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

Flow production lines with finite buffer capacities are used in practice for mass production, e.g., in the automotive and food industries. The decision regarding the allocation of buffer capacities...

The buffer allocation problem in production lines: Formulations, solution methods, and instances

M/M/s queue with impatient customers and retrials

We study multi-class retrial queueing systems with Poisson inputs, general service times, and an arbitrary numbers of servers and waiting places. A class-i blocked customer joins orbit i and waits in the orbit for retrial. Orbit i works like a single-server $$\cdot /M/1$$·/M/1 queueing system with exponential retrial time regardless of the orbit size. Such retrial systems are referred to as retrial systems with constant retrial rate. Our model is not only motivated by several telecommunication applications, such as wireless multi-access systems, optical networks, and transmission control protocols, but also represents independent theoretical interest. Using a regenerative approach, we provide sufficient stability conditions which have a clear probabilistic interpretation. We show that the provided sufficient conditions are in fact also necessary, in the case of a single-server system without waiting space and in the case of symmetric classes. We also discuss a very interesting case, when one orbit is unstable, whereas the rest of the system is stable.

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Sufficient stability conditions for multi-class constant retrial rate systems

This research develops an expert system to addresses a novel problem in the literature of buffer allocation and production lines. We investigate real-world unreliable unbalanced production lines where all time-based parameters are probabilistic including time between parts arrivals, processing times, time between failures, repairing times, and setup times. The main contributions of the paper are a twofold. First and foremost, the mean processing times of workstations and buffer capacities, unlike the existing literature, are considered as decision variables in a multi-objective optimization problem which maximizes the throughput rate and minimizes the total buffer capacities as well as the total cost of the mean process time reductions. Secondly, an efficient methodology is developed that can precisely reflect a real-world system without any unrealistic and/or restrictive assumptions on the probabilistic nature of the system, which are commonly assumed in the existing literature. One of the greatest challenges in this research is to estimate the throughput rate function since it highly depends on the random behavior of the system. Thus, a simulation optimization approach is developed based on the Design of Experiments and Response Surface Methodology to fit a regression model for throughput rate. Finally, Non-dominated Sorting Genetic Algorithm (NSGA-II) and Non-dominated Ranked Genetic Algorithm (NRGA) are used to generate high-quality solutions for the aforementioned problem. This methodology is run on a real numerical case. The experimental results confirm the advantages of the proposed methodology. This methodology is an innovative expert system with a knowledge-base developed through this simulation optimization approach. This expert system can be applied to complex production line problems in large or small scale with different types of decision variables and objective functions. The application of this expert system is transformative to other manufacturing systems.

An efficient simulation optimization methodology to solve a multi-objective problem in unreliable unbalanced production lines

Approximation of M/M/c retrial queue with PH-retrial times

Approximation of throughput in tandem queues with multiple servers and blocking

We consider the M/M/c retrial queues with multiclass of customers. We show that the stationary joint distribution for the number of customers in service facility and orbit converges to those of the ordinary M/M/c with discriminatory random order service (DROS) policy as retrial rate tends to infinity. Approximation formulae for the distributions of the number of customers in service facility, the mean number of customers in orbit and the sojourn time distribution of a customer are presented. The approximations are compared with exact and simulation results.

M/M/c Retrial Queue with Multiclass of Customers

Manufacturing system design is a complex challenge when a new factory is being built. Although some factories produce the same product, the layouts of the factories may be different. Manufacturing systems for automotive engines can be modelled with several types of queueing networks with finite buffers and unreliable machines. In this paper, three types of layout structures which are commonly used in automotive engine shops are compared with respect to maximizing profit that is determined by throughput and the investment cost of buffers. We assume that the service times are constant but inhomogeneous, and the time to failure and the time to repair are exponentially distributed. To solve this problem we used approximation methods which are based on aggregation and overlapping decomposition for computing performance measures, and a gradient search method for finding an optimal buffer allocation.

Comparison of three flow line layouts with unreliable machines and profit maximization

We consider the PH/PH/c retrial queues with PH-retrial time. Approximation formulae for the distribution of the number of customers in service facility, sojourn time distribution and the mean number of customers in orbit are presented. We provide an approximation for GI/G/c retrial queue with general retrial time by approximating the general distribution with phase type distribution. Some numerical results are presented.

Yang Woo Shin

Papers

Approximation of M/M/c retrial queue with PH-retrial times

Approximation of throughput in tandem queues with multiple servers and blocking

M/M/c Retrial Queue with Multiclass of Customers

Comparison of three flow line layouts with unreliable machines and profit maximization

APPROXIMATION OF PH/PH/c RETRIAL QUEUE WITH PH-RETRIAL TIME