Processus de Poisson généralisé autorégressif d'ordre 1

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Processus de Poisson généralisé autorégressif d'ordre 1

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Queues with Customer Induced Interruption

In this thesis we have introduced and studied the notion of self interruption of service by customers. Service interruption in queueing systems have been extensively discussed in literature (see, Krishnamoorthy, Pramod and Chakravarthy [38]) for the most recent survey. So far all work reported deal with cases in which service interruptions are generated by sources other than customers. However, there are situations where interruptions are due to the customers rather than the system. Such situations are especially arise at doctors clinic, banks, reservation counter etc. Our attempt is to quantify a few of such problems. Systematically we have proceed from single server queue (in Chapter 2) to multi-server queues (Chapter 3). In Chapte 4, we have studied a very general multiserver queueing model with service interruption and protection of service phases. We also introduced customer interruption in a retrial setup (in Chapter 5). All models (from Chapter 2 to Chapter 4) that were analyzed involve 'non-preemptive priority' for interrupted customers where as in the model discussed in Chapter 5 interruption of service by customers is not encouraged. So the interrupted customers cannot access the server as long as there are primary customers in the system. In Chapter 5 we have obtained an explicit expression for the stability condition of the system. In all models analyzed in this thesis, we have assumed that no more than one interruption is allowed for a customer while in service. Since the models are not analytically tractable, a large number of numerical illustrations were given in each chapter it illustrate the working of the systems. We can extend the models discussed in this thesis to several directions. For example some of the models can be analyzed with both server induced and customer induced interruptions the results for which are not available till date. Another possible extension of work is to the case where there is no bound on the number of interruptions a customer is permitted to have before service completion. More complex is the case where a customer is permitted to have a nite number (K ≥ 2) of We can extend the models discussed in this thesis to several directions.

Quasi-elastic barrier distribution of the (17)O+(64)Zn system and the derivation of the (17)O nuclear matter diffuseness

The quasi-elastic excitation function for the (17)O+(64)Zn system was measured at energies near and below the Coulomb barrier, at the backward angle theta(lab) = 161 degrees. The corresponding quasi-elastic barrier distribution was derived. The excitation function for the neutron stripping reactions was also measured, at the same angle and energies, and the experimental values of the spectroscopic factors were deduced by fitting the data. A reasonably good agreement was obtained between the experimental quasi-elastic barrier distribution with the coupled-channel calculations including a very large number of channels. Of the channels investigated, three dominated the coupling matrix: two inelastic channels, (64)Zn(2(1)(+)) and (17)O(1/(+)(2)), and one-neutron transfer channel, particularly the first one. On the other hand, a very good agreement is obtained when we use a nuclear diffuseness for the (17)O nucleus larger than the one for (16)O. We verify that quasi-elastic barrier distribution is a sensitive tool for determining nuclear matter diffuseness.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Quasi-stationarity in populations that are subject to large-scale mortality or emigration

We shall examine a model, first studied by Brockwell et al. [Adv Appl Probab 14 (1982) 709.], which can be used to describe the longterm behaviour of populations that are subject to catastrophic mortality or emigration events. Populations can suffer dramatic declines when disease, such as an introduced virus, affects the population, or when food shortages occur, due to overgrazing or fluctuations in rainfall. However, perhaps surprisingly, such populations can survive for long periods and, although they may eventually become extinct, they can exhibit an apparently stationary regime. It is useful to be able to model this behaviour. This is particularly true of the ecological examples that motivated the present study, since, in order to properly manage these populations, it is necessary to be able to predict persistence times and to estimate the conditional probability distribution of population size. We shall see that although our model predicts eventual extinction, the time till extinction can be long and the stationary exhibited by these populations over any reasonable time scale can be explained using a quasistationary distribution. (C) 2001 Elsevier Science Ltd. All rights reserved.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

A new technique to measure micromotion distribution around a cementless femoral stem.

The interfacial micromotion is closely associated to the long-term success of cementless hip prostheses. Various techniques have been proposed to measure them, but only a few number of points over the stem surface can be measured simultaneously. In this paper, we propose a new technique based on micro-Computer Tomography (μCT) to measure locally the relative interfacial micromotions between the metallic stem and the surrounding femoral bone. Tantalum beads were stuck at the stem surface and spread at the endosteal surface. Relative micromotions between the stem and the endosteal bone surfaces were measured at different loading amplitudes. The estimated error was 10μm and the maximal micromotion was 60μm, in the loading direction, at 1400N. This pilot study provided a local measurement of the micromotions in the 3 direction and at 8 locations on the stem surface simultaneously. This technique could be easily extended to higher loads and a much larger number of points, covering the entire stem surface and providing a quasi-continuous distribution of the 3D interfacial micromotions around the stem. The new measurement method would be very useful to compare the induced micromotions of different stem designs and to optimize the primary stability of cementless total hip arthroplasty.

Contractual allocation of decision rights and incentives: The case of automobile distribution

We analyze empirically the allocation of rights and monetary incentives in automobile franchise contracts. These contracts substantially restrict the decision rights of dealers and grant manufacturers extensive contractual completion and enforcement powers, converting the manufacturers, de facto, in a sort of quasi-judiciary instance. Variation in the allocation of decision rights andincentive intensity is explained by the incidence of moral hazard in the relation. In particular, when the cost of dealer moral hazard is higher and the risk of manufactureropportunism is lower, manufacturers enjoy more discretion in determining the performance required from their dealers and in using mechanisms such as monitoring, termination and monetary incentives to ensure such performance is provided. We also explore the existence of interdependencies between the different elements of the system. and find some complementarities between completion and termination rights, and between monitoring rights and the intensity of incentives.

The quasi-judicial role of large retailers: An efficiency hypothesis of their relation with suppliers

The paper explores an efficiency hypothesis regarding the contractual process between large retailers, such as Wal-Mart and Carrefour, and their suppliers. The empirical evidence presented supports the idea that large retailers play a quasi-judicial role, acting as "courts of first instance" in their relationships with suppliers. In this role, large retailers adjust the terms of trade to on-going changes and sanction performance failures, sometimes delaying payments. A potential abuse of their position is limited by the need for re-contracting and preserving their reputations. Suppliers renew their confidence in their retailers on a yearly basis, through writing new contracts. This renovation contradicts the alternative hypothesis that suppliers are expropriated by large retailers as a consequence of specific investments.

Le pergélisol dans les terrains sédimentaires à forte déclivité: distribution, régime thermique et instabilités

Résumé: Dans le contexte d'un climat de plus en plus chaud, la localisation du pergélisol dans les terrains sédimentaires à forte déclivité et l'évaluation des mouvements de terrain qui y ont cours s'avèrent primordiales. S'insérant dans cette problématique, ce travail de thèse s'articule autour de deux axes de recherche différents. D'un point de vue statique, cette recherche propose une étude de la distribution et des caractéristiques du pergélisol dans les éboulis de la zone périglaciaire alpine. D'un point de vue dynamique, une analyse de l'influence des caractéristiques du pergélisol (teneur en glace, température du pergélisol, etc.) et des variations des températures de l'air et du sol sur les vitesses de fluage des corps sédimentaires gelés est effectuée. Afin de répondre à ce double objectif, l'approche "terrain" a été privilégiée. Pour déterminer la répartition et les caractéristiques du pergélisol, les méthodes traditionnelles de prospection du pergélisol ont été utilisées, à savoir la mesure de la température du sol à la base du manteau neigeux (BTS), la mesure de la température du sol en continu ainsi que la méthode géoélectrique. Les mouvements de terrain ont pour leur part été mesurés à l'aide d'un GPS différentiel. L'étude de la distribution du pergélisol a été effectuée dans une quinzaine d'éboulis situés dans les régions du Mont Gelé (Verbier-Nendaz) et d'Arolla principalement. Dans la plupart des cas, un pergélisol a pu être mis en évidence dans la partie inférieure des accumulations sédimentaires, alors que la partie médiane des éboulis n'est, le plus souvent, pas gelée. Si cette absence de pergélisol se prolonge parfois dans les portions sommitales des pentes, les mesures réalisées montrent que dans d'autres cas des sédiments gelés y sont à nouveau présents. Les résistivités électriques mesurées dans les portions gelées des éboulis étudiés sont dans la plupart des cas nettement inférieures à celles mesurées sur les glaciers rocheux. Des études préalables ont montré que des circulations d'air internes sont responsables de l'anomalie thermique négative et, lorsqu'il existe, du pergélisol que l'on trouve dans la partie inférieure d'éboulis situés plus de 1000 m plus bas que la limite inférieure régionale du pergélisol discontinu. L'étude de quatre sites de basse altitude (1400-1900 m), et notamment l'équipement du site de Dreveneuse (Préalpes Valaisannes) avec deux forages, des capteurs de température de surface et un anémomètre a permis de vérifier et de préciser le mécanisme de ventilation actif au sein des éboulis froids de basse altitude. Ce mécanisme fonctionne de la manière suivante: en hiver, l'air contenu dans l'éboulis, plus chaud et plus léger que l'air extérieur, monte à l'intérieur de l'accumulation sédimentaire et est expulsé dans ses parties sommitales. Cet effet de cheminée provoque une aspiration d'air froid à l'intérieur de la partie inférieure de l'éboulis, causant ainsi un sur-refroidissement marqué du terrain. En été, le mécanisme s'inverse, l'éboulis étant plus froid que l'air environnant. De l'air froid est alors expulsé au bas de la pente. Une ventilation ascendante hivernale a pu être mise en évidence dans certains des éboulis de haute altitude étudiés. Elle est probablement en grande partie responsable de la configuration particulière des zones gelées observées. Même si l'existence d'un effet de cheminée n'a pu être démontrée dans tous les cas, du fait notamment de la glace interstitielle qui entrave le cheminement de l'air, des indices laissant présager son possible fonctionnement existent dans la quasi totalité des éboulis étudiés. L'absence de pergélisol à des altitudes qui lui sont favorables pourrait en tous les cas s'expliquer par un réchauffement du terrain lié à des expulsions d'air relativement chaud. L'étude des mouvements de terrain a été effectuée sur une dizaine de sites, principalement sur des glaciers rocheux, mais également sur une moraine de poussée et - II - Résumé ? abstract quelques éboulis. Plusieurs glaciers rocheux présentent des formes de déstabilisation récente (niches d'arrachement, blocs basculés, apparition de la matrice fine à la surface, etc.), ce qui témoigne d'une récente accélération des vitesses de déplacement. Ce phénomène, qui semble général à l'échelle alpine, est probablement à mettre sur le compte du réchauffement du pergélisol depuis une vingtaine d'années. Les vitesses mesurées sur ces formations sont souvent plus élevées que les valeurs habituellement proposées dans la littérature. On note par ailleurs une forte variabilité inter-annuelle des vitesses, qui semblent dépendre de la variation de la température moyenne annuelle de surface. Abstract: In the context of a warmer climate, the localisation of permafrost in steep sedimentary terrain and the measurement of terrain movements that occur in these areas is of great importance. With respect to these problems, this PhD thesis follows two different research axes. From a static point of view, the research presents a study of the permafrost distribution and characteristics in the talus slopes of the alpine periglacial belt. From a dynamic point of view, an analysis of the influence of the permafrost characteristics (ice content, permafrost temperature, etc.) and air and soil temperature variations on the creep velocities of frozen sedimentary bodies is carried out. In order to attain this double objective, the "field" approach was favoured. To determine the distribution and the characteristics of permafrost, the traditional methods of permafrost prospecting were used, i.e. ground surface temperature measurements at the base of the snow cover (BTS), year-round ground temperature measurements and DC-resistivity prospecting. The terrain movements were measured using a differential GPS. The permafrost distribution study was carried out on 15 talus slopes located mainly in the Mont Gelé (Verbier-Nendaz) and Arolla areas (Swiss Alps). In most cases, permafrost was found in the lower part of the talus slope, whereas the medium part was free of ice. In some cases, the upper part of the talus is also free of permafrost, whereas in other cases permafrost is present. Electrical resistivities measured in the frozen parts of the studied talus are in most cases clearly lower than those measured on rock glaciers. Former studies have shown that internal air circulation is responsible for the negative thermal anomaly and, when it exists, the permafrost present in the lower part of talus slopes located more than 1000 m below the regional lower limit of discontinuous permafrost. The study of four low-altitude talus slopes (1400-1900 m), and notably the equipment of Dreveneuse field site (Valais Prealps) with two boreholes, surface temperature sensors and an anemometer permitted to verify and to detail the ventilation mechanism active in low altitude talus slopes. This mechanism works in the following way: in winter, the air contained in the block accumulation is warmer and lighter than the surrounding air and therefore moves upward in the talus and is expelled in its upper part. This chimney effect induces an aspiration of cold air in the interior of the lower part of talus, that causes a strong overcooling of the ground. In summer, the mechanism is reversed because the talus slope is colder than the surrounding air. Cold air is then expelled in the lower part of the slope. Evidence of ascending ventilation in wintertime could also be found in some of the studied high-altitude talus slopes. It is probably mainly responsible for the particular configuration of the observed frozen areas. Even if the existence of a chimney effect could not be demonstrated in all cases, notably because of interstitial ice that obstructs Résumé ? abstract - III - the air circulation, indices of its presence exist in nearly all the studied talus. The absence of permafrost at altitudes favourable to its presence could be explained, for example, by the terrain warming caused by expulsion of relatively warm air. Terrain movements were measured at about ten sites, mainly on rock glaciers, but also on a push moraine and some talus slopes. Field observations reveal that many rock glaciers display recent destabilization features (landslide scars, tilted blocks, presence of fine grained sediments at the surface, etc.) that indicate a probable recent acceleration of the creep velocities. This phenomenon, which seems to be widespread at the alpine scale, is probably linked to the permafrost warming during the last decades. The measured velocities are often higher than values usually proposed in the literature. In addition, strong inter-annual variations of the velocities were observed, which seems to depend on the mean annual ground temperature variations.