The aim of this book is to analyse the various behaviour of Retrial queueing system. To motivate, many examples have been quoted.In this book, concepts like priority services,vacation policies,unreliable server,second optional service,negative arrival,vacation interruption and variable service rates have been discussed and 24 models have been developed. System performance measures of these models have been dealt and numerical and graphical studies have been done in elaborate manner. This book will be highly useful to those who are working in the area of queueing theory, Stochastic models in Operation Research and communication Engineering.
Here an attempt has been made to discuss the application of Queueing theory as applicable to hospital registration services i.e. outpatient registrations, inpatient registrations and registration for ICU admissions. Then illustrates the practical application of queueing theory to a simple problem in manpower planning: how large staff is required to give adequate service for a central laboratory? The problem is simple enough to be amenable to an analytic solution, and the optimal solution arrived at by the use of queueing theory resulted in a considerable saving to the central laboratory studied. A model of the patient care process, based on queueing theory, is described and its parameters defined empirically for application to an ICU unit. The model is descriptive, with an output of expected waiting times for various priorities of patient demand. The waiting times so estimated constitute an index of the quality of nursing care and afford a means of predicting changes in quality with changes in staffing or inpatient load. The model facilitates investigation of the relationships among three factors: patient condition, nurses' activity priorities, and patient load per nurse.
Metamodeling – A Study of Approximations in Queueing Models
This monograph gives an overview of current methods for solving to stochastic differencial equations both analytical and numerical and considers several applications of mathematical finance models in the context of derivative pricing. In particular, credit risk models are incorporated into the pricing of derivative contracts such as CDS with counterparty default risk etc. Also, monograph introduces contingent claims theory and summarizes some important applications such as Black-Sholes formulae computed for options on shares and futures, Chapmen-Kolmogorov equation, Heath-Jarrow-Morton methodology for interest-rate modeling.
A new model of a queueing system with two buffers, both finite in one case and only finite in other case were considered. The study of the features like blocking, splitting, feedback, balking and reneging can be done. In present work the study of splitting and up to some extent the study of blocking is done. The analytical solution of the tandem queue with splitting feature is in itself novel. In addition an algorithm is also studied for the stationary process of each case to determine the distribution of the queue length and other queue parameters as consequences. Although, solutions were not explicitly displayed in the closed forms, it can be accessed through the algorithm. The numerical examples demonstrate the behavior of the model and some imbalances that occurs.
This note contains some applications of stochastic models in finance. For example, we survey Markov Decision Processes, Bayesian Networks, Adaptive Control, Black-Scholes Pricing methods. This note involves the change point analysis in some financial models, risk management, portfolio selection and credit scoring in financial institutions. Some papers are too short, however, we have studied an observation.
The purpose of this study was to assess and model the stochastic nature of customer services provided by Commercial Bank of Ethiopia at Hawassa Branch. The study design adopted here was longitudinal. It considered the number of customers getting service in the Bank at time of 8:00 am to 4:00 pm for each working day from November 1-30, 2010.M/M/N model of queueing theory and non-linear regression models were used to analyze the data. Results from M/M/N indicated that the arrival rate was the highest in all weeks during the afternoon period from 2:00pm-4:00pm except Monday but it was the lowest during the lunch period from 11:30am-2:00pm. From steady-state probability of customers in the bank system, for every day throughout the month the maximum limiting probability existed before the number of customers becomes greater than the number of counter. The non-linear regression model output also supported the results of M/M/N model in predicting mean number of customers in the system, mean queue length, waiting time in queue and in the system. It is recommended that longitudinal studies need to be done to identify the busy and idle period within the month throughout the year.
The aim of this book is to summarize the obtained results of investigation of the boundary problems tied with distributions of boundary functionals for random processes and random walks with independent increments considered in the fluctuation theory and to draw attention to their connection with the risk theory. In the book special attention is paid to Levy processes with hyperexponentially distributed jumps. For them the unified prelimit and limit Pollaczeck-Khinchine formulas are established. They are used in the investigation of distributions of boundary functionals defining different characteristics of the risk and queueing processes. This monograph will be useful to the researchers working with probability theory and stochastic processes, in particular for those who deal with boundary problems for Levy processes and with their applications in risk theory, renewal theory, reliability theory, queueing theory, financial and actuarial mathematics, and in other applied areas. This book can be recommended to scientists, engineers, students, and post-graduate students of economical and mathematical specialities.
Modeling is a simplified representation of reality. Deterministic models provide exact or consistent prediction for every variable. Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Since uncertainty is pervasive, this means that the tools of this stochastic process can potentially prove useful in almost all facets of professional life and sometimes even in personal life as in gambling, personal finances economic forecasting, product demand, call center provisioning, product reliability and warranty analysis. Planning is an inevitable phenomenon in everyday life and stochastic modeling can help to maximize use of available manpower, finance and material resources. The Monte Carlo Simulation is an example of a stochastic model used in finance. Stochastic modeling is a practical tool for predicting employer and employee behavior and manpower stocks and flows based on rational assumptions. Models discussed in this book certainly build a strong base for students and researchers from business, industry, computer science, management studies and allied areas who seek the knowledge in applied stochastic processes.
In the present work we study the transient behavior of some two-state bulk queueing models with (i) Intermittently available server, i.e. the server goes either for rest or to attend some very urgent jobs when the queue length is greater than or equal to zero. The server has the option to start a fresh service instantaneously or to make interruption, but it is assumed that he completes the service in hand before the interruption, (ii) Multiple vacations, i.e. the server begins a vacation with probability ‘one’ each time the system becomes empty. If the server returns from a vacation to find the system not empty. If the server returns from a vacation to find no customers waiting, it begins another vacation immediately, and continues in this manner until it finds at least one customer waiting upon returning from a vacation (multiple vacations), and (iii) Non- exhaustive service, i.e. the server may go on vacation even if there are some customers waiting for service or vacations may start even when customers are present in the system.
The extreme financial markets volatility that the financial crisis unleashed in 2008, continues to challenge researchers on how best to keep track and model such market movements. This book, entitled "Jump Diffusion and Stochastic Volatility Models in Securities Pricing", seeks to add value to the endeavor of modeling volatility and jumps across various asset classes. The aim is to improve risk management efforts and for more accurate pricing of primary and derivative securities. The book presents jump diffusion and stochastic volatility models for the movements of equities, currencies, interest rates, house prices and temperature. All asset classes demonstrate the presence of jumps and stochastic volatility in the movement of their prices.The jumps conform to the Poisson model while stochastic volatility conforms to a normal and a fat-tailed Garch models. Maximum likelihood methods are used to estimate various parameters in the mixture of distributions.
Stochastic optimization problems are the study of dynamical systems subject to random perturbations which can be controlled in order to optimize some performance criterion. The research on control theory has developed considerably over last few years, inspired in particular by stochastic optimization problems emerging from mathematical nance. Problems involving linear dynamics and quadratic performance criteria are generally called linear regulator problems. The usual framework of control is the one given in probably the most studied control problem, the linear quadratic optimal control problem or the linear regulator problem, which deals with minimizing a performance index of a system governed by a set of dierential equations. The object of linear regulator control problems is to control the position of a certain process and at the same time, the force with which this process is being regulated, by punishing quadratic deviations from some targets of the process and the rate of regulation, respectively.
This book was divided in to six chapters.The book is to highlight the present work in its right perspective. Some relevant literature on this type of modeling either in insurance or elsewhere are presented. In the period of dynamic indetermination in science, there is hardly a serious piece of research, which, if treated realistically, does not involve operations on stochastic process. So it is natural to find growing awareness and interest in stochastic modeling every where. An insurance system can be defined as a mechanism for reducing the adverse financial impact of random events that prevent the fulfillment of reasonable expectation of human beings. This system covers both property and human-life values. An insurance contract promises to make good to the insured a certain sum in consideration for a payment in the form of premium from the insured. Insurances can be classified in to two divisions namely life insurances and non life insurances. The non life insurances cover motor, health, fire, marine etc. A stochastic insurance model would be to setup a projection model which looks at a single policy, an entire portfolio or an entire company.
The objective of this dissertation is to enhance the overall understanding of practical manufacturing systems primarily through queueing theory. Queueing theory is commonly used to evaluate the performance of manufacturing systems. A machine on the shop floor is subject to different kinds of interruptions. By systematically classifying different kinds of interruptions, suitable queueing models are proposed. The behavior of manufacturing systems is explored by first investigating the underlying structure of tandem queues. The identified structures, termed the intrinsic gap and intrinsic ratio, come with very nice properties, which we call the heavy-traffic and nearly-linear relationship properties. Based on those properties, new approximate models are developed to approximate the mean queue time of many single-server stations in series. By extending the results from tandem queues, an approximate model for an entire manufacturing system is derived. The model is used to quantify the performance of manufacturing systems and has been evaluated by simulation. The results demonstrate that the new method has strong capability to describe the performance of practical manufacturing systems.