Analysis of some Stochastic models in inventories and Queues

The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models.

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Development of thermo-analytical prediction and classification models for food in thermal devices using a multi sensor system and artificial neural networks

Die thermische Verarbeitung von Lebensmitteln beeinflusst deren Qualität und ernährungsphysiologischen Eigenschaften. Im Haushalt ist die Überwachung der Temperatur innerhalb des Lebensmittels sehr schwierig. Zudem ist das Wissen über optimale Temperatur- und Zeitparameter für die verschiedenen Speisen oft unzureichend. Die optimale Steuerung der thermischen Zubereitung ist maßgeblich abhängig von der Art des Lebensmittels und der äußeren und inneren Temperatureinwirkung während des Garvorgangs. Das Ziel der Arbeiten war die Entwicklung eines automatischen Backofens, der in der Lage ist, die Art des Lebensmittels zu erkennen und die Temperatur im Inneren des Lebensmittels während des Backens zu errechnen. Die für die Temperaturberechnung benötigten Daten wurden mit mehreren Sensoren erfasst. Hierzu kam ein Infrarotthermometer, ein Infrarotabstandssensor, eine Kamera, ein Temperatursensor und ein Lambdasonde innerhalb des Ofens zum Einsatz. Ferner wurden eine Wägezelle, ein Strom- sowie Spannungs-Sensor und ein Temperatursensor außerhalb des Ofens genutzt. Die während der Aufheizphase aufgenommen Datensätze ermöglichten das Training mehrerer künstlicher neuronaler Netze, die die verschiedenen Lebensmittel in die entsprechenden Kategorien einordnen konnten, um so das optimale Backprogram auszuwählen. Zur Abschätzung der thermische Diffusivität der Nahrung, die von der Zusammensetzung (Kohlenhydrate, Fett, Protein, Wasser) abhängt, wurden mehrere künstliche neuronale Netze trainiert. Mit Ausnahme des Fettanteils der Lebensmittel konnten alle Komponenten durch verschiedene KNNs mit einem Maximum von 8 versteckten Neuronen ausreichend genau abgeschätzt werden um auf deren Grundlage die Temperatur im inneren des Lebensmittels zu berechnen. Die durchgeführte Arbeit zeigt, dass mit Hilfe verschiedenster Sensoren zur direkten beziehungsweise indirekten Messung der äußeren Eigenschaften der Lebensmittel sowie KNNs für die Kategorisierung und Abschätzung der Lebensmittelzusammensetzung die automatische Erkennung und Berechnung der inneren Temperatur von verschiedensten Lebensmitteln möglich ist.

Formal Multilevel Hierarchical Verification of Synchronous MOS Circuits

I have designed and implemented a system for the multilevel verification of synchronous MOS VLSI circuits. The system, called Silica Pithecus, accepts the schematic of an MOS circuit and a specification of the circuit's intended digital behavior. Silica Pithecus determines if the circuit meets its specification. If the circuit fails to meet its specification Silica Pithecus returns to the designer the reason for the failure. Unlike earlier verifiers which modelled primitives (e.g., transistors) as unidirectional digital devices, Silica Pithecus models primitives more realistically. Transistors are modelled as bidirectional devices of varying resistances, and nodes are modelled as capacitors. Silica Pithecus operates hierarchically, interactively, and incrementally. Major contributions of this research include a formal understanding of the relationship between different behavioral descriptions (e.g., signal, boolean, and arithmetic descriptions) of the same device, and a formalization of the relationship between the structure, behavior, and context of device. Given these formal structures my methods find sufficient conditions on the inputs of circuits which guarantee the correct operation of the circuit in the desired descriptive domain. These methods are algorithmic and complete. They also handle complex phenomena such as races and charge sharing. Informal notions such as races and hazards are shown to be derivable from the correctness conditions used by my methods.

Probabilidad de ruina con un modelo de riesgo Markov-modulado y propiedades del proceso telegráfico

En esta tesis se entiende la intuición y las matemáticas del modelo generalizado de la teoría de la ruina, expuesto por Li y Lu quienes se remiten a los cálculos de la probabilidad de ruina de Reinhard. Teniendo en cuenta las definiciones, la media y la varianza del proceso telegráfico con saltos encontradas en la tesis doctoral de Óscar López. Luego se simula el proceso de riesgo y finalmente con un ejemplo se calcula la probabilidad de ruina numéricamente. Todo el proceso se va a realizar teniendo en cuenta reclamaciones con distribución exponencial.

Estimating the hidden number of scrapie affected holdings in great Britain using a simple, truncated count model allowing for heterogeneity.

None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted prevalence of scrapie in Great Britain applied multiple-list capture–recapture methods. The enforcement of new control measures on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application of multiple-list capture–recapture models. Alternative methods, still under the capture–recapture methodology, relying on repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture–recapture approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool for indication of heterogeneity as well as a new understanding of the Zelterman and Chao’s lower bound estimators to account for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates—in case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around 300 holdings per year. None of the covariates appear to inform the model significantly.

Bayesian estimation and selection of nonlinear vector error correction models: The case of the sugar-ethanol-oil nexus in Brazil

Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest that the long-run drivers of Brazilian sugar prices are oil prices and that there are nonlinearities in the adjustment processes of sugar and ethanol prices to oil price but linear adjustment between ethanol and sugar prices.

Estimating the hidden number of scrapie affected holdings in great Britain using a simple, truncated count model allowing for heterogeneity

None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted prevalence of scrapie in Great Britain applied multiple-list capture-recapture methods. The enforcement of new control measures on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application of multiple-list capture-recapture models. Alternative methods, still under the capture-recapture methodology, relying on repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture-recapture approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool for indication of heterogeneity as well as a new understanding of the Zelterman and Chao's lower bound estimators to account for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates-in case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around 300 holdings per year. None of the covariates appear to inform the model significantly.

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon-known as heterotachy-can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.

Phylogenetic mixture models can reduce node-density artifacts

We investigate the performance of phylogenetic mixture models in reducing a well-known and pervasive artifact of phylogenetic inference known as the node-density effect, comparing them to partitioned analyses of the same data. The node-density effect refers to the tendency for the amount of evolutionary change in longer branches of phylogenies to be underestimated compared to that in regions of the tree where there are more nodes and thus branches are typically shorter. Mixture models allow more than one model of sequence evolution to describe the sites in an alignment without prior knowledge of the evolutionary processes that characterize the data or how they correspond to different sites. If multiple evolutionary patterns are common in sequence evolution, mixture models may be capable of reducing node-density effects by characterizing the evolutionary processes more accurately. In gene-sequence alignments simulated to have heterogeneous patterns of evolution, we find that mixture models can reduce node-density effects to negligible levels or remove them altogether, performing as well as partitioned analyses based on the known simulated patterns. The mixture models achieve this without knowledge of the patterns that generated the data and even in some cases without specifying the full or true model of sequence evolution known to underlie the data. The latter result is especially important in real applications, as the true model of evolution is seldom known. We find the same patterns of results for two real data sets with evidence of complex patterns of sequence evolution: mixture models substantially reduced node-density effects and returned better likelihoods compared to partitioning models specifically fitted to these data. We suggest that the presence of more than one pattern of evolution in the data is a common source of error in phylogenetic inference and that mixture models can often detect these patterns even without prior knowledge of their presence in the data. Routine use of mixture models alongside other approaches to phylogenetic inference may often reveal hidden or unexpected patterns of sequence evolution and can improve phylogenetic inference.

Inference on microsatellite mutation processes in the invasive mite, Varroa destructor, using reversible jump Markov chain Monte Carlo

Varroa destructor is a parasitic mite of the Eastern honeybee Apis cerana. Fifty years ago, two distinct evolutionary lineages (Korean and Japanese) invaded the Western honeybee Apis mellifera. This haplo-diploid parasite species reproduces mainly through brother sister matings, a system which largely favors the fixation of new mutations. In a worldwide sample of 225 individuals from 21 locations collected on Western honeybees and analyzed at 19 microsatellite loci, a series of de novo mutations was observed. Using historical data concerning the invasion, this original biological system has been exploited to compare three mutation models with allele size constraints for microsatellite markers: stepwise (SMM) and generalized (GSM) mutation models, and a model with mutation rate increasing exponentially with microsatellite length (ESM). Posterior probabilities of the three models have been estimated for each locus individually using reversible jump Markov Chain Monte Carlo. The relative support of each model varies widely among loci, but the GSM is the only model that always receives at least 9% support, whatever the locus. The analysis also provides robust estimates of mutation parameters for each locus and of the divergence time of the two invasive lineages (67,000 generations with a 90% credibility interval of 35,000-174,000). With an average of 10 generations per year, this divergence time fits with the last post-glacial Korea Japan land separation. (c) 2005 Elsevier Inc. All rights reserved.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

The role of atmosphere feedbacks during ENSO in the CMIP3 models. Part III: the shortwave flux feedback

Previous studies using coupled general circulation models (GCMs) suggest that the atmosphere model plays a dominant role in the modeled El Nin ̃ o–Southern Oscillation (ENSO), and that intermodel differences in the thermodynamical damping of sea surface temperatures (SSTs) are a dominant contributor to the ENSO amplitude diversity. This study presents a detailed analysis of the shortwave flux feedback (aSW) in 12 Coupled Model Intercomparison Project phase 3 (CMIP3) simulations, motivated by findings that aSW is the primary contributor to model thermodynamical damping errors. A ‘‘feedback decomposition method,’’ developed to elucidate the aSW biases, shows that all models un- derestimate the dynamical atmospheric response to SSTs in the eastern equatorial Pacific, leading to un- derestimated aSW values. Biases in the cloud response to dynamics and the shortwave interception by clouds also contribute to errors in aSW. Changes in the aSW feedback between the coupled and corresponding atmosphere-only simulations are related to changes in the mean dynamics. A large nonlinearity is found in the observed and modeled SW flux feedback, hidden when linearly cal- culating aSW. In the observations, two physical mechanisms are proposed to explain this nonlinearity: 1) a weaker subsidence response to cold SST anomalies than the ascent response to warm SST anomalies and 2) a nonlinear high-level cloud cover response to SST. The shortwave flux feedback nonlinearity tends to be underestimated by the models, linked to an underestimated nonlinearity in the dynamical response to SST. The process-based methodology presented in this study may help to correct model ENSO atmospheric biases, ultimately leading to an improved simulation of ENSO in GCMs.

Incorporating technology buying behaviour into UK-based long term domestic stock energy models to provide improved policy analysis

The UK has a target for an 80% reduction in CO2 emissions by 2050 from a 1990 base. Domestic energy use accounts for around 30% of total emissions. This paper presents a comprehensive review of existing models and modelling techniques and indicates how they might be improved by considering individual buying behaviour. Macro (top-down) and micro (bottom-up) models have been reviewed and analysed. It is found that bottom-up models can project technology diffusion due to their higher resolution. The weakness of existing bottom-up models at capturing individual green technology buying behaviour has been identified. Consequently, Markov chains, neural networks and agent-based modelling are proposed as possible methods to incorporate buying behaviour within a domestic energy forecast model. Among the three methods, agent-based models are found to be the most promising, although a successful agent approach requires large amounts of input data. A prototype agent-based model has been developed and tested, which demonstrates the feasibility of an agent approach. This model shows that an agent-based approach is promising as a means to predict the effectiveness of various policy measures.