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Difference Equations And The Optimal Control Of Single Server Queueing Systems
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Book Synopsis Difference Equations and the Optimal Control of Single Server Queueing Systems by : F. C. Reed
Download or read book Difference Equations and the Optimal Control of Single Server Queueing Systems written by F. C. Reed and published by . This book was released on 1974 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report demonstrates the use of difference equations in solving optimal control problems in single server queueing systems. One obtains the discounted or relative cost function associated with a specific stationary policy by solving an appropriate system of difference equations. The policy improvement algorithm is applied parametrically leading to a characterization of the cost function satisfying the functional equation of optimality. It this cost function satisfies an appropriate sufficient condition, the associated stationary policy is optimal. (Modified author abstract).
Book Synopsis Difference Equations and the Optimal Control of Single Server Queueing Systems by : Frank C. Reed
Download or read book Difference Equations and the Optimal Control of Single Server Queueing Systems written by Frank C. Reed and published by . This book was released on 1974 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report demonstrates the use of difference equations in solving optimal control problems in single server queueing systems. One obtains the discounted or relative cost function associated with a specific stationary policy by solving an appropriate system of difference equations. The policy improvement algorithm is applied parametrically leading to a characterization of the cost function satisfying the functional equation of optimality. If this cost function satisfies an appropriate sufficient condition, the associated stationary policy is optimal. The method of solution is illustrated by solving three queueing optimization problems. These problems include optimal control of the M/G/1 queue with intermittent service, a bulk queueing version of this same problem, and control of the M/M/1 queue with selection of running speed. All of these problems have been investigated by other authors. Results in this report believed to be new include a complete characterization of optimal policies for the optimal control of the M/G/1 queue in the discounted case, the extension of the optimal control of the bulk queueing problem from instantaneous to general service, and the determination of an optimal speed selection policy for the M/M/1 queue without solving a sequence of truncated problems.
Book Synopsis Difference and Differential Equations with Applications in Queueing Theory by : Aliakbar Montazer Haghighi
Download or read book Difference and Differential Equations with Applications in Queueing Theory written by Aliakbar Montazer Haghighi and published by John Wiley & Sons. This book was released on 2013-07-10 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of topics that are used in stochastic processes, particularly in queueing theory, the book thoroughly discusses the relationship to systems of linear differential difference equations. The book demonstrates the applicability that queueing theory has in a variety of fields including telecommunications, traffic engineering, computing, and the design of factories, shops, offices, and hospitals. Along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform, Difference and Differential Equations with Applications in Queueing Theory provides: A discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models Applications in queue models whose solutions require differential difference equations and generating function methods Exercises at the end of each chapter along with select answers The book is an excellent resource for researchers and practitioners in applied mathematics, operations research, engineering, and industrial engineering, as well as a useful text for upper-undergraduate and graduate-level courses in applied mathematics, differential and difference equations, queueing theory, probability, and stochastic processes.
Book Synopsis On the Optimal Control of Single Server Queueing Systems by : Frank Curry Reed
Download or read book On the Optimal Control of Single Server Queueing Systems written by Frank Curry Reed and published by . This book was released on 1974 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Difference Equation Approach to the Optimal Control of a Multiclass Queue with Discounted Costs by : F. C. Reed
Download or read book A Difference Equation Approach to the Optimal Control of a Multiclass Queue with Discounted Costs written by F. C. Reed and published by . This book was released on 1975 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report considers the problem of dynamically selecting one of a finite number of customer classes to serve so that the total expected discounted cost over an infinite horizon is minimized. Decisions are allowed at the time of service completion, or if the server is idle, at the time of customer arrival. It is assumed that customers arrive according to independent Poisson processes with different arrival rates for the various customer classes. Service times are independently distributed and identically distributed for customers of a given class. The cost structure is linear and includes class-dependent holding costs, service costs, and rewards. Difference equations are used to derive a closed form expression for total expected discounted cost given the process begins with an arbitrary number of customers in each customer class in the queue and a non-preemptive priority discipline is used.
Book Synopsis Optimal Maintenance Policies for Single-server Queueing Systems Subject to Breakdowns by : Kut-Cheung Rick So
Download or read book Optimal Maintenance Policies for Single-server Queueing Systems Subject to Breakdowns written by Kut-Cheung Rick So and published by . This book was released on 1985 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Queueing Systems, Volume 2 by : Leonard Kleinrock
Download or read book Queueing Systems, Volume 2 written by Leonard Kleinrock and published by Wiley-Interscience. This book was released on 1976 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queueing Systems Volume 1: Theory Leonard Kleinrock This book presents and develops methods from queueing theory in sufficient depth so that students and professionals may apply these methods to many modern engineering problems, as well as conduct creative research in the field. It provides a long-needed alternative both to highly mathematical texts and to those which are simplistic or limited in approach. Written in mathematical language, it avoids the "theorem-proof" technique: instead, it guides the reader through a step-by-step, intuitively motivated yet precise development leading to a natural discovery of results. Queueing Systems, Volume I covers material ranging from a refresher on transform and probability theory through the treatment of advanced queueing systems. It is divided into four sections: 1) preliminaries; 2) elementary queueing theory; 3) intermediate queueing theory; and 4) advanced material. Important features of Queueing Systems, Volume 1: Theory include- * techniques of duality, collective marks * queueing networks * complete appendix on z-transforms and Laplace transforms * an entire appendix on probability theory, providing the notation and main results needed throughout the text * definition and use of a new and convenient graphical notation for describing the arrival and departure of customers to a queueing system * a Venn diagram classification of many common stochastic processes 1975 (0 471-49110-1) 417 pp. Fundamentals of Queueing Theory Second Edition Donald Gross and Carl M. Harris This graduated, meticulous look at queueing fundamentals developed from the authors' lecture notes presents all aspects of the methodology-including Simple Markovian birth-death queueing models; advanced Markovian models; networks, series, and cyclic queues; models with general arrival or service patterns; bounds, approximations, and numerical techniques; and simulation-in a style suitable to courses of study of widely varying depth and duration. This Second Edition features new expansions and abridgements which enhance pedagogical use: new material on numerical solution techniques for both steady-state and transient solutions; changes in simulation language and new results in statistical analysis; and more. Complete with a solutions manual, here is a comprehensive, rigorous introduction to the basics of the discipline. 1985 (0 471-89067-7) 640 pp.
Book Synopsis Analysis of a Single Server Fluid Queueing System with Feedback Using Stochastic Differential Equations by : Srikanth G. Mashetty
Download or read book Analysis of a Single Server Fluid Queueing System with Feedback Using Stochastic Differential Equations written by Srikanth G. Mashetty and published by . This book was released on 2004 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Annual Department of Defense Bibliography of Logistics Studies and Related Documents by : United States. Defense Logistics Studies Information Exchange
Download or read book Annual Department of Defense Bibliography of Logistics Studies and Related Documents written by United States. Defense Logistics Studies Information Exchange and published by . This book was released on 1975 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis OPTIMALCONTROL OF THE M/G/1 QUEUEING SYSTEM WITH REMOVABLE SERVER-LINEAR AND NON-LINEAR HOLDING COST FUNCTION. by : Peter Orkenyi
Download or read book OPTIMALCONTROL OF THE M/G/1 QUEUEING SYSTEM WITH REMOVABLE SERVER-LINEAR AND NON-LINEAR HOLDING COST FUNCTION. written by Peter Orkenyi and published by . This book was released on 1976 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report considers the M/G/1 queueing system with removable server. The cases of linear and non-linear customer holding cost functions are both considered. Non-instantaneous start-up times are allowed. The problem is to find an optimal policy for turning the server on and off. The optimality criteria considered are the average cost criterion, the undiscounted cost criterion and the discounted cost criterion. A certain class of simple policies, the hysteretic policies, is considered. Natural hysteretic policies and non- degenerate hysteretic policies are introduced. It is shown that there is a natural hysteretic policy which is average optimal, and that if the start-up times are instantaneous or the holding cost function convex, then there is a natural hysteretic policy which is undiscounted optimal. When discounting is used, the results are not as strong, except for the case where the holding cost function is linear. For the non-linear case we still obtain certain fairly weak sufficient conditions for a natural hysteretic policy to be optimal.
Book Synopsis Optimal Control of Queueing Systems with Variable Number of Exponential Servers by : Stanford University. Department of Operations Research
Download or read book Optimal Control of Queueing Systems with Variable Number of Exponential Servers written by Stanford University. Department of Operations Research and published by . This book was released on 1969 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general switching cost model is formulated, and the problem of characterizing the optimal policy for a certain class of systems possessing such a cost structure is addressed. The class of systems studied can be described in terms of a pair of state descriptors which render the underlying probabilistic structure Markovian. The state descriptor consists of a one-dimensional variable, called exogenous, which is subject to explicit control by the decision-maker, and a vector of variables, called endogenous, which are only implicitly controlled by the decision-maker. The variable server M/M/c queueing system is an example. In such a system the exogenous variable is the number of servers employed (bounded above by c), and the endogenous variable is the number of customers in the system. The cost structure consists of two components: a variable cost of the system being in a particular state, assumed to be proportional to the length of time spent in that state, and a switching cost incurred instantaneously whenever the value of the exogenous variable is changed. A framework is developed for the analysis of systems where the length of time between review points is a random variable dependent on the state of the system. A characterization of the optimal control policy is given. The M/M/c queueing system is considered in detail and some attention is also given to the GI/M/c queueing system.
Book Synopsis Stochastic Controls by : Jiongmin Yong
Download or read book Stochastic Controls written by Jiongmin Yong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation.
Book Synopsis Naval Research Logistics Quarterly by :
Download or read book Naval Research Logistics Quarterly written by and published by . This book was released on 1966 with total page 1092 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Course on Queueing Models by : Joti Lal Jain
Download or read book A Course on Queueing Models written by Joti Lal Jain and published by CRC Press. This book was released on 2016-04-19 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of engineering principles in divergent fields such as management science and communications as well as the advancement of several approaches in theory and computation have led to growing interest in queueing models, creating the need for a comprehensive text. Emphasizing Markovian structures and the techniques that occur in differen
Book Synopsis Stochastic Models in Queueing Theory by : Jyotiprasad Medhi
Download or read book Stochastic Models in Queueing Theory written by Jyotiprasad Medhi and published by Elsevier. This book was released on 2002-11-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate level textbook that covers the fundamental topics in queuing theory. The book has a broad coverage of methods to calculate important probabilities, and gives attention to proving the general theorems. It includes many recent topics, such as server-vacation models, diffusion approximations and optimal operating policies, and more about bulk-arrival and bull-service models than other general texts. - Current, clear and comprehensive coverage - A wealth of interesting and relevant examples and exercises to reinforce concepts - Reference lists provided after each chapter for further investigation
Book Synopsis Bulletin of the Operations Research Society of America by :
Download or read book Bulletin of the Operations Research Society of America written by and published by . This book was released on 1972 with total page 1230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
