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, 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. ACM Sigcomm 2006 published a paper [26] which was perceived to unify the deterministic and stochastic branches of the network calculus (abbreviated throughout as DNC and SNC) [39]. Unfortunately, this seemingly fundamental unification---which has raised the hope of a straightforward transfer of all results from DNC to SNC---is invalid. To substantiate this claim, we demonstrate that for the class of stationary and ergodic processes, which is prevalent in traffic modelling, the probabilistic arrival model from [26] is quasi-deterministic, i.e., the underlying probabilities are either zero or one. Thus, the probabilistic framework from [26] is unable to account for statistical multiplexing gain, which is in fact the raison d'etre of packet-switched networks. Other previous formulations of SNC can capture statistical multiplexing gain, yet require additional assumptions [12], [22] or are more involved [14], [9] [28], and do not allow for a straightforward transfer of results from DNC. So, in essence, there is no free lunch in this endeavor. Our intention in this paper is to go beyond presenting a negative result by providing a comprehensive perspective on network calculus. To that end, we attempt to illustrate the fundamental concepts and features of network calculus in a systematic way, and also to rigorously clarify some key facts as well as misconceptions. We touch in particular on the relationship between linear systems, classical queueing theory, and network calculus, and on the lingering issue of tightness of network calculus bounds. We give a rigorous result illustrating that the statistical multiplexing gain scales as Ω(√N), as long as some small violations of system performance constraints are tolerable. This demonstrates that the network calculus can capture actual system behavior tightly when applied carefully. Thus, we positively conclude that it still holds promise as a valuable systematic methodology for the performance analysis of computer and communication systems, though the unification of DNC and SNC remains an open, yet quite elusive task. The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that end-to-end performance measures computed with a network service curve are bounded by spl Oscr (H log H), where H is the number of nodes traversed by a flow. Using currently available techniques, which compute end-to-end bounds by adding single node results, the corresponding performance measures are bounded by spl Oscr (H sup 3 ). The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that end-to-end performance measures computed with a network service curve are bounded by O(Hlog H), where H is the number of nodes traversed by a flow. Using currently available techniques that compute end-to-end bounds by adding single node results, the corresponding performance measures are bounded by O(H3).