The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

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

Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods. † Correspondence: Chung-Ming Kuan, Institute of Economics, Academia Sinica, 128 Academia Road, Sec. 2, Taipei 115, Taiwan; ckuan@econ.sinica.edu.tw. †† I would like to express my sincere gratitude to the editor, Professor Steven Durlauf, for his patience and constructive comments on early drafts of this entry. I also thank Shih-Hsun Hsu and Yu-Lieh Huang for very helpful suggestions. The remaining errors are all mine.

Artificial neural networks

Technical foundations introduction software reliability and system reliability the operational profile software reliability modelling survey model evaluation and recalibration techniques practices and experiences best current practice of SRE software reliability measurement experience measurement-based analysis of software reliability software fault and failure classification techniques trend analysis in validation and maintenance software reliability and field data analysis software reliability process assessment emerging techniques software reliability prediction metrics software reliability and testing fault-tolerant SRE software reliability using fault trees software reliability process simulation neural networks and software reliability. Appendices: software reliability tools software failure data set repository.

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Handbook of software reliability engineering

We review the progress achieved during the recent five years in immunochemical biosensors (immunosensors) combined with nanoparticles for enhanced sensitivity. The initial part introduces antibodies as classic recognition elements. The optical sensing part describes fluorescent, luminescent, and surface plasmon resonance systems. Amperometry, voltammetry, and impedance spectroscopy represent electrochemical transducer methods; electrochemiluminescence with photoelectric conversion constitutes a widely utilized combined method. The transducing options function together with suitable nanoparticles: metallic and metal oxides, including magnetic ones, carbon-based nanotubes, graphene variants, luminescent carbon dots, nanocrystals as quantum dots, and photon up-converting particles. These sources merged together provide extreme variability of existing nanoimmunosensing options. Finally, applications in clinical analysis (markers, tumor cells, and pharmaceuticals) and in the detection of pathogenic microorganisms, toxic agents, and pesticides in the environmental field and food products are summarized.

Nanoparticle-Based Immunochemical Biosensors and Assays: Recent Advances and Challenges

A game theory approach in seller–buyer supply chain

Seller–buyer models of supply chain management with an asymmetric information structure

Spatial and temporal modelling of tourist movements using Semi-Markov processes

Modelling spatio-temporal movement of tourists using finite Markov chains

Little work has been done on extending existing models with imperfect debugging to the more realistic situation where new faults are generated from unsuccessful attempts at removing faults completely. This paper presents a software-reliability growth model which incorporates the possibility of introducing new faults into a software system due to the imperfect debugging of the original faults in the system. The original faults manifest themselves as primary failures and are assumed to be distributed as a nonhomogeneous Poisson process (NHPP). Imperfect debugging of each primary failure induces a secondary failure which is assumed to occur in a delayed sense from the occurrence time of the primary failure. The mean total number of failures, comprising the primary and secondary failures, is obtained. The authors also develop a cost model and consider some optimal release-policies based on the model. Parameters are estimated using maximum likelihood and a numerical example is presented. >

Panlop Zeephongsekul

Papers

A game theory approach in seller–buyer supply chain

Seller–buyer models of supply chain management with an asymmetric information structure

Spatial and temporal modelling of tourist movements using Semi-Markov processes

Modelling spatio-temporal movement of tourists using finite Markov chains

Software-reliability growth model: primary-failures generate secondary-faults under imperfect debugging