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

Recent trends in modeling of deteriorating inventory

http://www.di.unito.it/~horvath/firb2010/firb_2009_con_polimi/papers/survey.pdf

Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines

In this paper, JIT (Just-In-Time)-KANBAN literature survey was carried out and presented. The introductory section deals with the philosophy of JIT, and the concept involved in the push and pull system. The blocking mechanisms in the kanban system are also discussed elaborately. Besides these sections, the importance of measure of performance (MOP) and the application of the same with respect to JIT-KANBAN are presented. The recent trends in the JIT-KANBAN are discussed under the heading “Special cases”. In this review, 100 state-of-art research papers have been surveyed. The directions for the future works are also presented.

Literature review of JIT-KANBAN system

An analytic finite capacity queueing network model capturing the propagation of congestion and blocking

The MX/G/1 queueing system is studied under the following two situations: (1) At the end of a busy period, the server is turned off and inspects the length of the queue every time an arrival occurs. When the queue length reaches, or exceeds, a pre-specified value m for the first time, the server is turned on and serves the system until it is empty. (2) At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length is greater than, or equal to, a pre-specified value m at this time, he begins to serve the system until it is empty. For both cases, the mean waiting time of an arbitrary customer for a given value of m is derived, and the procedure to find the stationary optimal policy under a linear cost structure is presented.

Control policies for the M X /g/ 1 queueing system

We consider a production facility that produces items for which demand occurs according to a Poisson process. The facility is assumed to deteriorate while it is in operation, with an increasing fai...

Production-Inventory Systems with Preventive Maintenance

An arbitrary configuration of an open queueing network with exponential service times and finite buffers is analyzed. We offer an iterative procedure for approximating the marginal occupancy probabilities for each queue of the system. The method decomposes the queueing network into individual queues and analyzes each in isolation using information from only its nearest neighbors. Based upon the SIMP approximation previously used for tandem queues, it replaces each server's service time with a clearance time, which includes blocking, and each server's arrival rate by an equivalent acceptance rate. The procedure is easy to implement and requires modest memory and computer time. Extensive numerical experiments, performed for various topologies, yield accurate results compared with those obtained by exact or simulation methods.

Approximation analysis of open acyclic exponential queueing networks with blocking

Performance evaluation and design of a CONWIP system with inspections

We consider an open queueing network consisting of servers linked in an arbitrary configuration with exponential service times and separated by intermediate finite buffers. The model allows any number of saturated servers (never starved) and exit servers (never blocked). The considered blocking mechanism is blocking-after-service. In the case of simultaneous blocking, blocked customers enter the destination node on a first-blocked-first-enter basis. If feedback loops exist in the network, deadlocks may arise. We assume that a deadlock is detected and resolved instantaneously by transferring all the blocked customers simultaneously. In this paper, we present an approximation method to analyze this kind of networks. The method decomposes the original network into subsystems. Each subsystem is composed of one or many upstream servers and one downstream server, separated by a finite buffer. The upstream and downstream servers are characterized by exponential service time distributions. Based on the symmetrical approach [2], we develop an algorithm to determine the unknown parameters corresponding to each subsystem. The class of models considered in this paper includes the class of open loss models for feed-forward networks considered by Lee and Pollock [11]. For this class of models, we can show that the system of equations in our algorithm is equivalent to the one used in the algorithm proposed by Lee and Pollock. As a result, our algorithm provides the same results as the algorithm of Lee and Pollock for this class of models. However, it is observed that our algorithm takes less CPU execution time than the one proposed by Lee and Pollock. For the cases of networks with feedback loops, extensive numerical experiments show that the new algorithm, in general, converges very fast and yields accurate results compared with those obtained by simulation as long as deadlocks do not occur too frequently. Moreover, for the merge configuration, we provide the proof of the convergence of the algorithm as well as the existence and uniqueness of the solution by exploiting the properties associated with a symmetric approach.

Hyo-Seong Lee

Papers

Control policies for the M X /g/ 1 queueing system

Production-Inventory Systems with Preventive Maintenance

Approximation analysis of open acyclic exponential queueing networks with blocking

Performance evaluation and design of a CONWIP system with inspections

Performance evaluation of open queueing networks with arbitrary configuration and finite buffers