Mathematical Methods in The Theory of Queuing

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes.

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.

The present reprint contains all of the articles accepted and published in the Special Issue "Probability and Stochastic Processes with Applications to Communications, Systems and Networks" from the MDPI Mathematics journal. This Special Issue is devoted to probability, statistics, stochastic processes and their different applications in system and network analysis. The Special Issue includes works related to the analysis and applications of different queuing models, which begin with general approaches in modeling queuing systems and networks; an analysis of probabilistic and statistical methods in telecommunication; an asymptotic analysis of queuing networks in the condition of a large load; general complex networks and their structures, e.g., topology and graph theory; mathematical methods and models in smart cities; exclusive statistical methods, such as statistical estimates in bio/ecology, medicine and neural networks; and studies that estimate parameters in complex technical systems, etc. We hope that the scientific results collected in this reprint will help foster future research related to probability, stochastic processes and their applications.

The most recent methods in various branches of lattice path and enumerative combinatorics along with relevant applications are nicely grouped together and represented in this research contributed volume. Contributions to this edited volume will be mainly research articles however it will also include several captivating, expository articles (along with pictures) on the life and mathematical work of leading researchers in lattice path combinatorics and beyond. There will be four or five expository articles in memory of Shreeram Shankar Abhyankar and Philippe Flajolet and honoring George Andrews and Lajos Takács. There may be another brief article in memory of Professors Jagdish Narayan Srivastava and Joti Lal Jain.