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.

Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Queueing Theory And Other Applications Of Stochastic Processes Queueing And Inventory Models With Rest Periods

In this thesis we study the effect of rest periods in queueing systems without exhaustive service and inventory systems with rest to the server. Most of the works in the vacation models deal with exhaustive service. Recently some results have appeared for the systems without exhaustive service.

Some aspects of history of Indian mathematics in 18th and early 19th century

This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.

Some characterization problems associated with the bivariate exponential and geometric distributions

It is highly desirable that any multivariate distribution possessescharacteristic properties that are generalisation in some sense of the corresponding results in the univariate case. Therefore it is of interest to examine whether a multivariate distribution can admit such characterizations. In the exponential context, the question to be answered is, in what meaning— ful way can one extend the unique properties in the univariate case in a bivariate set up? Since the lack of memory property is the best studied and most useful property of the exponential law, our first endeavour in the present thesis, is to suitably extend this property and its equivalent forms so as to characterize the Gumbel's bivariate exponential distribution. Though there are many forms of bivariate exponential distributions, a matching interest has not been shown in developing corresponding discrete versions in the form of bivariate geometric distributions. Accordingly, attempt is also made to introduce the geometric version of the Gumbel distribution and examine several of its characteristic properties. A major area where exponential models are successfully applied being reliability theory, we also look into the role of these bivariate laws in that context. The present thesis is organised into five Chapters

Some Problems In Algebra And Topology A Study Of Fuzzy Convexity With Special Reference To Separation Properties

This thesis is a study of abstract fuzzy convexity spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop a fuzzy convexity theoryin abstract situations. The purpose of this thesis is to introduce fuzzy convexity theory in abstract situations

A Unified Framework for Regularization Networks and Support Vector Machines

Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples -- in particular the regression problem of approximating a multivariate function from sparse data. We present both formulations in a unified framework, namely in the context of Vapnik's theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Ahorro para el retiro en Colombia: patrones y determinantes

La decisión de los individuos acerca del ahorro para el retiro ha sido abordada teóricamente bajo la hipótesis de que el sistema de seguridad social se comporta como un sustituto de otros mecanismos de ahorro. Este documento presenta evidencia de los patrones y determinantes del ahorro para el retiro en Colombia a partir de la Gran Encuesta Integrada de Hogares de 2007. Los resultados muestran que el 63% de los ocupados declaran no ahorrar para su vejez. A partir de modelos de selección discreta se encuentra que individuos jóvenes, de sexo masculino, con menor nivel educativo, residentes en zonas rurales, y trabajadores cuenta propia, presentan menores probabilidades de ah orrar para el retiro; además las características socioeconómicas resultan significativas en la determinación del mecanismo de ahorro utilizado.

Natural disasters and clientelism: the case of floods and landslides in Colombia

What are the effects of natural disasters on electoral results? Some authors claim that catastrophes have a negative effect on the survival of leaders in a democracy because voters have a propensity to punish politicians for not preventing or poorly handling a crisis. In contrast, this paper finds that these events might be beneficial for leaders. Disasters are linked to leader survival through clientelism: they generate an in-flow of resources in the form of aid, which increase money for buying votes. Analyzing the rainy season of 2010-2011 in Colombia, considered its worst disaster in history, I use a difference-in-differences strategy to show that in the local election incumbent parties benefited from the disaster. The result is robust to different specifications and alternative explanations. Moreover, places receiving more aid and those with judicial evidence of vote-buying irregularities, are more likely to reelect the incumbent, supporting the mechanism proposed by this paper.

On the design of education conditional cash transfer programs and non education outcomes: the case of teenage pregnancy

We investigate the effect of education Conditional Cash Transfer programs (CCTs) on teenage pregnancy. Our main concern is with how the size and sign of the effect may depend on the design of the program. Using a simple model we show that an education CCT that conditions renewal on school performance reduces teenage pregnancy; the program can increase teenage pregnancy if it does not condition on school performance. Then, using an original data base, we estimate the causal impact on teenage pregnancy of two education CCTs implemented in Bogot´a (Subsidio Educativo, SE, and Familias en Acci´on, FA); both programs differ particularly on whether school success is a condition for renewal or not. We show that SE has negative average effect on teenage pregnancy while FA has a null average effect. We also find that SE has either null or no effect for adolescents in all age and grade groups while FA has positive, null or negative effects for adolescents in different age and grade groups. Since SE conditions renewal on school success and FA does not, we can argue that the empirical results are consistent with the predictions of our model and that conditioning renewal of the subsidy on school success crucially determines the effect of the subsidy on teenage pregnancy

Parametric pension reform and the intensive margin of labor supply, evidence from Colombia

We analyze the effect of a parametric reform of the fully-funded pension regime in Colombia on the intensive margin of the labor supply. We take advantage of a threshold defined by law in order to identify the causal effect using a regression discontinuity design. We find that a pension system that increases retirement age and the minimum weeks during which workers must contribute to claim pension benefits causes an increase of around 2 hours on the number of weekly worked hours; this corresponds to 4% of the average number of weekly worked hours or around 14% of a standard deviation of weekly worked hours. The effect is robust to different specifications, polynomial orders and sample sizes.

Publicness of goods and violent conflict : evidence from Colombia

How the degree of publicness of goods affect violent conflict? Based on the theoretical model in Esteban and Ray (2001) we find that the effect of the degree of publicness depends on the group size. When the group is small (large), the degree of publicness increases (decreases) the likelihood of conflict. This opens an empirical question that we tackle using microdata from the Colombian conflict at the municipality level. We use three goods with different publicness degree to identify the sign of the effect of publicness on conflict. These goods are coca crops (private good), road density (public good subject to congestion) and average education quality (a purer public good). After dealing with endogeneity issues using an IV approach, we find that the degree of publicness reduces the likelihood of both paramilitary and guerrilla attacks. Moreover, coca production exacerbates conflict and the provision of both public goods mitigates conflict. These results are robust to size, geographical, and welfare controls. Policies that improve public goods provision will help to fight the onset of conflict.

Small-area variation in health care affecting the choice of cesarean delivery: the case of a Colombian health insurer

In the midst of health care reform, Colombia has succeeded in increasing health insurance coverage and the quality of health care. In spite of this, efficiency continues to be a matter of concern, and small-area variations in health care are one of the plausible causes of such inefficiencies. In order to understand this issue, we use individual data of all births from a Contributory-Regimen insurer in Colombia. We perform two different specifications of a multilevel logistic regression model. Our results reveal that hospitals account for 20% of variation on the probability of performing cesarean sections. Geographic area only explains 1/3 of the variance attributable to the hospital. Furthermore, some variables from both demand and supply sides are found to be also relevant on the probability of undergoing cesarean sections. This paper contributes to previous research by using a hierarchical model and by defining hospitals as cluster. Moreover, we also include clinical and supply induced demand variables.