Provides methods of analysing Markov chains based on Lyapunov functions.

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.

This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical understanding of phenomena describing systems in highly inhomogeneous and disordered media, including the KPZ universality class (describing the evolution of interfaces in two dimensions), random walks in random environment and percolative systems. PASI fosters a collaboration between North American and Latin American researchers and students. The conference that inspired this volume took place in January 2012 in both Santiago de Chile and Buenos Aires. Researchers and graduate students will find timely research in probability theory, statistical physics and related disciplines.

Matrix-analytic methods are fundamental to the analysis of a family of Markov processes rich in structure and of wide applicability. They are extensively used in the modelling and performance analysis of computer systems, telecommunication networks, network protocols and many other stochastic systems of current commercial and engineering interest.This volume deals with: (1) various aspects of the theory of block-structured Markov chains; (2) analysis of complex queueing models; and (3) parameter estimation and specific applications to such areas as cellular mobile systems, FS-ALOHA, the Internet and production systems.

The need to evaluate computer and communication systems performance and dependability is continuously growing as a consequence of both the increasing complexity of systems and the user requirements in terms of timing behaviour. The 10th International Conference on Modelling Techniques and Tools for C- puter Performance Evaluation, held in Palma in September 1998, was organised with the aim of creating a forum in which both theoreticians and practitioners could interchange recent techniques, tools, and experiences in these areas. This meeting follows the predecessor conferences of this series: 1984 Paris 1988 Palma 1994 Wien 1985 Sophia Antipolis 1991 Torino 1995 Heidelberg 1987 Paris 1992 Edinburgh 1997 Saint Malo The tradition of this conference series continued this year where many high quality papers were submitted. The Programme Committee had a di cult task in selecting the best papers. Many ne papers could not be included in the program due to space constraints. All accepted papers are included in this volume. Also, a set of submissions describing performance modelling tools was transformed into tool presentations and demonstrations. A brief description of these tools is included in this volume. The following table gives the overall statistics for the submissions.

This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

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.

This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.

This volume consists of a collection of invited articles, written by some of the most distinguished probabilists, most of whom have been personally responsible for advances in the various subfields of probability.