The work describes techniques for solving systems of linear and differential equations. It explains the definition of conversion from system of linear to system of differential equations. The method of the elementary transmission and the transform algorithm are presented. Both of methods are demonstrated on simply examples and properties of conversion are shown. The work compares fast and accurate solutions of methods and algorithm. For computing examples and solving experiments following programs were used: TKSL and TKSL/C. The program TKSL/C was enriched with the graphic user interface which makes the conversion of systems and computing results easier.

M. Tech. (Department of Mechanical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / The purpose of this research was to develop optimal numerical solutions that can be employed during the design of cross bored thick-walled compound cylinders. The geometric design parameters of a cross bored compound cylinder that were optimized include shrinkage pressure, cross bore size, shape, location, and obliquity. Finite Element Analysis (FEA) modeling software called Abaqus version 2019 was used to generate numerical solutions. A total of 48 different part models were created and analyzed in this work. The generated FEA results from these models were validated using analytical solutions developed from Lame’s theory. The effects of shrinkage pressure on hoop stresses and Stress Concentration Factor (SCF) were studied to determine the optimal conditions. The optimum shrinkage pressure obtained was henceforth used for further analysis in this work. In addition, using one factor at time optimization technique, an optimization process was carried out to determine the optimal combination of the cross bore configuration geometry that gives minimum SCF. These parameters of cross bore configuration geometry include different sizes of either circular or elliptical-shaped cross bore, positioned at radial, offset, and/or inclined. The analyses of the effects of shrinkage pressure ranging from 4.4733 to 223.662 MPa on 11 different part models, established that the shrinkage pressure of 89.464 MPa generated the minimum SCF magnitude of 3.02. After analyzing 8 different circular cross bore size ratios ranging from 0.1 to 0.8, at the radial position, it was established that the hoop stress increases with an increase in a cross bore size. The smallest cross bore size ratio of 0.1 gave the lowest hoop stress and minimum SCF of 3.02. Whereas the highest stress was developed at the cross-size ratio of 0.8 with an SCF magnitude of 6.75. The minimum magnitude of SCF translates to a reduction of the pressure carrying capacity of the compound cylinder by 67% than a similar plain compound cylinder. Generally, offsetting of the circularly shaped cross bore from the radial position, led to a reduction of the magnitude of SCFs. For instance, from the 8 offset positions analyzed, the minimum SCF occurred at the offset position of 0.006 m with a magnitude of 2.50. This SCF magnitude indicated a reduction of pressure carrying capacity of 60% in comparison to a similar plain compound cylinder. Evaluation of 12 different diameter ratios of elliptical-shaped cross bore ranging from 0.5 to 10, at the radial position, established the lowest SCF magnitude of 1.33 that occurred at a diameter ratio of 5. Henceforth, this optimum diameter ratio was used for further analysis. This aforesaid SCF magnitude translated to a reduction of the pressure carrying capacity of the compound cylinder by 24.81% when compared to a similar plain compound cylinder. Besides, offsetting of elliptically shaped cross bore generally decreased the magnitudes of SCFs. Therefore, for elliptically shaped cross bore, the lowest SCF occurred at radial position with magnitude of 1.33. A general comparison between the effects of circular and elliptical cross bore, established that the elliptical-shaped cross bores generated both lower hoop stresses and SCFs than those of circularly shaped cross bores. On the other hand, oblique elliptical offset cross bores along the Z-axis of the compound cylinder led to an increase in SCFs. As the oblique angle increased from 0 0 to 75 0, the SCFs also increased progressively, however, there was a significant increase in SCF when the inclination angle increased from 60 0 to 75 0. The lowest and highest SCF magnitude was 1.52 and 1.92 at 15 0 and 6.19 at 75 0, respectively. Overall, the optimum geometric configuration of a cross bore in a thick compound cylinder was found to be elliptically shaped, offset at radial position which is an obliquity angle of 0 0 having a diameter ratio a/b of 5.

[pt] A tecnologia de poços inteligentes já possui muitos anos de experiência de campo. Inúmeras publicações tem descrito como o controle de fluxo remoto e os sistemas de monitoração podem diminuir o número de intervenções, o número de poços e aumentar a eficiência do gerenciamento de reservatórios. Apesar da maturidade dos equipamentos de completação o conceito de poço inteligente integrado como um elemento chave do Digital Oil Field ainda não está completmente desenvolvido. Sistemas permanentes de monitoração nesse contexto tem um papel fundamental como fonte da informação a respeito do sistema de produção real visando calibração de modelos e minimização de incerteza. Entretanto, cada sensor adicional representa aumento de complexidade e de risco operacional. Um entendimento fundamentado do que realmente é necessário, dos tipos de sensores aplicáveis e quais técnicas de análises estão disponíveis para extrair as informações necessárias são pontos chave para o sucesso do projeto de um poço inteligente. Este trabalho propõe uma nova forma de tratar os dados em tempo real de poços inteligentes através da centralização do pré-processamento dos dados. Um modelo poço inteligente numérico para temperatura em regime transiente foi desenvolvido, testado e validado com a intenção de gerar dados sintéticos. A aplicação foi escolhida sem perda de generalidade como um exemplo representativo para validação dos algorítmos de limpeza e extração de características desenvolvidos. Os resultados mostraram aumento da eficiência quando comparados com o estado da arte e um potencial para capturar a influência mútua entre os processos de produção. / [en] Intelligent Well (IW) technology has built-up several years production experience. Numerous publications have described how remote flow control and monitoring capabilities can lead to fewer interventions, a reduced well count and improved reservoir management. Despite the maturity of IW equipment, the concept of the integrated IW as a key element in the Digital Oil Field still not fully developed. Permanent monitoring systems in this framework play an important role as source of the necessary information about actual production system aiming model calibration and uncertainty minimization. However, each extra permanently installed sensor increases the well s installation complexity and operational risk. A well-founded understanding of what data is actually needed and what analysis techniques are available to extract the required information are key factors for the success of the IW project. This work proposes a new framework to real-time data analysis through centralizing pre-processing. A numeric IW transient temperature model is developed, tested and validated to generate synthetic data. It was chosen without loss off generality as a representative application to test and validate the cleansing and feature extraction algorithms developed. The results achieved are compared with the state of the art ones showing advantages regarding efficiency and potential to capture mutual influence among processes.

A cirurgia micrográfica de Mohs (CMM) é realizada em fases sucessivas de retirada tumoral. Cada fase demora de uma a duas horas, dependendo do tamanho da lesão; portanto, é muito importante conseguir predizer o número de fases da cirurgia a fim de poder programar melhor o tempo de uso da sala cirúrgica e da equipe cirúrgica, o uso de anestésicos, os custos da cirurgia, melhor orientar o paciente e assegurar a remoção completa do tumor. Com o intuito de encontrar fatores preditivos do número de fases da CMM no tratamento do carcinoma espinocelular da cabeça, realizou-se o levantamento dos prontuários de 44 pacientes submetidos a 51 CMM no ambulatório de cirurgia dermatológica da Divisão de Dermatologia do HC-FMUSP/SP, de 1994 a 2003. Foram constituídos três grupos quanto ao número de fases da CMM: uma fase, duas fases e três ou mais fases. Os grupos foram comparados em relação às variáveis: duração da lesão até a cirurgia, morfologia, tamanho e limites da lesão, tumor primário ou recidivado, grau de diferenciação histológica do tumor e localização anatômica do tumor. Identificou-se um único fator significante na análise univariada: a distribuição dos tumores recidivados segundo o número de fases da cirurgia e que diferiu da distribuição dos tumores primários (p=0,081, teste exato de Fisher), sendo maior o número de fases para os tumores recidivados. Na análise multivariada, não houve fatores estatisticamente significantes que pudessem estar associados ao número de fases da cirurgia. Na análise da razão de chances, observou-se maior chance de apresentar maior número de fases para as variáveis: limites clínicos imprecisos, tumor ulcerado, tumor recidivado, tumor mais agressivo histologicamente e tumor maior que 1 cm. / Mohs micrographic surgery (MMS) is proceeded in successive stages of cancer removal. Each stage lasts from 1 to 2 hours, depending on the tumor size. So it is very important to predict the number of phases of the surgery so that one can plan better the time of the surgical room use, the time of the surgeon and his team, the use of anaesthetics, the surgical costs, to give the patient better orientations about his surgery and to ensure complete tumor erradication. With the intention to find predictive factors of the number of stages of MMS in the treatment of squamous cell carcinoma, we reviewed the record of 44 patients on a total of 51 surgeries proceeded in the dermatologic surgical clinic of the Dermatological Division of HC-FMUSP/SP from 1994 to 2003. For the number of stages in the MMS we established 3 groups: 1 stage, 2 stages and 3 or more stages. These groups were compared with regard to this variables: continuance of the lesion until the surgery, morphology and size of the lesion, lesion limits, primary or recurrent cancer, histological grade (Broders) and anatomic localization. In the univariated analysis one single factor was significant: the distribution of the recurrent cancers related to the number of stages of the surgery that was different from the distribution of the primary ones (p=0.081, Fisher\'s exact test), been higher the number of stages for the recurrent cancers. In the multivariated analysis, there were no statistically significant factors associated with higher number of stages of the surgery. In the analysis of the odss ratio, we noted a higher chance of a higher number of stages for the variables: inaccurate clinical limits, ulcerated lesions, recurrent cancer, higher aggressive histology and tumor bigger than 1 cm.

A cirurgia micrográfica de Mohs (CMM) é realizada em fases sucessivas de retirada tumoral. Cada fase demora de uma a duas horas, dependendo do tamanho da lesão; portanto, é muito importante conseguir predizer o número de fases da cirurgia a fim de poder programar melhor o tempo de uso da sala cirúrgica e da equipe cirúrgica, o uso de anestésicos, os custos da cirurgia, melhor orientar o paciente e assegurar a remoção completa do tumor. Com o intuito de encontrar fatores preditivos do número de fases da CMM no tratamento do carcinoma espinocelular da cabeça, realizou-se o levantamento dos prontuários de 44 pacientes submetidos a 51 CMM no ambulatório de cirurgia dermatológica da Divisão de Dermatologia do HC-FMUSP/SP, de 1994 a 2003. Foram constituídos três grupos quanto ao número de fases da CMM: uma fase, duas fases e três ou mais fases. Os grupos foram comparados em relação às variáveis: duração da lesão até a cirurgia, morfologia, tamanho e limites da lesão, tumor primário ou recidivado, grau de diferenciação histológica do tumor e localização anatômica do tumor. Identificou-se um único fator significante na análise univariada: a distribuição dos tumores recidivados segundo o número de fases da cirurgia e que diferiu da distribuição dos tumores primários (p=0,081, teste exato de Fisher), sendo maior o número de fases para os tumores recidivados. Na análise multivariada, não houve fatores estatisticamente significantes que pudessem estar associados ao número de fases da cirurgia. Na análise da razão de chances, observou-se maior chance de apresentar maior número de fases para as variáveis: limites clínicos imprecisos, tumor ulcerado, tumor recidivado, tumor mais agressivo histologicamente e tumor maior que 1 cm. / Mohs micrographic surgery (MMS) is proceeded in successive stages of cancer removal. Each stage lasts from 1 to 2 hours, depending on the tumor size. So it is very important to predict the number of phases of the surgery so that one can plan better the time of the surgical room use, the time of the surgeon and his team, the use of anaesthetics, the surgical costs, to give the patient better orientations about his surgery and to ensure complete tumor erradication. With the intention to find predictive factors of the number of stages of MMS in the treatment of squamous cell carcinoma, we reviewed the record of 44 patients on a total of 51 surgeries proceeded in the dermatologic surgical clinic of the Dermatological Division of HC-FMUSP/SP from 1994 to 2003. For the number of stages in the MMS we established 3 groups: 1 stage, 2 stages and 3 or more stages. These groups were compared with regard to this variables: continuance of the lesion until the surgery, morphology and size of the lesion, lesion limits, primary or recurrent cancer, histological grade (Broders) and anatomic localization. In the univariated analysis one single factor was significant: the distribution of the recurrent cancers related to the number of stages of the surgery that was different from the distribution of the primary ones (p=0.081, Fisher\'s exact test), been higher the number of stages for the recurrent cancers. In the multivariated analysis, there were no statistically significant factors associated with higher number of stages of the surgery. In the analysis of the odss ratio, we noted a higher chance of a higher number of stages for the variables: inaccurate clinical limits, ulcerated lesions, recurrent cancer, higher aggressive histology and tumor bigger than 1 cm.

Le calcul rigoureux vise à produire des représentations certifiées pour les solutions de nombreux problèmes, notamment en analyse fonctionnelle, comme des équations différentielles ou des problèmes de contrôle optimal. En effet, certains domaines particuliers comme l’ingénierie des systèmes critiques ou les preuves mathématiques assistées par ordinateur ont des exigences de fiabilité supérieures à ce qui peut résulter de l’utilisation d’algorithmes relevant de l’analyse numérique classique.Notre objectif consiste à développer des algorithmes à la fois efficaces et validés / certifiés, dans le sens où toutes les erreurs numériques (d’arrondi ou de méthode) sont prises en compte. En particulier, nous recourons aux approximations polynomiales rigoureuses combinées avec des méthodes de validation a posteriori à base de points fixes. Ces techniques sont implémentées au sein d’une bibliothèque écrite en C, ainsi que dans un développement de preuve formelle en Coq, offrant ainsi le plus haut niveau de confiance, c’est-à-dire une implémentation certifiée.Après avoir présenté les opérations élémentaires sur les approximations polynomiales rigoureuses, nous détaillons un nouvel algorithme de validation pour des approximations sous forme de séries de Tchebychev tronquées de fonctions D-finies, qui sont les solutions d’équations différentielles ordinaires linéaires à coefficients polynomiaux. Nous fournissons une analyse fine de sa complexité, ainsi qu’une extension aux équations différentielles ordinaires linéaires générales et aux systèmes couplés de telles équations. Ces méthodes dites symboliques-numériques sont ensuite utilisées dans plusieurs problèmes reliés : une nouvelle borne sur le nombre de Hilbert pour les systèmes quartiques, la validation de trajectoires de satellites lors du problème du rendez-vous linéarisé, le calcul de polynômes d’approximation optimisés pour l’erreur d’évaluation, et enfin la reconstruction du support et de la densité pour certaines mesures, grâce à des techniques algébriques. / Rigorous numerics aims at providing certified representations for solutions of various problems, notably in functional analysis, e.g., differential equations or optimal control. Indeed, specific domains like safety-critical engineering or computer-assisted proofs in mathematics have stronger reliability requirements than what can be achieved by resorting to standard numerical analysis algorithms. Our goal consists in developing efficient algorithms, which are also validated / certified in the sense that all numerical errors (method or rounding) are taken into account. Specifically, a central contribution is to combine polynomial approximations with a posteriori fixed-point validation techniques. A C code library for rigorous polynomial approximations (RPAs) is provided, together with a Coq formal proof development, offering the highest confidence at the implementation level.After providing basic operations on RPAs, we focus on a new validation algorithm for Chebyshev basis solutions of D-finite functions, i.e., solutions of linear ordinary differential equations (LODEs) with polynomial coefficients. We give an in-depth complexity analysis, as well as an extension to general LODEs, and even coupled systems of them. These symbolic-numeric methods are finally used in several related problems: a new lower bound on the Hilbert number for quartic systems; a validation of trajectories arising in the linearized spacecraft rendezvous problem; the design of evaluation error efficient polynomial approximations; and the support and density reconstruction of particular measures using algebraic techniques.

La préservation de la chaîne du froid est un paramètre particulièrement important dans le cadre de la distribution urbaine, où les fréquentes ouvertures de portes induisent une charge thermique d’infiltration. Afin de réduire les transferts de masse et de chaleur et de protéger l’ouverture, des rideaux d’air ont récemment été installés au niveau de l’ouverture des camions frigorifiques. L’objet de la présente étude est d’étudier ce type confinement. Deux modèles CFD ont été développés pour simuler les champs de températures et de vitesses dans un camion réfrigéré clos. Ils ont permis de montrer que la variation de la vitesse de soufflage ne modifie pas de manière significative la structure des écoulements. Différents conduits d’air sont modélisés. Les résultats numériques montrent que la configuration avec un conduit ouvert améliore fortement le renouvellement d’air. Puis, une étude numérique est réalisée dans le but d’étudier les infiltrations de chaleur et de masse au cours de l’ouverture des portes. Ces écoulements sont bien prédits par le modèle CFD, excepté à la transition entre les deux régimes d’infiltration. Une caisse expérimentale a été équipée d’un dispositif de rideau d’air composé d’un jet ambiant, d’un jet froid ou d’un jet double. En parallèle, un modèle numérique CFD a été développé pour étudier l’influence de différents paramètres. Une bonne concordance entre les résultats numériques et expérimentaux a été observée. L’efficacité du rideau d’air ambiant est maximale lorsque le point d’impact du rideau se situe dans le plan de l’ouverture. Le rideau double maintient efficacement l’homogénéité de la température pour de courtes ouvertures. Le rideau d’air froid est la meilleur configuration, il limite fortement l’augmentation de température de l’enceinte et permet des gains énergétiques importants. / Cold chain safety is a key parameter for urban distribution where the frequent door-opening induces a heat infiltration. In order to reduce heat and mass transfer, air curtain have recently been installed to protect the doorway of refrigerated truck. The aim of this work is to study this type of door insulation. Two CFD numerical models were developed to simulate the temperature and velocity fields in a closed refrigerated truck. These models showed that modifying the blowing velocity does not modify the air flow structure inside the cavity. Different air chutes were modelled. Numerical results demonstrate that the configuration with a convergent and an open duct strongly improves the air renewal. A numerical investigation was performed in order to study heat and mass infiltration rates during the opening. The infiltration flow rate is well predicted by the CFD model, except at the transition between both flow regimes. An experimental truck was equipped with an air curtain setup, composed by an ambient air jet, a cold air jet or a double jet. In parallel, a numerical CFD model was developed to study the influence of various parameters. Experimental and numerical results were found to be in good agreement. The maximum efficiency of the ambient air curtain is reached when the impact point of the jet occurs in the door plane at the ground level. This configuration is only relevant for short opening times. The double air curtain efficiently maintains the temperature homogeneity for short openings. The cold air curtain is the best configuration which strongly limits the temperature increase during the opening and allows important energy savings.

Les engrenages roues et vis sans fin sont une solution avantageuse pour transmettre le couple entre des axes perpendiculaires non concourants. Ces engrenages offrent une solution simple et efficace en terme de coût dans les applications de transmission de puissance, où un grand rapport de réduction est nécessaire, en comparaison avec les engrenages classiques à axes parallèles qui nécessitent normalement deux ou trois étapes pour obtenir les mêmes réductions avec une augmentation conséquente de complexité et du nombre de pièces. L’usure de surface est un des modes de défaillance observés dans la vie des engrenages roues et vis sans fin qui influe sur la portée de contact, les caractéristiques de transmission et le bruit résultant. La première étape de ces travaux est la mise au point d’un modèle numérique pour étudier le comportement quasi statique des engrenages roues et vis sans fin avec une roue en bronze et une vis en acier. Le modèle est basé sur la résolution des équations de compatibilité des déplacements ainsi que sur la méthode des coefficients d’influence. Les effets globaux de flexion et les effets locaux de contact ont été séparés. Les effets de contact ont été obtenus par la théorie de Boussinesq. Les coefficients de flexion sont estimés par la combinaison d’un calcul Éléments Finis et des fonctions d’interpolation, permettant d’une part de prendre en compte l’environnement de l'engrenage (la géométrie des arbres, des jantes et des voiles, l’emplacement des roulements,...) et d’autre part de réduire significativement les temps de calculs. Dans une seconde étape, une méthodologie est proposée pour modéliser l’usure de la surface de dent de la roue. Le modèle de contact quasi-statique de la répartition des charges est combiné avec un modèle d’usure d’Archard. Ce modèle suppose que la profondeur d’usure est directement proportionnelle à la pression de contact et à la distance de glissement et inversement proportionnelle à la dureté du matériau. Cette loi d’usure est modifiée pour prendre en compte l’influence des conditions de lubrification en utilisant un coefficient d’usure local, dépendant de l’épaisseur du film lubrifiant, rapportée à l’amplitude des rugosités des surfaces. L’enlèvement de matière par l’usure du flanc de la roue influe sur la répartition des pressions et donc les modifications de la géométrie des dents doivent être incluses dans la prédiction de l’usure. Le calcul des pressions de contact est ainsi mis à jour pour tenir compte des changements de géométrie. Enfin, pour valider le modèle développé des comparaisons du modèle avec des résultats expérimentaux issus de la bibliographie ont été effectuées. / Worm gears are one of the technical devices for transmitting torque between spatial crossed axes. They provide a simple and cost effective solution in power transmission applications, where a high reduction ratio is required. Comparable conventional parallel axis gearing would normally require two or three stages to achieve the same reduction, with a consequent increase in complexity and number of parts. Surface wear is one of the failure modes observed in life worm gear sets which affects the contact patterns, the other transmission characteristics and the resultant noise. The first step of this work is the development of a numerical model to study provide the quasi-static behavior of worm gears with bronze wheel and steel worm. The model is based on solving of the equation of displacement compatibility and the influence coefficient method. The global effects of bending and local effects of contact are separated. The contact effects are obtained with the theory of Boussinesq. Bending effects are estimated by the combination of one standard FEM computation and interpolation functions. These methods allow, on the one hand, to take into account the environment of the gear (shaft shape, rim, web, bearing location ...) and on the other to reduce significantly the computation time. In a second step, a methodology is proposed for predicting the wear of the wheel tooth surface. In this process, a quasi-static contact model of the load distribution is combined with Archard's wear model. This model assumes that the wear depth is directly proportional to the contact pressure and sliding distance and inversely proportional to the hardness of the material. The wear law is modified to take into account the influence of the lubrication conditions using a local wear coefficient, depending on the lubricant film thickness, relative to the amplitude of surface roughness. Removal of material by wear on the wheel flank affects the pressure distribution, therefore the changes in teeth must be included in the prediction of wear. The calculation of contact pressures must also be updated to take into account the modification of the gear flank geometry. The last step concerns the validation of the numerical. Comparisons have been carried out between the model results and experimental ones issued from the bibliography.

Cette thèse porte sur la commande H∞ par loop-shaping pour les systèmes linéaires à temps invariant d'ordre faible avec ou sans retard et dépendant de paramètres inconnus. L'objectif est d'obtenir des correcteurs H∞ paramétriques, c'est-à-dire dépendant explicitement des paramètres inconnus, pour application à des viseurs gyrostabilisés.L'existence de ces paramètres inconnus ne permet plus l'utilisation des techniques numériques classiques pour la résolution du problème H∞ par loop-shaping. Nous avons alors développé une nouvelle méthodologie permettant de traiter les systèmes linéaires de dimension finie grâce à l'utilissation de techniques modernes de calcul formel dédiées à la résolution des systèmes polynomiaux (bases de Gröbner, variétés discriminantes, etc.).Une telle approche présente de multiples avantages: étude de sensibilités du critère H∞ par rapport aux paramètres, identification de valeurs de paramètres singulières ou remarquables, conception de correcteurs explicites optimaux/robustes, certification numérique des calculs, etc. De plus, nous montrons que cette approche peut s'étendre à une classe de systèmes à retard.Plus généralement, cette thèse s'appuie sur une étude symbolique des équations de Riccati algébriques. Les méthodologies génériques développées ici peuvent s'étendre à de nombreux problèmes de l'automatique, notamment la commande LQG, le filtrage de Kalman ou invariant. / This PhD thesis deals with the H∞ loop-shaping design for low order linear time invariant systems depending on unknown parameters. The objective of the PhD thesis is to obtain parametric H∞ controllers, i.e. controllers which depend explicitly on the unknown model parameters, and to apply them to the stabilization of gyrostabilized sights.Due to the unknown parameters, no numerical algorithm can solve the robust control problem. Using modern symbolic techniques dedicated to the solving of polynomial systems (Gröbner bases, discriminant varieties, etc.), we develop a new methodology to solve this problem for finite-dimensional linear systems.This approach shows several advantages : we can study the sensibilities of the H∞ criterion to the parameter variations, identify singular or remarquable values of the parameters, compute controllers which depend explicitly on the parameters, certify the numerical computations, etc. Furthermore, we show that this approach can be extended to a class of linear time-delay systems.More generally, this PhD thesis develops an algebraic approach for the study of algebraic Riccati equations. Thus, the methodology obtained can be extended to many different problems such as LQG control and Kalman or invariant filtering.

This thesis focuses on the methodology of controlling dynamic systems in real time. It contents a review of the control theory basis and the elementary base of regulators construction. Then the list of matemathic formulaes follows as well as the math basis for the system simulations using a difeerential count and the problem of difeerential equations solving. Furthermore, there is a systematic approach to the design of general regulator enclosed, using modern simulation techniques. After the results confirmation in the Matlab system, the problematics of transport delay & quantization modelling follow.