By deploying time series analysis, Fourier transform, functional analysis, min-plus convolution, and fractional order systems and noise, this book proposes fractal traffic modeling and computations of delay bounds, aiming to improve the quality of service in computer communication networks. As opposed to traditional studies of teletraffic delay bounds, the author proposes a novel fractional noise, the generalized fractional Gaussian noise (gfGn) approach, and introduces a new fractional noise, generalized Cauchy (GC) process for traffic modeling. Researchers and graduates in computer science, applied statistics, and applied mathematics will find this book beneficial. Ming Li, PhD, is a professor at Ocean College, Zhejiang University, and the East China Normal University. He has been an active contributor for many years to the fields of computer communications, applied mathematics and statistics, particularly network traffic modeling, fractal time series, and fractional oscillations. He has authored more than 200 articles and 5 monographs on the subjects. He was identified as the Most Cited Chinese Researcher by Elsevier in 2014–2020. Professor Li was recognized as a top 100,000 scholar in all fields in 2019–2020 and a top 2% scholar in the field of Numerical and Computational Mathematics in 2021 by Prof. John P. A. Ioannidis, Stanford University.

"By deploying time series analysis, Fourier transformation, functional analysis, min-plus convolution, and fractional order systems and noise, this book proposes fractal traffic modeling and computations of delay bounds, aiming to improve the quality of service in computer communication networks. As opposed to traditional studies of teletraffic delay bounds, the author proposes a novel fractional noise, generalized fractional Gaussian noise (gfGn) approach, and introduces a new fractional noise, generalized Cauchy (GC) process for traffic modeling. Researchers and graduates in computer science, applied statistics, and applied mathematics will find the book beneficial"--

This book provides a comprehensive theory of mono- and multi-fractal traffic, including the basics of long-range dependent time series and 1/f noise, ergodicity and predictability of traffic, traffic modeling and simulation, stationarity tests of traffic, traffic measurement and the anomaly detection of traffic in communications networks. Proving that mono-fractal LRD time series is ergodic, the book exhibits that LRD traffic is stationary. The author shows that the stationarity of multi-fractal traffic relies on observation time scales, and proposes multi-fractional generalized Cauchy processes and modified multi-fractional Gaussian noise. The book also establishes a set of guidelines for determining the record length of traffic in measurement. Moreover, it presents an approach of traffic simulation, as well as the anomaly detection of traffic under distributed-denial-of service attacks. Scholars and graduates studying network traffic in computer science will find the book beneficial.

Introduces a new convolution representation of a fractional derivative and the classification of fractional vibrations Proposes equivalent motion equations of six classes of fractional vibrators Establishes a mathematical explanation of the Rayleigh damping assumption Sets up a method for the record length requirement of ocean surface waves Proposes an optimal controller of irregular wave maker

A collection of work from top researchers in the field, this book covers all aspects of self-similar network traffic. Readers will gain a better understanding of these networks through a broad introduction to the topic, as well as suggestions for future research.

Orthogonal Frequency Division Multiplexing (OFDM) has been the waveform of choice for most wireless communications systems in the past 25 years. This book addresses the "what comes next? question by presenting the recently proposed waveform known as Orthogonal Time-Frequency-Space (OTFS), which offers a better alternative for high-mobility environments. The OTFS waveform is based on the idea that the mobile wireless channels can be effectively modelled in the delay-Doppler domain. This domain provides a sparse representation closely resembling the physical geometry of the wireless channel. The key physical parameters such as relative velocity and distance of the reflectors with respect to the receiver can be considered roughly invariant in the duration of a frame up to a few milliseconds. This enables the information symbols encoded in the delay-Doppler domain to experience a flat fading channel even when they are affected by multiple Doppler shifts present in high-mobility environments. Delay-Doppler Communications: Principles and Applications covers the fundamental concepts and the underlying principles of delay-Doppler communications. Readers familiar with OFDM will be able to quickly understand the key differences in delay-Doppler domain waveforms that can overcome some of the challenges of high-mobility communications. For the broader readership with a basic knowledge of wireless communications principles, the book provides sufficient background to be self-contained. The book provides a general overview of future research directions and discusses a range of applications of delay-Doppler domain signal processing. - This is the first book on delay-Doppler communications - It is written by three of the leading authorities in the field - It includes a wide range of applications With this book, the reader will be able to: - Recognize the challenges of high-mobility channels affected by both multipath and multiple Doppler shifts in physical layer waveform design and performance - Understand the limitations of current multicarrier techniques such as OFDM in high-mobility channels - Recognize the mathematical and physical relations between the different domains for representing channels and waveforms: time-frequency, time-delay, delay-Doppler - Understand the operation of the key blocks of a delay-Doppler modulator and demodulator both analytically and by hands-on MATLAB examples - Master the special features and advantages of OTFS with regard to detection, channel estimation, MIMO, and multiuser MIMO - Realize the importance of delay-Doppler communications for current and future applications, e.g., 6G and beyond