La simulation à événements discrets (SED) est une technique dans laquelle le simulateur joue une histoire suivant une chronologie d'événements, chaque événement se produisant en des points discrets de la ligne continue du temps. Lors de l'implémentation, un événement peut être représenté par un message et une heure d'occurrence. Le type du message n'est lié qu'au modèle et donc sans conséquences pour le simulateur. En revanche, les variables de temps ont un rôle critique dans le simulateur, pour construire la chronologie des événements, dans R+. Or ces variables sont souvent représentées pas des types de données produisant des approximations, tels que les nombres flottants. Cette approximation des valeurs du temps dans la simulation peut altérer la ligne de temps et conduire à des résultats incorrects. Par ailleurs, il est courant de collecter des données à partir de systèmes réels afin de prédire des phénomènes futurs, comme les prévisions météorologiques. Les résultats de cette collecte, à l'aide d'instruments et procédures de mesures, incluent une quantification d'incertitude, habituellement présentée sous forme d'intervalles. Or répondre à une question requiert parfois l'évaluation des résultats pour toutes les valeurs comprises dans l'intervalle d'incertitude. Cette thèse propose des types de données pour une gestion sans erreur du temps en SED, y compris pour des valeurs irrationnelles et périodiques. De plus, nous proposons une méthode pour obtenir tous les résultats possibles d'une simulation soumise à des événements dont l'heure d'occurrence comporte une quantification d'incertitude. / Discrete-Event Simulation (DES) is a technique in which the simulation engine plays a history following a chronology of events. The technique is called “discrete-event” because the processing of each event of the chronology takes place at discrete points of a continuous time-line. In computer implementations, an event could be represented by a message, and a time occurrence. The message data type is usually defined as part of the model and the simulator algorithms do not operate with them. Opposite is the case of time variables; simulator has to interact actively with them for reproducing the chronology of events over R+, which is usually represented by approximated data types as floating-point. The approximation of time values in the simulation can affect the time-line preventing the generation of correct results. In addition, it is common to collect data from real systems to predict future phenomena, for example for weather forecasting. When collecting data using metrological instruments and procedures, the measurement results include uncertainty quantifications, usually defined as intervals. However, sometimes, answering a question requires evaluating the results of all values in the uncertainty interval. This thesis proposes data types for handling representation of time properly in DES, including irrational and periodic time values. Moreover, we propose a method for obtaining every possible simulation result of DES models when feeding them events with uncertainty quantification on their time component.

Dans cette thèse, nous nous intéressons à deux modèles de feux de forêts définis sur Z. On étudie le modèle des feux de forêts sur Z avec propagation non instantanée dans le chapitre 2. Dans ce modèle, chaque site a trois états possibles : vide, occupé ou en feu. Un site vide devient occupé avec taux 1. Sur chaque site, des allumettes tombent avec taux λ. Si le site est occupé, il brûle pendant un temps exponentiel de paramètre π avant de se propager à ses deux voisins. S’ils sont eux-mêmes occupés, ils brûlent, sinon le feu s’éteint. On étudie l’asymptotique des feux rares c’est à dire la limite du processus lorsque λ → 0 et π → ∞. On montre qu’il y a trois catégories possibles de limites d’échelles, selon le régime dans lequel λ tend vers 0 et π vers l’infini. On étudie formellement et brièvement dans le chapitre 3 le modèle des feux de forêts sur Z en environnement aléatoire. Dans ce modèle, chaque site n’a que deux états possibles : vide ou occupé. On se donne un paramètre λ > 0, une loi ν sur (0 ,∞) et une suite (κi)i∈Z de variables aléatoires indépendantes identiquement distribuées selon ν. Un site vide i devient occupé avec taux κi. Sur chaque site, des allumettes tombent avec taux λ et détruisent immédiatement la composante de sites occupés correspondante. On étudie l’asymptotique des feux rares. Sous une hypothèse raisonnable sur ν, on espère que le processus converge, avec une renormalisation correcte, vers un modèle limite. On s’attend à distinguer trois processus limites différents / The aim of this work is to study two differents forest-fire processes defined on Z. In Chapter 2, we study the so-called one dimensional forest-fire process with non instantaeous propagation. In this model, each site has three possible states: ’vacant’, ’occupied’ or ’burning’. Vacant sites become occupied at rate 1. At each site, ignition (by lightning) occurs at rate λ. When a site is ignited, a fire starts and propagates to neighbors at rate π. We study the asymptotic behavior of this process as λ → 0 and π → ∞. We show that there are three possible classes of scaling limits, according to the regime in which λ → 0 and π → ∞. In Chapter 3, we study formally and briefly the so-called one dimensional forest-fire processes in random media. Here, each site has only two possible states: ’vacant’ or occupied’. Consider a parameter λ > 0, a probability distribution ν on (0 ,∞) as well as (κi)i∈Z an i.i.d. sequence of random variables with law ν. A vacant site i becomes occupied at rate κi. At each site, ignition (by lightning) occurs at rate λ. When a site is ignited, the fire destroys the corresponding component of occupied sites. We study the asymptotic behavior of this process as λ → 0. Under some quite reasonable assumptions on the law ν, we hope that the process converges, with a correct normalization, to a limit forest fire model. We expect that there are three possible classes of scaling limits

Doctor of Philosophy / Department of Agricultural Economics / Jason S. Bergtold / Jessica L. Heier Stamm / Applied research in agricultural economics often involves a discrete process. Most commonly, these applications entail a conceptual framework, such as random utility, that describes a discrete-variable data-generating process. Assumptions in the conceptual framework then imply a particular empirical model. Common approaches include the binary logit and probit models and the multinomial logit when more than two outcomes are possible. Conceptual frameworks based on a discrete choice process have also been used even when the dependent variable of interest is continuous. In any case, the standard models may not be well suited to the problem at hand, as a result of either the assumptions they require or the assumptions they impose. The general theme of this dissertation is to adopt seldom-used empirical models to standard research areas in the field through applied studies. A common motivation in each paper is to lessen the exposure to specification concerns associated with more traditional models. The first paper is an attempt to provide insights into what --- if any --- weather patterns farmers respond to with respect to cropping decisions. The study region is a subset of 11 north-central Kansas counties. Empirically, this study adopts a dynamic multinomial logit with random effects approach, which may be the first use of this model with respect to farmer land-use decisions. Results suggest that field-level land-use decisions are significantly influenced by past weather, at least up to ten years. Results also suggest, however, that that short-term deviations from the longer trend can also influence land-use decisions. The second paper proposes multiple-output artificial neural networks (ANNs) as an alternative to more traditional approaches to estimating a system of acreage-share equations. To assess their viability as an alternative to traditional estimation, ANN results are compared to a linear-in-explanatory variables and parameters heteroskedastic and time-wise autoregressive seemingly unrelated regression model. Specifically, the two approaches are compared with respect to model fit and acre elasticities. Results suggest that the ANN is a viable alternative to a simple traditional model that is misspecified, as it produced plausible acre-response elasticities and outperformed the traditional model in terms of model fit. The third paper proposes ANNs as an alternative to the traditional logit model for contingent valuation analysis. With the correct network specifications, ANNs can be viewed as a traditional logistic regression where the index function has been replaced by a flexible functional form. The paper presents methods for obtaining marginal effect and willingness-to-pay (WTP) measures from ANNs, which has not been provided by the existing literature. To assess the viability of this approach, it is compared with the traditional logit and probit models as well an additional semi-nonparametric estimator with respect to model fit, marginal effects, and WTP estimates. Results suggest ANNs are viable alternative and may be preferable if misspecification of the index function is a concern.

Modified discrete cosine transform (MDCT) derived from DCT IV has emerged as the most suitable choice for transform domain audio coding applications due to its time domain alias cancellation property and de-correlation capability. In the present research work, we focus on MDCT domain analysis of audio signals for compression and other applications. We have derived algorithms for linear filtering in DCT IV and DST IV domains for symmetric and non-symmetric filter impulse responses. These results are also extended to MDCT and MDST domains which have the special property of time domain alias cancellation. We also derive filtering algorithms for the DCT II and DCT III domains. Comparison with other methods in the literature shows that, the new algorithm developed is computationally MAC efficient. These results are useful for MDCT domain audio processing such as reverb synthesis, without having to reconstruct the time domain signal and then perform the necessary filtering operations. In audio coding, the psychoacoustic model plays a crucial role and is used to estimate the masking thresholds for adaptive bit-allocation. Transparent quality audio coding is possible if the quantization noise is kept below the masking threshold for each frame. In the existing methods, the masking threshold is calculated using the DFT of the signal frame separately for MDCT domain adaptive quantization. We have extended the spectral integration based psychoacoustic model proposed for sinusoidal modeling of audio signals to the MDCT domain. This has been possible because of the detailed analysis of the relation between DFT and MDCT; we interpret the MDCT coefficients as co-sinusoids and then apply the sinusoidal masking model. The validity of the masking threshold so derived is verified through listening tests as well as objective measures. Parametric coding techniques are used for low bit rate encoding of multi-channel audio such as 5.1 format surround audio. In these techniques, the surround channels are synthesized at the receiver using the analysis parameters of the parametric model. We develop algorithms for MDCT domain analysis and synthesis of reverberation. Integrating these ideas, a parametric audio coder is developed in the MDCT domain. For the parameter estimation, we use a novel analysis by synthesis scheme in the MDCT domain which results in better modeling of the spatial audio. The resulting parametric stereo coder is able to synthesize acceptable quality stereo audio from the mono audio channel and a side information of approximately 11 kbps. Further, an experimental audio coder is developed in the MDCT domain incorporating the new psychoacoustic model and the parametric model.

In this thesis we have shown that a seemingly complicated mathematical structure can exhibit 'tame behaviour'. The structure we have dealt with is a field (a space in which there are addition and multiplication which satisfy natural properties) together with a dense subset (a subset which has spread in all parts of the this set, as Q does in R) and a discrete subset (a subset comprised of single points which keep certain distances from one another). This tameness is essentially with regards to not being trapped with the 'Godel phenomeonon' as the Peano arithmetic does.

Thousands of call centers operate in the United States employing millions of people. Since personnel costs represent as much as 80% of the total operating expense of these centers, it is important for call center managers to determine an appropriate staffing level required to maintain the desired operating performance. Historically, queueing models serve an important role in this regard. The one most commonly used is the Erlang-C model. The Erlang-C model has several assumptions, however, which are required for the predicted performance measures to be valid. One assumption that has received significant attention from researchers is that callers have infinite patience and will not terminate a call until the service is complete regardless of the wait time. Since this assumption is not likely to occur in reality, researchers have suggested using Erlang-A instead. Erlang-A does consider caller patience and allows for calls to be abandoned prior to receiving service. However, the use of Erlang-A still requires an assumption that is very unlikely to occur in practice - the assumption that all agents provide service at the same rate. Discrete event simulation is used to examine the effects of agent heterogeneity on the operating performance of a call center compared to the theoretical performance measures obtained from Erlang-A. Based on the simulation results, it is concluded that variability in agent service rate does not materially affect call center performance except to the extent that the variability changes the average handle time of the call center weighted by the number of calls handled and not weighted by agent. This is true regardless of call center size, the degree of agent heterogeneity, and the distribution shape of agent variability. The implication for researchers is that it is unnecessary to search for an analytic solution to relax the Erlang-A assumption that agents provide service at the same rate. Several implications for managers are discussed including the reliability of using Erlang-A to determine staffing levels, the importance of considering the service rates of the agents rather than the average handle time, and the unintended consequence of call routing schemes which route calls to faster rather than slower agents.

This research outlines a study that was performed to determine the effects of user interface design variations on the usability and solution quality of complex, multivariate discrete-event simulations. Specifically, this study examined four key research questions: what are the user interface considerations for a given simulation model, what are the current best practices in user interface design for simulations, how is usability best evaluated for simulation interfaces, and specifically what are the measured effects of varying levels of usability of interface elements on simulation operations such as data entry and solution analysis. The overall goal of the study was to show the benefit of applied usability practices in simulation design, supported by experimental evidence from testing two alternative simulation user interfaces designed with varying usability. The study employed directed research in usability and simulation design to support design of an experiment that addressed the core problem of interface effects on simulation. In keeping with the study goal of demonstrating usability practices, the experimental procedures were analogous to the development processes recommended in supporting literature for usability-based design lifecycles. Steps included user and task analysis, concept and use modeling, paper prototypes of user interfaces for initial usability assessment, interface development and assessment, and user-based testing of actual interfaces with an actual simulation model. The experimental tests employed two interfaces designed with selected usability variations, each interacting with the same core simulation model. The experimental steps were followed by an analysis of quantitative and qualitative data gathered, including data entry time, interaction errors, solution quality measures, and user acceptance data. The study resulted in mixed support for the hypotheses that improvements in usability of simulation interface elements will improve data entry, solution quality, and overall simulation interactions. Evidence for data entry was mixed, for solution quality was positive to neutral, and for overall usability was very positive. As a secondary benefit, the study demonstrated application of usability-based interface design best practices and processes that could provide guidelines for increasing usability of future discrete-event simulation interface designs. Examination of the study results also provided suggestions for possible future research on the investigation topics.

In the study of kinetic theory and especially in the study of rarefied gas dynamics one often turns to the Boltzmann equation. The mathematical theory developed by Ludwig Boltzmann was at first sight applicable in aerospace engineering and fluid mechanics. As of today, the methods in kinetic theory are extended to other fields, for instance, molecular biology and socioeconomics, which makes the need of finding efficient solution methods still important. In this thesis, we study the underlying theory of the continuous and discrete Boltzmann equation for monatomic gases. We extend the theory where needed, such that, we cover the case of colliding molecules that possess different levels of internal energy. Mainly, we discuss discrete velocity models and present explicit calculations for a model of a gas consisting of polyatomic molecules modelled with two levels of internal energy. / I studiet av kinetisk teori och speciellt i studiet av dynamik för tunna gaser vänder man sig ofta till Boltzmannekvationen. Den matematiska teorien utvecklad av Ludwig Boltzmann var vid första anblicken tillämpbar i flyg- och rymdteknik och strömningsmekanik. Idag generaliseras metoder i kinetisk teori till andra områden, till exempel inom molekylärbiologi och socioekonomi, vilket gör att vi har ett fortsatt behov av att finna effektiva lösningsmetoder. Vi studerar i denna uppsats den underliggande teorin av den kontinuerliga och diskreta Boltzmannekvationen för monatomiska gaser. Vi utvidgar teorin där det behövs för att täcka fallet då kolliderande molekyler innehar olika nivåer av intern energi. Vi diskuterar huvudsakligen diskreta hastighetsmodeller och presenterar explicita beräkningar för en modell av en gas bestående av polyatomiska molekyler modellerad med två lägen av intern energi.

Osteoarthritis is a progressive degenerative joint disease which causes pain, inflammation, and eventual loss of joint function. This debilitating disease affects approximately 3% of U.S. adults over 30 years old, with direct medical costs of over $100 billion each year. Post-traumatic osteoarthritis is a sub-set of osteoarthritis initiated by injuries such as a fracture of the joint surface. When a surgeon reconstructs a fractured joint, there are often residual incongruities on the surface, which can lead to elevated contact stresses. Increased cartilage contact stress has been shown to be a major risk factor for developing post-traumatic osteoarthritis. Computational modeling offers a method of detecting elevated contact stresses and thereby assessing the associated risk of a patient developing post-traumatic osteoarthritis. Discrete element analysis (DEA) is a computational method capable of fast and reliable contact stress predictions that has been used successfully to predict knee and ankle osteoarthritis. The purpose of this study was to validate the accuracy of DEA models of both intact and fractured hips by directly comparing experimentally measured intra-articular contact stresses in human cadaveric hips to corresponding DEA predictions. Overall correlation was greater than 90% for both intact and fractured hips. The validated DEA algorithm was then applied to a series of 3 patients with a hip fracture and another series of 19 patients with surgical hip re-alignment. As anticipated, changes in contact stress correlated well with pain and function (p < 0.05). This validated DEA model appears to be a clinically useful tool for identifying patients who are at higher risk for developing osteoarthritis as a result of elevated joint contact stresses.

The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we study the controllability and observability of time-invariant linear nabla fractional systems.We investigate the time-variant case in Chapter 5 and we define the state transition matrix in fractional calculus. In the last chapter, the results are summarized and directions for future work are stated.