We consider the performance modeling and evaluation of network systems powered with renewable energy sources such as solar and wind energy. Such energy sources largely depend on environmental conditions, which are hard to predict accurately. As such, it may only make sense to require the network systems to support a soft quality of service (QoS) guarantee, i.e., to guarantee a service requirement with a certain high probability. In this paper, we intend to build a solid mathematical foundation to help better understand the stochastic energy constraint and the inherent correlation between QoS and the uncertain energy supply. We utilize a calculus approach to model the cumulative amount of charged energy and the cumulative amount of consumed energy. We derive upper and lower bounds on the remaining energy level based on a stochastic energy charging rate and a stochastic energy discharging rate. By building the bridge between energy consumption and task execution (i.e., service), we study the QoS guarantee under the constraint of uncertain energy sources. We further show how performance bounds can be improved if some strong assumptions can be made.
We develop our analytical framework based on stochastic network calculus @cite_14 @cite_22 @cite_6 @cite_7 . Unlike deterministic network calculus @cite_19 @cite_3 , which searches for the worst-case performance bounds, stochastic network calculus tries to derive performance bounds, but with a small probability that the bounds may not hold true. Since most renewable energy sources, such as solar and wind energy, are not deterministic, stochastic network calculus is a good fit for the performance evaluation of systems using renewable energy. Nevertheless, traditional stochastic network calculus was not originally targeted at modeling such systems. Substantial work is thus required to extend this useful theory.
@cite_14 @cite_22 @cite_7 @cite_6 @cite_3 @cite_19
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Network calculus is a min-plus system theory for performance evaluation of queuing networks. Its elegance steins from intuitive convolution formulas for concatenation of deterministic servers. Recent research dispenses with the worst-case assumptions of network calculus to develop a probabilistic equivalent that benefits from statistical multiplexing. Significant achievements have been made, owing for example to the theory of effective bandwidths; however, the outstanding scalability set up by concatenation of deterministic servers has not been shown. This paper establishes a concise, probabilistic network calculus with moment generating functions. The presented work features closed-form, end-to-end, probabilistic performance bounds that achieve the objective of scaling linearly in the number of servers in series. The consistent application of moment generating functions put forth in this paper utilizes independence beyond the scope of current statistical multiplexing of flows. A relevant additional gain is demonstrated for tandem servers with independent cross-traffic Network calculus, a theory dealing with queuing systems found in computer networks, focuses on performance guarantees. The development of an information theory for stochastic service-guarantee analysis has been identified as a grand challenge for future networking research. Towards that end, stochastic network calculus, the probabilistic version or generalization of the (deterministic) Network Calculus, has been recognized by researchers as a crucial step. Stochastic Network Calculus presents a comprehensive treatment for the state-of-the-art in stochastic service-guarantee analysis research and provides basic introductory material on the subject, as well as discusses the most recent research in the area. This helpful volume summarizes results for stochastic network calculus, which can be employed when designing computer networks to provide stochastic service guarantees. Features and Topics: Provides a solid introductory chapter, providing useful background knowledge Reviews fundamental concepts and results of deterministic network calculus Includes end-of-chapter problems, as well as summaries and bibliographic comments Defines traffic models and server models for stochastic network calculus Summarizes the basic properties of stochastic network calculus under different combinations of traffic and server models Highlights independent case analysis Discusses stochastic service guarantees under different scheduling disciplines Presents applications to admission control and traffic conformance study using the analysis results Offers an overall summary and some open research challenges for further study of the topic Key Topics: Queuing systems Performance analysis and guarantees Independent case analysis Traffic and server models Analysis of scheduling disciplines Generalized processor sharing Open research challenges Researchers and graduates in the area of performance evaluation of computer communication networks will benefit substantially from this comprehensive and easy-to-follow volume. Professionals will also find it a worthwhile reference text. Professor Yuming Jiang at the Norwegian University of Science and Technology (NTNU) has lectured using the material presented in this text since 2006. Dr Yong Liu works at the Optical Network Laboratory, National University of Singapore, where he researches QoS for optical communication networks and Metro Ethernet networks. A basic calculus is presented for stochastic service guarantee analysis in communication networks. Central to the calculus are two definitions, maximum-(virtual)-backlog-centric (m. b. c) stochastic arrival curve and stochastic service curve, which respectively generalize arrival curve and service curve in the deterministic network calculus framework. With m. b. c stochastic arrival curve and stochastic service curve, various basic results are derived under the (min, +)algebra for the general case analysis, which are crucial to the development of stochastic network calculus. These results include (i)superposition of flows, (ii)concatenation of servers, (iii) output characterization, (iv)per-flow service under aggregation, and (v)stochastic backlog and delay guarantees. In addition, to perform independent case analysis, stochastic strict server is defined, which uses an ideal service process and an impairment process to characterize a server. The concept of stochastic strict server not only allows us to improve the basic results (i)-(v)under the independent case, but also provides a convenient way to find the stochastic service curve of a serve. Moreover, an approach is introduced to find the m.b.c stochastic arrival curve of a flow and the stochastic service curve of a server. Network Calculus.- Application of Network Calculus to the Internet.- Basic Min-plus and Max-plus Calculus.- Min-plus and Max-plus System Theory.- Optimal Multimedia Smoothing.- FIFO Systems and Aggregate Scheduling.- Adaptive and Packet Scale Rate Guarantees.- Time Varying Shapers.- Systems with Losses. From the Publisher: Providing performance guarantees is one of the most important issues for future telecommunication networks. This book describes theoretical developments in performance guarantees for telecommunication networks from the last decade. Written for the benefit of graduate students and scientists interested in telecommunications-network performance this book consists of two parts.