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

In many practical multiserver queueing systems, servers not only serve randomly arriving customers but also work on the secondary jobs with infinite backlog during their idle time In this paper, we propose a c-server model with a two-threshold policy, denoted by (e d), to evaluate the performance of this class of systems With such a policy, when the number of idle servers has reached d (<c), then e (<d) idle agents will process secondary jobs These e servers keep working on the secondary jobs until they find waiting customers exist in the system at a secondary job completion instant Using the matrix analytic method, we obtain the stationary performance measures for evaluating different (e, d) policies © 2006 Wiley Periodicals, Inc Naval Research Logistics, 2007

Quantifying the performance effects of idle time utilization in multiserver systems

A queueing model of the Markov-modulated Poisson process (MMPP) with thresholds was investigated. The customer arrival with various arrival rates in the model was viewed as the MMPP. In contrast to the Poisson’s arrival process, the MMPP can better describe the situation that the arrival rate changes with changing conditions; therefore, the model fits better with reality. The threshold conversion was added to the model based on the general MMPP/M/C model. When the number of customers in the system exceeds a threshold, all servers work to serve; when the number of customers in the system is less than another threshold, some servers are shut down. This is the congestion-based staffing policy with two thresholds. Specifically, the problems in the slab stocking stage of slab production at the Iron and Steel Complex in China were analysed. In the slab production process, because the rate of the upstream steelmaking is not constant, the rate of slab reaching the slab yard is uncertain. The crane service is used to store slabs in a warehouse. Because the slab arrival rate varies, different numbers of cranes in service need to be optimized for cost control. Thus, MMPP was used to describe slab arrival with varied arrival rates. Therefore, an MMPP/M/C queue with thresholds was used to analyse and solve the practical problems, and the optimal number of service cranes was obtained to minimize the cost of slab stocking.

Zhe George Zhang

Papers

Quantifying the performance effects of idle time utilization in multiserver systems

MMPP/M/C queue with congestion-based staffing policy and applications in operations of steel industry

Designing a Sustainable Two-Tier Service System with Customer’s Asymmetric Preference for Servers

Simulation optimization in security screening systems subject to budget and waiting time constraints

A note on workload control for an under-utilized server of M/G/1 system