A general theory on spectral properties of state-homogeneous finite-state quasi-birth-death process

Cataloged from PDF version of article.In this paper a spectral theory pertaining to Quasi-Birth±Death Processes (QBDs) is presented. The QBD, which is a generalization of the birth±death process, is a powerful tool that can be utilized in modeling many stochastic phenomena. Our theory is based on the application of a matrix polynomial method to obtain the steady-state probabilities in state-homogeneous ®nite-state QBDs. The method is based on ®nding the eigenvalue±eigenvector pairs that solve a matrix polynomial equation. Since the computational e ort in the solution procedure is independent of the cardinality of the counting set, it has an immediate advantage over other solution procedures. We present and prove di erent properties relating the quantities that arise in the solution procedure. By also compiling and formalizing the previously known properties, we present a formal uni®ed theory on the spectral properties of QBDs, which furnishes a formal framework to embody much of the previous work. This framework carries the prospect of furthering our understanding of the behavior the modeled systems manifest. Ó 2001 Elsevier Science B.V. All rights reserved

Models of production lines as quasi-birth-death processes

The aim of this work is to illustrate the suitability of quasi-birth-death processes (QBDs) for stochastic modelling of production lines. With this end in mind, first, an introduction to QBDs is made, so that the reader who may not be acquainted with this aspect of stochastic modelling may be introduced to the basics of the topic. Then, a formal definition of QBD is given and the QBDs are contrasted with the traditional birth-death processes. Later, examples of QBD models pertaining to production lines are presented. The rational of this exposition is to show how QBDs present themselves within the context of production lines and to show the kind of work that needs to be performed to fully specify the corresponding QBD. By compiling the aforementioned models, the strength of QBDs in modelling production lines is demonstrated. © 2002 Elsevier Science Ltd. All rights reserved

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277

On the validity of aggregation in the study of unreliable continuous transfer lines

Contains fulltext : 45277.pdf (publisher's version ) (Open Access)Flow line production systems consist of a number of stages (arranged in series) at which operations are performed on a work-piece. Operations at the stages are performed by machines or by equipment that are either perfectly reliable or subject to failure. While obtaining analytical results for the performance of a system with many machines, subject to failure, is considered to be an impossible task, also the approximate models are to be questioned. Approximate models are of two types: aggregation models or decomposition models. Assumptions have to be investigated on validity. By examining the up times and down times of the aggregated distribution by means of a discrete-event simulation model, the authors find that down times of aggregated machines in many situations do not follow an exponential distribution. An alternative distribution with the required characteristics is proposed and directions are given how to calculate its parameters.11 p