Research On The Theory And The Application Of Stochastic Network Calculus

Network Calculus is a theory for performance guarantee analysis of computer networks. Since originated in early 1990 s, network calculus has attracted great interest from many researchers. By introducing the min-plus algebra, complex network systems can be transformed into analytically tractable systems in the context of inetwork calculus. Comparing to classic queueing theory, network calculus is more suitable for modern Internet networks, and it has overcome many difficulties and problems that would be encountered by using queueing theory in the performance analysis of Internet networks. For instance, the characteristics of heavy tail and long-range dependence in Internet traffic are very hard to be modeled by queueing theory.There are two branches in network calculus: deterministic network calculus and stochastic network calculus. Deterministic network calculus can provide quality of service(QoS) guarautees by a hundred percent, but it usually leads to low network resources utilization at the same time. Stochstic network calculus prodives QoS guaratees with certain probalility(as required), it can dramatically improve network resources utilization compare to derterminstic network calculus. This feature makes it gain more researchers' s attention. Although great progress has been made in stochastic network calculus in recent years, there are crucial yet still open challenges in this area, such as loss analysis and multi-server systems analysis. This thesis is devoted to rise to some of these challenges and apply stochastic network calculus to some new fields.This thesis first studies the stochastic network calculus theory and makes some extensions to it, which mainly contains two aspects. One is making stochastic network calculus be capable of analyzing a new performance parameter. The other is making stochastic network calculus be capable of applied to some new scenarios.Current stochastic network calculus cannot be directly for loss analysis. Loss is an important parameter of Quality of Service. However, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Although some efforts have been made to analyze loss by deterministic network calculus, few results of loss analysis obtained in the context of stochastic netork calculus. To address the difficulties in loss analysis, we introduce loss period as a new concept into stochastic network calculus. To reflct the influence of buffer size on loss, we also introduce a new parameter named as loss factor into stochastic network calculus, and then we derive the loss bound via this parameter.Current stochastic network calculus cannot be applied to stochastic multi-server systems. Multi-server systems have become increasingly common in various kinds of networks and network applications. However, very few analytical results based on stochastic network calculus are available for multi-server systems, especially for stochastic servers. The difficulty in the research is that exsiting stochastic server models are not suitable for the analysis. In this thesis, we adopt a new kind of stochastic server model, and besides of the five basic properties in exsiting theory systrem, we prove it possesses a new property that is critical for the performance analysis of stochastic multi-server systems.This thesis also aims to apply stochastic network calculus to the performance analysis in two new industry fields, cloud computing and solar energy generating.Applying stochastic network calculus to the analysis of the response time bound in cloud computing. Cloud computing is a newly emerged Internet-based computing paradigm, through which the shared hardware and software resources can be provided as services to computers or other devices on demand. Corresponding to concepts of stochastic traffic model and stochastic server model in stochastic network calculus, we propose stochastic task request arrival model and stochastic cloud computing resource model for cloud computing. Based on these models and the results in the study of multi-server systems, we dervrive the response time bound which is a key parameter of the SLA in cloud computing.Applying stochastic network calculus to the performance analysis of solar energy generating systems. As a kind clean and renewable new energy, solar energy has gained more and more favor of people and has been used in many fields. An important field is converting solar energy into electrical energy. In this thesis, we explore the bounds of the residual energy, the power shortage and the wasted energy in solar energy generating systems. Due to different characteristics, we build one pair of stochastic power generation model and stochastic energy demand model for each of the three performance parameters. We directly make use of the results obtain in the previous loss analysis to get the wasted energy bound.In summary, we have made some efforts to refine the stochastic network calculus theory, and based on which, we analyze the performance of cloud computing and solar energy generating systems by this theory. The analytical method could help to the plan and deployment of the systems.