orders of magnitude faster than other proposals, especially when dealing with large topologies. We also extend the SMART algorithm to obtain a mapping resilient to fiber span failures, node failures and double-link failures. Finally, we show that the scalability of the standard heuristic approaches is additionally limited (contrary to SMART) when applied to double-link failures.

Self-calibrating designs are gaining momentum in both the computation and communication worlds. Instead of relying on the worst-case characterisation of design parameters, self calibrating systems determine autonomously the boundary of correct behaviour, and set design parameters accordingly. We focus on the communication task. We model errors due to over-aggressive operation and derive a channel model. We show that self-synchronising codes achieve completely reliable communication over this channel model, and study a known example, LEDR (level encoded 2-phase dual-rail), which is an improvement of the well-known dual-rail code. Then, we introduce a family of coding schemes which are a generalisation of LEDR, and study their performance over our channel model. We observe that the wiring overhead can be significantly reduced at the expense of a limited loss in reliability. Finally, we extend our channel model to include additive noise, and show that in this more general situation a specific instance of our coding scheme has similar or better performance than LEDR, at a smaller wiring overhead.

We study the connectivity and capacity of finite area ad hoc wireless networks, with an increasing number of nodes (dense networks). We find that the properties of the network strongly depend on the shape of the attenuation function. For power law attenuation functions, connectivity scales, and the available rate per node is known to decrease like 1//spl radic/n. On the contrary, if the attenuation function does not have a singularity at the origin and is uniformly bounded, we obtain bounds on the percolation domain for large node densities, which show that either the network becomes disconnected, or the available rate per node decreases like 1/n.

We consider the problem of how throughput in a wireless network with randomly located nodes scales as the number of users grows. Following the physical model of Gupta and Kumar, we show that randomly scattered nodes can achieve the optimal 1/(n)/sup 1/2/ per-node transmission rate of arbitrarily located nodes. This contrasts with previous achievable results suggesting that a 1/(n log n)/sup 1/2/ reduced rate is the price to pay for the additional randomness introduced into the system. Our results rely on percolation theory arguments. In the high density regime the network is fully connected but generates excessive interference. In the low density regime the network loses connectivity. Percolation theory ensures that a wireless backbone forms in the transition region between this two extreme scalings. This backbone does not cover all the nodes, nevertheless it is sufficiently rich in crossing paths so that it can transport all the traffic in the network. By operating the network in this transition region between order and disorder, we are able to prove our tight bound.

We consider a wireless sensor network, where nodes switch between an active (on) and a sleeping (off) mode, to save energy. Their switching on/off schedules are completely non-coordinated. Their positions are distributed according to a Poisson process, and their connectivity range is larger or equal to their sensing range. The durations of active and sleeping periods are such that the number of active nodes at any particular time is so low that the network is always disconnected. Is it possible to use such a network for time-critical monitoring of an area? Such a scenario requires indeed to have bounds on the latency, which is the delay elapsed between the time at which an incoming event is sensed by some node of the network, and the time at which this information is retrieved by the data collecting sink. A positive answer is provided to this question under some assumptions discussed in the paper. More precisely, we prove that the messages sent by a sensing node reach the sink with a fixed asymptotic speed, which does not depend on the random location of the nodes, but only on the network parameters (node density, connectivity range, duration of active and sleeping periods). The results are obtained rigorously by using an extension of first passage percolation theory.

We study an approach to quality-of-service (QoS) that offers end-users the choice between two service classes defined according to their level of transmission protection. The fully protected (FP) class offers end-users a guarantee of survivability in the case of a single-link failure; all FP traffic is protected using a 1:1 protection scheme at the wavelength-division multiplexing (WDM) layer. The best effort protected (BEP) class is not protected; instead restoration at the IP layer is provided. The FP service class mimics what Internet users receive today. The BEP traffic is designed to run over the large amounts of unused bandwidth that exist in today's Internet. The goal is to increase the load carried on backbone networks without reducing the QoS received by existing customers. To support two such services, we have to solve two problems: the off-line problem of mapping logical links to pairs of disjoint fiber paths, and an on-line scheduling problem for differentiating packets from two classes at the IP layer. We provide an algorithm based on a Tabu Search meta-heuristic to solve the mapping problem, and a simple but efficient scheduler based on weighted fair queueing for service differentiation at the IP layer. We consider numerous requirements that carriers face and illustrate the tradeoffs they induce. We demonstrate that we can successfully increase the total network load by a factor between three and ten and still meet all the carrier requirements.

The impact of interferences on the connectivity of large-scale ad-hoc networks is studied using percolation theory. We assume that a bi-directional connection can be set up between two nodes if the signal to noise ratio at the receiver is larger than some threshold. The noise is the sum of the contribution of interferences from all other nodes, weighted by a coefficient /spl gamma/, and of a background noise. We find that there is a critical value of /spl gamma/ above which the network is made of disconnected clusters of nodes. We also prove that if /spl gamma/ is nonzero but small enough, there exist node spatial densities for which the network contains a large (theoretically infinite) cluster of nodes, enabling distant nodes to communicate in multiple hops. Since small values of /spl gamma/ cannot be achieved without efficient CDMA codes, we investigate the use of a very simple TDMA scheme, where nodes can emit only every n-th time slot. We show qualitatively that it even achieves a better connectivity than the previous system with a parameter /spl gamma//n.

We measure and analyze the single-hop packet delay through operational routers in the Sprint Internet protocol (IP) backbone network. After presenting our delay measurements through a single router for OC-3 and OC-12 link speeds, we propose a methodology to identify the factors contributing to single-hop delay. In addition to packet processing, transmission, and queueing delay at the output link, we observe the presence of very large delays that cannot be explained within the context of a first-in first-out output queue model. We isolate and analyze these outliers. Results indicate that there is very little queueing taking place in Sprint's backbone. As link speeds increase, transmission delay decreases and the dominant part of single-hop delay is packet processing time. We show that if a packet is received and transmitted on the same linecard, it experiences less than 20 μs of delay. If the packet is transmitted across the switch fabric, its delay doubles in magnitude. We observe that processing due to IP options results in single-hop delays in the order of milliseconds. Milliseconds of delay may also be experienced by packets that do not carry IP options. We attribute those delays to router idiosyncratic behavior that affects less than 1% of the packets. Finally, we show that the queueing delay distribution is long-tailed and can be approximated with a Weibull distribution with the scale parameter a=0.5 and the shape parameter b=0.6 to 0.82.

Our goal is to design a traffic model for uncongested IP backbone links that is simple enough to be used in network operation, and that is protocol and application agnostic in order to be as general as possible. The proposed solution is to model the traffic at the flow level by a Poisson shot-noise process. In our model, a flow is a generic notion that must be able to capture the characteristics of any kind of data stream. We analyze the accuracy of the model with real traffic traces collected on the Sprint IP backbone network. Despite its simplicity, our model provides a good approximation of the real traffic observed in the backbone and of its variation. Finally, we discuss three applications of our model to network design and management.

No abstract available.

We consider a large-scale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely ad-hoc network and a hybrid network, where fixed base stations can be reached in multiple hops. We assume here that power constraints are modeled by a maximal distance above which two nodes are not (directly) connected. We find that the introduction of a sparse network of base stations does significantly help in increasing the connectivity, but only when the node density is much larger in one dimension than in the other. We explain the results by percolation theory. We obtain analytical expressions of the probability of connectivity in the 1D case. We also show that at a low spatial density of nodes, bottlenecks are unavoidable. Results obtained on actual population data confirm our findings.

We measure and analyze the single-hop packet delay through operational routers in a backbone IP network. First we present our delay measurements through a single router. Then we identify step-by-step the factors contributing to single-hop delay. In addition to packet processing, transmission, and queueing delays, we identify the presence of very large delays due to non-work-conserving router behavior. We use a simple output queue model to separate those delay components. Our step-by-step methodology used to ohtain the pure queueing delay is easily applicable to any single-hop delay measurements. After obtaining the queueing delay, we analyze the tail of its distribution, and find that it is long tailed and fits a Weihull distrihution with the scale parameter, a = 0.5, and the shape parameter, b = 0.58 to 0.6. The measured average queueing delay is larger than predicted by M/M/l, M/G/l, and FBM models when the link utilization is below 70%, but its absolute value is quite small.

LCA

By extending the system theory under the (min, +) algebra to the time-varying setting, we solve the problem of constrained traffic regulation and develop a calculus for dynamic service guarantees. For a constrained traffic-regulation problem with maximum tolerable delay d and maximum buffer size q, the optimal regulator that generates the output traffic conforming to a subadditive envelope f and minimizes the number of discarded packets is a concatenation of the g-clipper with g(t) = min[f(t+ d), f (t)+q] and the maximal f-regulator. The g-clipper is a bufferless device, which optimally drops packets as necessary in order that its output be conformant to an envelope g. The maximal f-regulator is a buffered device that delays packets as necessary in order that its output be conformant to an envelope f. The maximal f-regulator is a linear time-invariant filter with impulse response f, under the (min, +) algebra. To provide dynamic service guarantees in a network, we develop the concept of a dynamic server as a basic network element. Dynamic servers can be joined by concatenation, "filter bank summation," and feedback to form a composite dynamic server. We also show that dynamic service guarantees for multiple input streams sharing a work-conserving link can be achieved by a dynamic service curve earliest deadline scheduling algorithm, if an appropriate admission control is enforced.

We consider a scenario where multimedia data are sent over a network offering a guaranteed service. A smoothing device writes the stream into a transmitting device with limited input buffer; at the destination, the decoder waits for an initial playback delay and reads the stream from the receiver buffer. We assume that some limited look-ahead is possible at the source, and that the playback buffer size is limited. First, we consider the case where the stream is delivered from the source directly to the destination buffer. We obtain closed-form expressions of the minimal required values in the case of a CBR smoothing. Then we consider the case where the stream is first transmitted through a backbone network to an intermediate server, which relays the multimedia data to the final destination via an access network. We compute the requirements on playback delay, buffer sizes and amount of look-ahead.

Network calculus is a collection of results based on MinPlus algebra, which applies to deterministic queuing systems found in communication networks. It can be used, for example, to understand the computations for delays used in the IETF guaranteed service, why re-shaping delays can be ignored in shapers or spacer-controllers, a common model for schedulers, etc. This short tutorial presents the basic results of network calculus and their application to some fundamental performance bounds in communication networks.

For pt. I see ibid., vol.4, p.93-6 (May 2000). We model some queuing systems arising in guaranteed service networks (such as RSVP/IP or ATM) as nonlinear min-plus systems that can be bounded by linear systems. We apply this method to the window flow control problem previously studied by Chang (1997), Agrawal and Rajan (1996), to the optimal smoothing of video through a network offering guaranteed service. We revisit the greedy shaper, and we also show how the same method enables us to compute the losses in a shaper by modelling it as a linear min-plus system. Finally, we describe the time-varying shaper.

Fault identification and location in optical networks is hampered by a multitude of factors: the redundancy and the lack of coordination (internetworking) of the managements at the different layers (WDM, SDH/SONET, ATM, IP); the large number of alarms a single failure can trigger; the difficulty in detecting some failures; and the resulting need to cope with missing or false alarms. Moreover, the problem of multiple fault location is NP-complete, so that the processing time may become an issue for large meshed optical networks. We propose an algorithm for locating multiple failures at the physical layer of a WDM network. They can be either hard failures, that is, unexpected events that suddenly interrupt the established channels; or soft failures, that is, events that progressively degrade the quality of transmission; or both, hard failures are detected at the WDM layer. Soft failures can sometimes be detected at the optical layer if proper testing equipment is deployed, but often require performance monitoring at a higher layer (SDH, ATM, or IP). Both types of failures, and both types of error monitoring, are incorporated in our algorithm, which is based on a classification and abstraction of the components of the optical layer and of the upper layer. Our algorithm does not rely on timestamps nor on failure probabilities, which are difficult to estimate and to use in practice. Moreover, our algorithm also handles missing and false alarms. The nonpolynomial computational complexity of the problem is pushed ahead into a precomputational phase, which is done off-line, when the optical channels are set up or cleared down. This results in fast on-line location of the failing components upon reception of the ringing alarms.

Connection admission control (CAC) algorithms are used to decide whether an incoming connection should be accepted or rejected in a node of a network offering reservation based services in order to maintain the guaranteed quality of service (QoS) in the network. In this paper, we consider the statistical CAC algorithm proposed by Elwalid et al. (see IEEE JSAC, vol.13, no.6, p.1048-56, 1995). The traffic model is made of on-off sources and the QoS parameter is the loss probability. Based on the traffic descriptors of existing and incoming connections, the algorithm takes its decision by computing an upper bound of this probability and checking whether it is larger than a given tolerance /spl epsiv/. Usually this tolerance is a fixed, given parameter. We propose here to adapt /spl epsiv/ to react to the actual losses experienced at the node using a simple regulation mechanism: if the actual loss rate is much smaller than the targeted loss rate, /spl epsiv/ is increased to make a more aggressive usage of the available resources, and vice versa if the actual loss rate is too high. We discuss the influence of the regulation parameters and we show that despite its simplicity this regulated CAC improves significantly the performance of its non-tunable counterpart.

This paper describes two variants of the Kohonen's self-organizing feature map (SOFM) algorithm. Both variants update the weights only after presentation of a group of input vectors. In contrast, in the original algorithm the weights are updated after presentation of every input vector. The main advantage of these variants is to make available a finer grain of parallelism, for implementation on machines with a very large number of processors, without compromising the desired properties of the algorithm. In this work it is proved that, for one-dimensional (1-D) maps and 1-D continuous input and weight spaces, the strictly increasing or decreasing weight configuration forms an absorbing class in both variants, exactly as in the original algorithm. Ordering of the maps and convergence to asymptotic values are also proved, again confirming the theoretical results obtained for the original algorithm. Simulations of a real-world application using two-dimensional (2-D) maps on 12-D speech data are presented to back up the theoretical results and show that the performance of one of the variants is in all respects almost as good as the original algorithm. Finally, the practical utility of the finer parallelism made available is confirmed by the description of a massively parallel hardware system that makes effective use of the best variant.

Implementing a neural network on a digital or mixed analog and digital chip yields the quantization of the synaptic weights dynamics. This paper addresses this topic in the case of Kohonen's self-organizing maps. We first study qualitatively how the quantization affects the convergence and the properties, and deduce from this analysis the way to choose the parameters of the network (adaptation gain and neighborhood). We show that a spatially decreasing neighborhood function is far more preferable than the usually rectangular neighborhood function, because of the weight quantization. Based on these results, an analog nonlinear network, integrated in a standard CMOS technology, and implementing this spatially decreasing neighborhood function is then presented. It can be used in a mixed analog and digital circuit implementation.