Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

An overview of time-based and condition-based maintenance in industrial application

In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences for example, chi-squared, Hellinger, Kullback--Leibler. We show how uncertainty regions based on φ-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with φ-divergence uncertainty is tractable for most of the choices of φ typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.

This paper was accepted by Gerard P. Cachon, optimization.

/pdf/robust-solutions-of-optimization-problems-affected-by-1xadn6mpyh.pdf

Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

(1966). Mathematical Theory of Reliability. Journal of the Operational Research Society: Vol. 17, No. 2, pp. 213-215.

https://link.springer.com/content/pdf/10.1057%2Fjors.1966.43.pdf

Mathematical Theory of Reliability

Stock price prediction is an important topic in finance and economics which has spurred the interest of researchers over the years to develop better predictive models. The autoregressive integrated moving average (ARIMA) models have been explored in literature for time series prediction. This paper presents extensive process of building stock price predictive model using the ARIMA model. Published stock data obtained from New York Stock Exchange (NYSE) and Nigeria Stock Exchange (NSE) are used with stock price predictive model developed. Results obtained revealed that the ARIMA model has a strong potential for short-term prediction and can compete favourably with existing techniques for stock price prediction.

/pdf/stock-price-prediction-using-the-arima-model-31m1gr6vfe.pdf

Stock Price Prediction Using the ARIMA Model

We consider a production system in a general configuration with a new control strategy: the push policy for the part sending and the kanban mechanism for the work-in-process (WIP). The production system is composed of many stations (or workshops) such as an entry station, a set of workstations, a central station, and an exit station. This type of system is modeled as an open queueing network (OQN) in a general configuration with a Markov-type part sending policy and a machine no blocking (MNB) mechanism. The most important performance measures of the production system are the total throughput of the workstations and the total blocking flow of blocked parts sent from the workstations to the central station. This paper discusses an optimization problem with multiple objectives: allocate kanbans to the workstations so as to simultaneously maximize the total throughput and minimize the total blocking flow. Based on a semi-open decomposition approach, several useful properties of the system are characterized. These properties are used to develop a marginal algorithm for the optimization problem. Moreover, a dynamic simulation approach is devised as a tool for evaluating the quality of the solutions obtained by the algorithm. Numerical experiments are provided to demonstrate the efficiency of the algorithm through the simulation approach.

Allocating kanbans for a production system in a general configuration with a new control strategy

Motivated by some real stochastic service systems, we study a feedback retrial queue with customer balking and unreliable servers (servers subject to breakdowns). A customer will either join a retr...

On retrial queue with customer balking and feedback subject to server breakdowns

This paper presents modified preventive maintenance policies for an operating system that works at random processing times and is imperfectly maintained. The system may suffer from one of the two types of failures based on a time-dependent imperfect maintenance mechanism: type-Ⅰ (minor) failure, which can be rectified by minimal repair, and type-Ⅱ (catastrophic) failure, which can be removed by corrective maintenance. When the system needs to be maintained, two policies "preventive maintenance-first (PMF) and preventive maintenance-last (PML)" may be applied. In each maintenance interval, before any type-Ⅱ failure occurs, the system is maintained at a planned time \begin{document}$ T $\end{document} or at the completion of a working time, whichever occurs first and last, which are called PMF and PML, respectively. After any maintenance activity, the system improves but its failure characteristic is also altered. At the \begin{document}$ N $\end{document} -th maintenance, the system is replaced rather than maintained. For each policy, the optimal preventive maintenance schedule ( \begin{document}$ T $\end{document} , \begin{document}$ N $\end{document} ) \begin{document}$ ^{*} $\end{document} that minimizes the mean cost rate function is derived analytically and determined numerically in terms of its existence and uniqueness. The proposed models provide a general framework for analyzing the maintenance policies in reliability theory.

https://www.aimsciences.org/article/exportPdf?id=21fce79c-db61-4a13-942a-e06829fcd7d5

Optimal preventive "maintenance-first or -last" policies with generalized imperfect maintenance models

This paper presents a review of methodologies for analyzing stochastic manufacturing and service systems. On the basis of the scale and level of details of operations, we can study stochastic systems using micro-, meso-, and macro-scopic models. Such a classification unifies stochastic modeling theory. For each model type, we highlight the advantages and disadvantages and the applicable situations. Micro-scopic models are based on quasi-birth-and-death process because of the phase-type distributed service times and/or Markov arrival processes. Such models are appropriate for modeling the detailed operations of a manufacturing system with relatively small number of servers (production facilities). By contrast, meso-scopic and macro-scopic models are based on the functional central limit theorem (FCLT) and functional strong law of large numbers (FSLLN), respectively, under heavy-traffic regimes. These high-level models are appropriate for modeling large-scale service systems with many servers, such as call centers or large service networks. This review will help practitioners select the appropriate level of modeling to enhance their understanding of the dynamic behavior of manufacturing or service systems. Enhanced understanding will ensure that optimal policies can be designed to improve system performance. Researchers in operation analytics and optimization of manufacturing and logistics also benefit from such a review.

/pdf/hierarchical-modeling-of-stochastic-manufacturing-and-5lhye9e1ex.pdf

Hierarchical modeling of stochastic manufacturing and service systems

This paper addresses an important question of how to achieve an appropriate and nearly uniform work-load for an under-utilized staff in a waiting line situation by scheduling an appropriate amount of supplementary work during the idle time. We present an M/G/1 queue with a special server's vacation policy to model this situation. In this system, after serving all arriving customers, the server can perform a random maximum number H of possible supplementary jobs before staying idle. The distribution of H can be determined by a supplementary job assignment policy to reduce the idle time proportion. Major performance measures are obtained to evaluate this class of policies. Numerical examples are presented to illustrate the application of this study.

http://orstw.org.tw/IJOR/vol3no1/paper-7-IJOR-vol3_1_-Zhang.pdf

Zhe George Zhang

Papers

Allocating kanbans for a production system in a general configuration with a new control strategy

On retrial queue with customer balking and feedback subject to server breakdowns

Optimal preventive "maintenance-first or -last" policies with generalized imperfect maintenance models

Hierarchical modeling of stochastic manufacturing and service systems

Adjusting the Workload of an Under-utilized Server by Scheduling Supplementary Work