Analytic Methods In Applied Probability

This volume is dedicated to F. I. Karpelevich, an outstanding Russian mathematician who made important contributions to applied probability theory. The book contains original papers focusing on several areas of applied probability and its uses in modern industrial processes, telecommunications, computing, mathematical economics, and finance. It opens with a review of Karpelevich's contributions to applied probability theory and includes a bibliography of his works. Other articles discuss queueing network theory, in particular, in heavy traffic approximation (fluid models). The book is suitable for graduate students, theoretical and applied probabilists, computer scientists, and engineers.

Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.

Matrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. In the current literature, a mixed bag of techniques is used-some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of the matrix analytic approach are included.

Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions. New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book.

This book constitutes the refereed proceedings of the First International Conference on Analytical and Computational Methods in Probability Theory and its Applications, ACMPT 2017, held in Moscow, Russia, in October 2017. The 42 full papers presented were carefully reviewed and selected from 173 submissions. The conference program consisted of four main themes associated with significant contributions made by A.D.Soloviev. These are: Analytical methods in probability theory, Computational methods in probability theory, Asymptotical methods in probability theory, the history of mathematics.