A tight bound on the throughput of queueing networks with blocking

In this paper, we present a bounding methodology that allows to compute a tight lower bound on the cycle time of fork--join queueing networks with blocking and with general service time distributions. The methodology relies on two ideas. First, probability masses fitting (PMF) discretizes the service time distributions so that the evolution of the modified network can be modelled by a Markov chain. The PMF discretization is simple: the probability masses on regular intervals are computed and aggregated on a single value in the orresponding interval. Second, we take advantage of the concept of critical path, i.e. the sequence of jobs that covers a sample run. We show that the critical path can be computed with the discretized distributions and that the same sequence of jobs offers a lower bound on the original cycle time. The tightness of the bound is shown on computational experiments. Finally, we discuss the extension to split--and--merge networks and approximate estimations of the cycle time.queueing networks, blocking, throughput, bound, probability masses fitting, critical path.

Probability masses fitting in the analysis of manufacturing flow lines

A new alternative in the analysis of manufacturing systems with finite buffers is presented. We propose and study a new approach in order to build tractable phase-type distributions, which are required by state-of-the-art analytical models. Called "probability masses fitting" (PMF), the approach is quite simple: the probability masses on regular intervals are computed and aggregated on a single value in the corresponding interval, leading to a discrete distribution. PMF shows some interesting properties: it is bounding, monotonic and it conserves the shape of the distribution. After PMF, from the discrete phase-type distributions, state-of-the-art analytical models can be applied. Here, we choose the exactly model the evolution of the system by a Markov chain, and we focus on flow lines. The properties of the global modelling method can be discovered by extending the PMF properties, mainly leading to bounds on the throughput. Finally, the method is shown, by numerical experiments, to compute accurate estimations of the throughput and of various performance measures, reaching accuracy levels of a few tenths of percent.stochastic modelling, flow lines, probability masses fitting, discretization, bounds, performance measures, distributions.

Tight Bounds for Consensus Systems Convergence

We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set, by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with period smaller than a certain value converge to zero, and bounds exist on that value. We provide a stronger bound holding for both polyhedral norms and polyhedral seminorms. In the latter case, the matrix products do not necessarily converge to 0, but all trajectories of the associated system converge to a common invariant space. We prove our bound to be tight, in the sense that for any polyhedral seminorm, there is a set of matrices such that not all infinite products converge, but every periodic product with period smaller than our bound does converge. Our technique is based on an analysis of the combinatorial structure of the face lattice of the unit ball of the nonincreasing seminorm. The bound we obtain is equal to half the size of the largest antichain in this lattice. Explicitly evaluating this quantity may be challenging in some cases. We therefore link our problem with the Sperner property: the property that, for some graded posets, -- in this case the face lattice of the unit ball -- the size of the largest antichain is equal to the size of the largest rank level. We show that some sets of matrices with invariant polyhedral seminorms lead to posets that do not have that Sperner property. However, this property holds for the polyhedron obtained when treating sets of stochastic matrices, and our bound can then be easily evaluated in that case. In particular, we show that for the dimension of the space $n \geq 8$, our bound is smaller than the previously known bound by a multiplicative factor of $\frac{3}{2 \sqrt{\pi n}}$

Images de l'Europe dans l'enseignement de la géographie

L'iconographie des livres solaires de géographie participe fortement à la construction des représentations et à l'élaboration d'une conception de l'Europe

Enseigner de la géographie aux jeunes écoliers du primaire en France: quelques repères chronologiques

History of the teaching of géography in primary in Francechronologie de l'enseignement de la géographie à l'école primaire en Franc

Le terrain, les programmes scolaires et les figures du géographe

Fieldwork and practice are at the joining point of pedagogical concern and geographical thought. But, in despite of many pedagogical injunctions from the 1880thies to the 1980thies, fieldworks stay scares at school. This may be related to the different figures of the Geographer: office geographer, open-air geographer and workshop geographer. These three figures of the Geographer can be associated, from the Enlightment to the beginning of the XXIth century, with three modalities for scholar geography: as memory branch of learning, as experimental and general science and as a teaching method based upon documents.Le terrain et les pratiques de terrain sont à la jonction des préoccupations des pédagogues et des géographes. Mais, contrairement à ce qu'il était souvent demandé des années 1880 aux années 1980, les pratiques du terrain sont loin de s'être généralisées dans le cadre de la géographie scolaire. Ceci peut être mis en regard avec les différentes figures du géographe qui apparaissent sur une période plus ample : le géographe de cabinet, le géographe de plein-vent et le géographe d'atelier. Ces trois figures du géographe correspondent à trois régimes de la géographie scolaire : la discipline de mémoire, la géographie leçon de choses et la pédagogie par le document

Efficient Algorithms for the Consensus Decision Problem

We address the problem of determining if a discrete time switched consensus system converges for any switching sequence and that of determining if it converges for at least one switching sequence. For these two problems, we provide necessary and sufficient conditions that can be checked in singly exponential time. As a side result, we prove the existence of a polynomial time algorithm for the first problem when the system switches between only two subsystems whose corresponding graphs are undirected, a problem that had been suggested to be NP-hard by Blondel and Olshevsky.Comment: Small modifications after comments from reviewer

Enseigner la France en géographie aux jeunes écoliers (1788-2008)

For the last two centuries, the ways of teaching geography of France to the young French pupils from 9 to 11 years old have known many transformations. The objectives and the finality have changed. These transformations result from the general changes in pedagogical methods at school, but also from the particular changes of how the French conceive their own territory and national identity.Since the beginning of the 19th century Geography taught in primary schools differs from the geography made for colleges and high schools, which has remained for a long time within the tradition of historical geography from the Ancient time to the modern period. At the end of the 19th century the 3rd French Republic put France and its colonies as the centre and the horizon of the geography studies. Geography at school was a main way to build up a national identity.In the 20th century, and more particularly during the sixties, thanks to the development of new media, space as perceived by young children became wider and more various. New curricula have been opened to new spatial dimensions: Europe and the world. The building of a national identity blends with regional, European and world wide scalar levels. Even if the latest curriculum is more focused on France.L'évolution de la façon dont la géographie de la France est présentée aux petits Français âgés de 9 à 11 ans montre les transformations des méthodes pédagogiques, en particulier celles en usage dans la leçon de géographie ; elle témoigne des transformations des finalités de l'enseignement de la géographie à l'école élémentaire et reflète autant l'évolution de l'espace français que la façon dont les Français pensent leur territoire.La géographie destinée aux élèves des écoles communales se différencie d'emblée des savoirs géographiques enseignés dans l'enseignement secondaire en rompant d'emblée avec la tradition de la géographie historique. La IIIe République fait ensuite de la France et de ses colonies l'horizon de la géographie de l'école primaire et le cadre identitaire des jeunes français. Depuis les années soixante l'espace perçu par les jeunes enfants via les différents médias s'est considérablement élargi et diversifié et les programmes scolaires se sont ouverts sur l'Europe et le monde, associant la construction de l'identité nationale avec d'autres niveaux scalaires de référence : la région, l'Europe, le monde ; même si le dernier programme est plus centré sur la France

Reachability of Consensus and Synchronizing Automata

We consider the problem of determining the existence of a sequence of matrices driving a discrete-time consensus system to consensus. We transform this problem into one of the existence of a product of the transition (stochastic) matrices that has a positive column. We then generalize some results from automata theory to sets of stochastic matrices. We obtain as a main result a polynomial-time algorithm to decide the existence of a sequence of matrices achieving consensus.Comment: Update after revie

Moins d’antibiotiques, moins de résistances

peer reviewedAnalyse de Butler CC, Dunstan F, Heginbothom M, et al. Containing antibiotic resistance: decreased antibiotic-resistant coliform urinary tract infections with reduction in antibiotic prescribing by general practices. Brit J Gen Pract 2007;57:785-92