Download or read book Models for the Optimal Control of Markovian Closed Queueing Systems with Adjustable Service Rates written by Emerson Arlin Torbett and published by . This book was released on 1972 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report considers the problem of determining an optimal dynamic control policy for a closed queueing system in which the service facilities may be operated at more than one service rate. The optimality criterion is to minimize the long-run expected average cost per unit time. The author formulates a general control model whose cost structure includes: (1) an operating cost for running each service facility; (2) a switching cost for starting-up and shutting-down the facilities; (3) a holding cost rate for customers waiting or in service; (4) a service facility profit, earned whenever a service completion occurs. After reviewing some results from the theory of semi-Markov decision processes and proving that an optimal stationary deterministic policy exists for Markovian Closed Queueing Systems, analytical results are presented that specify the form of the optimal policy for several models of two-state closed queueing systems and investigate the behavior of the optimal policy as the number of customers in the system is increased. Several interesting future research topics are also identified in the dynamic control area, as well as in the static design area. Of particular interest are optimization problems that have applications to multiprogramming computer systems. (Author).
Download or read book Optimal Control of a Queue with Variable Service Rates written by Thomas Buskirk Crabill and published by . This book was released on 1969 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Methods in Queueing Theory written by A. B. Clarke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: On May 10-12, 1973 a Conference on Mathematical Methods in Graph Theory was held at Western Michigan University in Kalamazoo. The theme of this Conference was recent advances in the application of analytic and algebraic methods to the analysis of queues and queueing networks. In addition some discussion was given to statistical analy ses in queues, control problems and graphical methods. A total of 83 individuals from both industry and academic estab lishments participated in the Conference. A list of these partici pants can be found on page 373. A total of 18 papers were presented, with sUbstantial time being devoted to their informal discussion. This volume constitutes the proceedings of the Conference, and includes all papers presented. TABLE OF CONTENTS MARCEL F. NEUTS The Markov Renewal Branching Process • 1 RALPH L. DISNEY and W. PETER CHERRY Some Topics in Queueing Network Theory 23 JULIAN KEILSON Convexity and Complete Monotonicity in Queueing Distributions and Associated Limit Behavior . • • • • • . . • • • •• • • 45 G. F. NEWELL Graphical Representation of Queue Evolution for Multiple-Server Systems • . • • • • • • • • • • 63 N. U. PRABHU Wiener-Hopf Techniques in Queueing Theory 81 / IAJOS TAKACS Occupation Time Problems in the Theory of Queues 91 TAPAN P. BAGCHI and J. G. C. TEMPLETON Some Finite waiting Space Bulk Queueing Systems 133 U.
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 1974 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Controlled Queueing Systems written by Mikhail Yu. Kitaev and published by CRC Press. This book was released on 1995-08-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book completely devoted to controlled queueing systems. The book gathers the newest results of the theory of Markov decision processes related to queueing models and demonstrates their applications to main types of control in queueing systems, including control of arrivals, control of service mechanism, and control of service discipline. Emphasis is placed on conditions providing further "good" structural properties of Markov optimal strategies such as monotonicity, threshold or hysteretic character, and priority. Each chapter is followed by exercises, most of which allow the reader to complete technical fragments of proofs. The text assumes the reader is familiar with standard courses of analysis, probability theory, and queueing theory.
Download or read book OPTIMAL MARKOVIAN QUEUEING SYSTEMS written by K. CHUANG` and published by . This book was released on 1963 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Optimal Control of Markovian Systems with Applications to Queuing Systems written by Charles Fred Klein and published by . This book was released on 1977 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Technical Report written by and published by . This book was released on 1973 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Queueing Theory 2 written by Vladimir Anisimov and published by John Wiley & Sons. This book was released on 2021-03-05 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This second volume includes eight chapters written by experts wellknown in their areas. The book conducts a stability analysis of certain types of multiserver regenerative queueing systems; a transient evaluation of Markovian queueing systems, focusing on closed-form distributions and numerical techniques; analysis of queueing models in service sectors using analytical and simulation approaches; plus an investigation of probability distributions in queueing models and their use in economics, industry, demography and environmental studies. This book also considers techniques for the control of information in queueing systems and their impact on strategic customer behavior, social welfare and the revenue of monopolists. In addition, applications of maximum entropy methods of inference for the analysis of a stable M/G/1 queue with heavy tails, and inventory models with positive service time - including perishable items and stock supplied using various algorithmic control policies ((s; S); (r;Q), etc.).
Download or read book Optimal Control of Queueing Systems with Intermittent Service written by Joseph Daniel Blackburn and published by . This book was released on 1971 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report describes models for single-server queueing systems with Poisson arrivals and general service-time distribution which are controlled by turning the server on-and-off. The objective is an operating policy which minimizes (maximizes) expected discounted cost (reward) over an infinite horizon. Four distinct models of intermittent service systems are considered. The cost structure for these models includes fixed costs for starting-up and shutting-down the service facility, a server operating cost per unit time and either a holding cost for waiting customers or a reward for serving customers. Two of the models are based on different assumptions concerning the holding cost function. The two remaining models include provisions for balking (an arriving customer chooses not to join the queue) and reneging (customers leaving the queue without being served). For each of the models, there exists an optimal policy characterized by a pair of critical numbers (N, M): turn the server on whenever the number of customers equals (or exceeds) M and turn the server off whenever the number of customers is less than or equal to N. Algorithms for computing the optimal critical numbers are described. (Author).
Download or read book Optimal Design of Queueing Systems written by Shaler Stidham Jr. and published by Chapman and Hall/CRC. This book was released on 2009-03-27 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First Comprehensive Book on the Subject Focusing on the underlying structure of a system, Optimal Design of Queueing Systems explores how to set the parameters of a queueing system, such as arrival and service rates, before putting it into operation. It considers various objectives, comparing individually optimal (Nash equilibrium), socially optimal, class optimal, and facility optimal flow allocations. After an introduction to basic design models, the book covers the optimal arrival rate model for a single-facility, single-class queue as well as dynamic algorithms for finding individually or socially optimal arrival rates and prices. It then examines several special cases of multiclass queues, presents models in which the service rate is a decision variable, and extends models and techniques to multifacility queueing systems. Focusing on networks of queues, the final chapters emphasize the qualitative properties of optimal solutions. Written by a long-time, recognized researcher on models for the optimal design and control of queues and networks of queues, this book frames the issues in the general setting of a queueing system. It shows how design models can control flow to achieve a variety of objectives.
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.
Download or read book Journal of the Operations Research Society of Japan written by Nihon Operēshonzu Risāchi Gakkai and published by . This book was released on 1977 with total page 1292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control of a Queueing System with Variable Service Rates Uncertain Customer Satisfaction and Finite Waiting Room written by Frank C. Reed and published by . This book was released on 1974 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report considers optimal service policies for queueing systems in which customer satisfaction depends on the policy employed. The model has application to optimal defensive firing policies as the defense system becomes saturated. (Author).
Download or read book Robust Fluid Control of Multiclass Queueing Networks written by Hua Su (S.M.) and published by . This book was released on 2006 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis applies recent advances in the field of robust optimization to the optimal control of multiclass queueing networks. We develop models that take into account the uncertainty of interarrival and service time in multiclass queueing network problems without assuming a specific probability distribution, while remaining highly tractable and providing insight into the corresponding optimal control policy. Our approach also allows us to adjust the level of robustness of the solution to trade off performance and protection against uncertainty. We apply robust optimization to both open and closed queueing networks. For open queueing networks, we study control problems that involve sequencing, routing and input control decision, and optimize the total holding cost. For closed queueing networks, we focus on the sequencing problem and optimize the throughput. We compare the robust solutions to those derived by fluid control, dynamic programming and stochastic input control. We show that the robust control policy leads to better performance. Robust optimization emerges as a promising methodology to address a wide range of multiclass queueing networks subject to uncertainty, as it leads to representations of randomness that make few assumptions on the underlying probabilities. It also remains numerically tractable, and provides theoretical insights into the structure of the optimal control policy.
Download or read book Control of Entry to a Queueing System written by and published by . This book was released on 1979 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the control of entry of queueing systems. An M/M/1 model with a single class of customers and an infinite time horizon studied by Naor (1969) provides the starting point for this work. Each customer receives a fixed reward for service and pays a holding cost at a fixed rate per unit of time he spends in the system. Each customer may choose to join the system or not. A self-optimizing customer decides whether or not to join by acting to maximize his own expected net benefit. A social optimizing customer decides by acting to maximize the gain rate of the system, the sum of the expected net benefits per unit time of all arrivals. Socially optimal control of the model is provided by establishing a balking point for the customers that is no greater than the balking point a self-optimizing customer would determine. Naor's approach is compared with the semi-Markov decision process formulation of Yechiali (1971). The results for this first model are extended to show that the gain rate can only increase as the arrival rate of the customers increases while the social balking point can only decrease as the arrival rate increases. A semi-Markov approach is used to formulate an expanded model with several classes of customers, each with its own reward and holding cost rate. Socially optimal control of this model is shown to be provided by establishing a balking point for each class that is no greater than the balking point a member of the class would determine if he acted to maximize his own expected net benefit.
