Dynamic Scheduling of a Multi-class Queue I: Problem Formulation and Descriptive Results PDF Download
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Author: Stanford University. Department of Operations Research Publisher: ISBN: Category : Languages : en Pages : 30
Book Description
The author considers an M/G/1 queue with several customer classes. It is not required that the queue be stable or even that the mean service time be finite for any class. The economic framework is linear, featuring a holding cost per unit time and fixed service reward for each class. Future costs and rewards are continuously discounted using a positive interest rate. The problem is to decide, at the completion of each service and given the state of the system, which class to admit next. The objective is to maximize expected net present value over an infinite planning horizon. The problem is formulated as a Markov renewal decision process. One very special type of scheduling rule, called a static policy, simply enforces a specified priority ranking. The return function under a static policy is explicity presented. In a subsequent paper it will be shown that there exists a static optimal policy. (Author).
Author: Stanford University. Department of Operations Research Publisher: ISBN: Category : Languages : en Pages : 30
Book Description
The author considers an M/G/1 queue with several customer classes. It is not required that the queue be stable or even that the mean service time be finite for any class. The economic framework is linear, featuring a holding cost per unit time and fixed service reward for each class. Future costs and rewards are continuously discounted using a positive interest rate. The problem is to decide, at the completion of each service and given the state of the system, which class to admit next. The objective is to maximize expected net present value over an infinite planning horizon. The problem is formulated as a Markov renewal decision process. One very special type of scheduling rule, called a static policy, simply enforces a specified priority ranking. The return function under a static policy is explicity presented. In a subsequent paper it will be shown that there exists a static optimal policy. (Author).
Author: Stanford University. Department of Operations Research Publisher: ISBN: Category : Languages : en Pages : 34
Book Description
The author continues the study of the dynamic scheduling problem introduced and formulated in the paper's predecessor. The positive interest rate is considered fixed throughout. It is shown that there exists a static optimal policy, and the corresponding optimal priority ranking is exhibited. Broadening the formulation to allow inserted idel time, it is shown that the previous optimal policy need be changed only be refusing to serve (under any circumstances) a certain number of the lowest priority classes. (Author).
Author: Lawrence M. Wein Publisher: Forgotten Books ISBN: 9780666231024 Category : Business & Economics Languages : en Pages : 48
Book Description
Excerpt from Dynamic Scheduling of a Multiclass Make-to-Stock Queue The goal of this paper is to investigate the scheduling problem faced by a single machine, make-to - stock production facility in a dynamic stochastic environment. This facility is pictured in Figure 1, where it is assumed that there is an ample amount of raw material inventory of product k, for k 1, K. The scheduler decides when to release a raw product k job onto the shop floor, at which time the job becomes a unit of product k work-in-process (wip) inventory. These decisions will be referred to as release decisions. There is a single machine that transforms units of product k wip inventory into units of product k finished goods inventory. The machine is modeled as a multiclass queue, in that the machine may work on only one unit at a time, and each product has its own general processing time distribution. Demand for each product can be any arbitrary point process that satisfies a functional central limit theorem (for example, a compound Poisson process). About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Leonard Kleinrock Publisher: Wiley-Interscience ISBN: Category : Mathematics Languages : en Pages : 584
Book Description
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.
Author: J. Michael Harrison Publisher: ISBN: Category : Languages : en Pages : 33
Book Description
The author considers a single server queueing system with several classes of customers who arrive according to independent Poisson processes. The service time distributions are arbitrary, and a linear cost structure is assumed. The problem is to decide, at the completion of each service and given the state of system, which class (if any) to admit next into service. The objective is to maximize the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon, the interest rate being positive. One very special type of scheduling rule, called a modified static policy, simply enforces a (non-preemptive) priority ranking except that certain classes are never served. It is shown that there is a modified static policy which is optimal, and a simple algorithm for its computation is presented. (Modified author abstract).
Author: J. Michael Harrison Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
The author considers a single server queueing system with two classes of customers who arrive according to independent Poisson processes. The two service time distributions are arbitrary, and a linear holding cost and fixed service reward for each class is considered. The problem is to decide, at the completion of each service and given the state of the system, which class (if any) to admit next into service. (Modified author abstract).
Author: Stanford University. Department of Operations Research
Author: Stanford University. Department of Operations Research
Author: Stanford University. Department of Operations Research
Author: Tesuji Hirayama
Author: Lawrence M. Wein
Author: Leonard Kleinrock
Author: J. Michael Harrison
Author: United States. Defense Logistics Studies Information Exchange
Author: J. Michael Harrison
Author: Lawrence M. Wein
Author: J. Michael Harrison