Philippe Jacquet

Highway Vehicular Delay Tolerant Networks: Information Propagation Speed Properties

In this paper, we provide a full analysis of the information propagation speed in bidirectional vehicular delay tolerant networks such as roads or highways. The provided analysis shows that a phase transition occurs concerning the information propagation speed, with respect to the vehicle densities in each direction of the highway. We prove that under a certain threshold, information propagates on average at vehicle speed, while above this threshold, information propagates dramatically faster at a speed that increases quasi-exponentially when the vehicle density increases. We provide the exact expressions of the threshold and of the average information propagation speed near the threshold, in case of finite or infinite radio propagation speed. Furthermore, we investigate in detail the way information propagates under the threshold, and we prove that delay tolerant routing using cars moving on both directions provides a gain in propagation distance, which is bounded by a sublinear power law with respect to the elapsed time, in the referential of the moving cars. Combining these results, we thus obtain a complete picture of the way information propagates in vehicular networks on roads and highways, which may help designing and evaluating appropriate vehicular ad hoc networks routing protocols. We confirm our analytical results using simulations carried out in several environments (The One and Maple).

Bandwidth reservation in multihop wireless networks: complexity and mechanisms

We show that link interferences in multihop wireless networks make the problem of selecting a path satisfying bandwidth requirements an NP-complete problem, even under simplified rules for bandwidth reservation. This is in sharp contrast to path selection in wireline networks where efficient polynomial algorithms exist. We also describe a distributed mechanism for the problem of slot allocation according to bandwidth reservation in a wireless slotted environment.

Impact of jitter-based techniques on flooding over wireless ad hoc networks: Model and analysis

Jitter is used in wireless ad hoc networks to reduce the number of packet collisions and the number of transmissions. This is done by scheduling random back-off for each packet to be transmitted and by piggybacking multiple packets in a single transmission. This technique has been standardized by the IETF in RFC 5148. This paper investigates on the impact of the standardized jitter mechanism on network-wide packet dissemination - i.e. flooding, an important component for many protocols used today. A novel analytical model is introduced, capturing standard jitter traits. From this model is derived accurate characterization of the effects of jittering on flooding performance, including the additional delay for flooded packets on each traversed network interface, the reduction of the number of transmissions over each network interface, and the increased length of transmissions, depending on jitter parameters. This paper also presents an analysis of the use of jitter in practice, over an 802.11 wireless link layer based on CSMA. The analytical results are then validated via statistical discrete event simulations. The paper thus provides a comprehensive overview of the impact of jittering in wireless ad hoc networks.

An Universal Predictor Based on Pattern Matching: Preliminary results 1

We consider here an universal predictor based on pattern matching. For a given string x1, x2…, xn, the predictor will guess the next symbol xn+1 in such a way that the prediction error tends to zero as n →∞ provided the string x 1 n = x1, x2, …, xn, is generated by a mixing source. We shall prove that the rate of convergence of the prediction error is 0(n-e) for any e > 0. In this preliminary version, we only prove our results for memoryless sources and a sketch for mixing sources. However, we indicate that our algorithm can predict equally successfully the next k symbols as long as k= 0(1).

A novel technique to monitor carburizing processes

This paper presents the principle and testing of a novel technique developed for carburizing processes monitoring. The technique relies upon an experimental device made of a thin iron foil with a carburizing atmosphere on one side and a decarburizing atmosphere on the other. The principle of carburizing control is based on the fact that when steady-state of carbon diffusion is reached across the thin iron foil, the measured mass flux of carbon on the decarburizing side is related to the inflow of carbon into the parts during the carburizing treatment. Hence, as a probe could be inserted directly into a given furnace, it would provide an in situ control facility. The proposed device could then be used for controlling atmospheric or low-pressure (vacuum) carburizing treatments. The results presented here are limited to atmospheric conditions. Nevertheless, they gave the incentive to the researchers to pursue the development of the device to allow for measurements in a low-pressure furnace and to refine the experimental bench to quantify thoroughly the phenomena involved within the foil.

On the throughput-delay trade-off in georouting networks

We study the scaling properties of a georouting scheme in a wireless multi-hop network of n mobile nodes. Our aim is to increase the network capacity quasi linearly with n while keeping the average delay bounded. In our model, mobile nodes move according to an i.i.d. random walk with velocity v and transmit packets to randomly chosen destinations. The average packet delivery delay of our scheme is of order 1/v and it achieves the network capacity of order n/(log n log log n). This shows a practical throughput-delay trade-off, in particular when compared with the seminal result of Gupta and Kumar which shows network capacity of order √(n/log n) and negligible delay and the groundbreaking result of Grossglauser and Tse which achieves network capacity of order n but with an average delay of order √n/v. The foundation of our improved capacity and delay trade-off relies on the fact that we use a mobility model that contains free space motion, a model that we consider more realistic than classic brownian motions. We confirm the generality of our analytical results using simulations under various interference models.

Counting Markov Types, Balanced Matrices, and Eulerian Graphs

The method of types is one of the most popular techniques in information theory and combinatorics. Two sequences of equal length have the same type if they have identical empirical distributions. In this paper, we focus on Markov types, that is, sequences generated by a Markov source (of order one). We note that sequences having the same Markov type share the same so-called balanced frequency matrix that counts the number of distinct pairs of symbols. We enumerate the number of Markov types for sequences of length over an alphabet of size . This turns out to be asymptotically equivalent to estimating the number of the balanced frequency matrices, the number of integer solutions of a system of linear Diophantine equations, and the number of connected Eulerian multigraphs. For fixed , we prove that the number of Markov types is asymptotically equal to d(m) n^m²^-m/(m²-m)! where we give an integral representation for d(m). For m →∞, we conclude that asymptotically the number of types is equivalent to √2m^3m/2e^m²/m^2m22^mπ^m/2 n^m2-m provided that m = o(n^1/4). These findings are derived by analytical techniques ranging from analytic combinatorics, to multidimensional generating functions, to the saddle point method.

Classification of Markov sources through joint string complexity: Theory and experiments

We propose a classification test to discriminate Markov sources based on the joint string complexity. String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we define the joint string complexity as the cardinality of the set of words which both strings have in common. In this paper we analyze the average joint complexity when both strings are generated by two Markov sources. We provide fast converging asymptotic expansions and present some experimental results showing usefulness of the joint complexity to text discrimination.

Joint sequence complexity analysis: Application to social networks information flow

In this paper we study joint sequence complexity and its applications for finding similarities between sequences up to the discrimination of sources. The mathematical concept of the complexity of a sequence is defined as the number of distinct subsequences of it. Sequences containing many common parts have a higher joint complexity. The analysis of a sequence in subcomponents is done by suffix trees, which is a simple, fast, and low complexity method to store and recall them from the memory, especially for short sequences. Joint complexity is used for evaluating the similarity between sequences generated by different Markov sources. Markov models well describe the generation of natural text, and their performance can be predicted via linear algebra, combinatorics, and asymptotic analysis. We exploit datasets from different natural languages, for both short and long sequences, with very promising results. The goal is to perform automated online sequence analysis on information streams, e.g., on social networks such as Twitter. ® 2014 Alcatel-Lucent.

Multi-lane vehicle-to-vehicle networks with time-varying radio ranges: Information propagation speed properties

We study the information propagation speed in multi-lane vehicle-to-vehicle networks such as roads or highways. We focus on the impact of time-varying radio ranges and of multiple lanes of vehicles, varying in speed and in density. We assess the existence of a vehicle density threshold under which information propagates on average at the fastest vehicle speed and above which information propagates dramatically faster. We first prove that no such phase transition occurs if there is only one lane, regardless of the density of vehicles, when one takes into account real-time radio communication range variations at the MAC layer. We then prove that, on the other hand, a phase transition exists as soon as there are multiple lanes with different vehicle speeds and appropriate densities. We characterize conditions under which the phase transition occurs and we derive bounds on the corresponding threshold as a simple relationship between the vehicle density on the fastest lane and the sum of densities on the other lanes. Our results intrinsically encompass a wide range of vehicular network scenarios, including one-way and two-way roads, as well as special cases such as road side units and/or parked cars being used as relays. We confirm our analytical results using simulations.