This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of understanding the phenomenon of statistical multiplexing. The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the important ideas of Palm distributions associated with traffic models and their role in performance measures. Also presented are recent ideas of large buffer, and many sources asymptotics that play an important role in understanding statistical multiplexing. In particular, the important concept of effective bandwidths as mappings from queueing level phenomena to loss network models is clearly presented along with a detailed presentation of loss network models and accurate approximations for large networks. Table of Contents: Introduction to Traffic Models and Analysis / Queues and Performance Analysis / Loss Models for Networks / Statistical Multiplexing

This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of introducing an appropriate mathematical framework for modeling and analysis as well as understanding the phenomenon of statistical multiplexing. The models, techniques, and results presented form the core of traffic engineering methods used to design, control and allocate resources in communication networks.The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the important ideas of Palm distributions associated with traffic models and their role in computing performance measures. The monograph also covers stochastic network theory including Markovian networks. Recent results on network utility optimization and connections to stochastic insensitivity are discussed. Also presented are ideas of large buffer, and many sources asymptotics that play an important role in understanding statistical multiplexing. In particular, the important concept of effective bandwidths as mappings from queueing level phenomena to loss network models is clearly presented along with a detailed discussion of accurate approximations for large networks.

This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of introducing an appropriate mathematical framework for modeling and analysis as well as understanding the phenomenon of statistical multiplexing. The models, techniques, and results presented form the core of traffic engineering methods used to design, control and allocate resources in communication networks.The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the important ideas of Palm distributions associated with traffic models and their role in computing performance measures. The monograph also covers stochastic network theory including Markovian networks. Recent results on network utility optimization and connections to stochastic insensitivity are discussed. Also presented are ideas of large buffer, and many sources asymptotics that play an important role in understanding statistical multiplexing. In particular, the important concept of effective bandwidths as mappings from queueing level phenomena to loss network models is clearly presented along with a detailed discussion of accurate approximations for large networks. Table of Contents: Introduction to Traffic Models and Analysis / Queues and Performance Analysis / Loss Models for Networks / Stochastic Networks and Insensitivity / Statistical Multiplexing

This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMC) and continuous time Markov chain (CTMC). We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probability technique, and the uniformization. We try to minimize the theoretical aspects of the Markov chain so that the book is easily accessible to readers without deep mathematical backgrounds. We then introduce how to develop a Markov chain model with simple applications: a forwarding system, a cellular system blocking, slotted ALOHA, Wi-Fi model, and multichannel based LAN model. The examples cover CTMC, DTMC, birth-death process and non birth-death process. We then introduce more difficult examples in Chapter 4, which are related to wireless LAN networks: the Bianchi model and Multi-Channel MAC model with fixed duration. These models are more advanced than those introduced in Chapter 3 because they require more advanced concepts such as renewal-reward theorem and the queueing network model. We introduce these concepts in the appendix as needed so that readers can follow them without difficulty. We hope that this textbook will be helpful to students, researchers, and network practitioners who want to understand and use mathematical modeling techniques. Table of Contents: Performance Modeling / Markov Chain Modeling / Developing Markov Chain Performance Models / Advanced Markov Chain Models

Networks naturally appear in many high-impact domains, ranging from social network analysis to disease dissemination studies to infrastructure system design. Within network studies, network connectivity plays an important role in a myriad of applications. The diversity of application areas has spurred numerous connectivity measures, each designed for some specific tasks. Depending on the complexity of connectivity measures, the computational cost of calculating the connectivity score can vary significantly. Moreover, the complexity of the connectivity would predominantly affect the hardness of connectivity optimization, which is a fundamental problem for network connectivity studies. This book presents a thorough study in network connectivity, including its concepts, computation, and optimization. Specifically, a unified connectivity measure model will be introduced to unveil the commonality among existing connectivity measures. For the connectivity computation aspect, the authors introduce the connectivity tracking problems and present several effective connectivity inference frameworks under different network settings. Taking the connectivity optimization perspective, the book analyzes the problem theoretically and introduces an approximation framework to effectively optimize the network connectivity.Lastly, the book discusses the new research frontiers and directions to explore for network connectivity studies. This book is an accessible introduction to the study of connectivity in complex networks. It is essential reading for advanced undergraduates, Ph.D. students, as well as researchers and practitioners who are interested in graph mining, data mining, and machine learning.

The last decade has seen an unprecedented growth in the demand for wireless services. These services are fueled by applications that often require not only high data rates, but also very low latency to function as desired. However, as wireless networks grow and support increasingly large numbers of users, these control algorithms must also incur only low complexity in order to be implemented in practice. Therefore, there is a pressing need to develop wireless control algorithms that can achieve both high throughput and low delay, but with low-complexity operations. While these three performance metrics, i.e., throughput, delay, and complexity, are widely acknowledged as being among the most important for modern wireless networks, existing approaches often have had to sacrifice a subset of them in order to optimize the others, leading to wireless resource allocation algorithms that either suffer poor performance or are difficult to implement. In contrast, the recent results presented in this book demonstrate that, by cleverly taking advantage of multiple physical or virtual channels, one can develop new low-complexity algorithms that attain both provably high throughput and provably low delay. The book covers both the intra-cell and network-wide settings. In each case, after the pitfalls of existing approaches are examined, new systematic methodologies are provided to develop algorithms that perform provably well in all three dimensions.

This book provides a quick reference and insights into modeling and optimization of software-defined networks (SDNs). It covers various algorithms and approaches that have been developed for optimizations related to the control plane, the considerable research related to data plane optimization, and topics that have significant potential for research and advances to the state-of-the-art in SDN. Over the past ten years, network programmability has transitioned from research concepts to more mainstream technology through the advent of technologies amenable to programmability such as service chaining, virtual network functions, and programmability of the data plane. However, the rapid development in SDN technologies has been the key driver behind its evolution. The logically centralized abstraction of network states enabled by SDN facilitates programmability and use of sophisticated optimization and control algorithms for enhancing network performance, policy management, and security.Furthermore, the centralized aggregation of network telemetry facilitates use of data-driven machine learning-based methods. To fully unleash the power of this new SDN paradigm, though, various architectural design, deployment, and operations questions need to be addressed. Associated with these are various modeling, resource allocation, and optimization opportunities.The book covers these opportunities and associated challenges, which represent a ``call to arms'' for the SDN community to develop new modeling and optimization methods that will complement or improve on the current norms.