SGER: Queuing System Performance Guarantees with Stochastic and Possibilistic Network Calculus under Legendre Transform

在过去的十年里，人们一直致力于推广网络微积分--一种将确定性排队系统的理论推广到随机排队系统的理论。本研究旨在为这一追求提供答案，并建立一种基于可能性的网络演算理论，进一步扩展这一研究的范围。这种开发背后的关键方法是在样本路径级别应用勒让德变换。试点研究已经显示出一些独特的特征，包括：i)业务和服务的对称和分解表征；ii)去除高度非线性的(min，+)卷积和去卷积算子；iii)通过随机变量求和来表示单节点和汇接系统的性能界限；iv)重新获取通过动量生成函数定义的有效带宽(容量)和大偏差特性；以及v)大偏差区域中的紧界和改进的比例因子。该研究将为排队系统和其他服务系统的性能保证提供一种新的理论，以期提供更准确的系统性能评估和更好的系统资源管理。这种新理论将证明在不同的工程和社会系统中提供性能保证的愿景是合理的，例如通信网络(无线、传感器网络和高速互联网)、供应链和物流系统、运输和医疗保健提供系统；使私营部门能够产生更多增值商业模式(例如，溢价与最佳努力？服务级别)；并影响公共部门建设强有力的基础设施和有效地承担其重要的社会责任。

There has been a persistent pursuit during the past decade for generalizing network calculus - a theory of deterministic queuing systems to its stochastic counterpart. This research is to offer an answer for this pursuit and to establish a possibility-based network calculus theory that further extends the scope of this research line. The key methodology behind such a development is to apply Legendre transform at the sample-path level. Pilot research has shown some distinguished features that include: i) symmetric and decomposed characterization for traffic and service; ii) removal of highly nonlinear (min,+) convolution and de-convolution operators; iii) representation of single-node and tandem system performance bounds by summation of random variables; iv) recapture of effective bandwidth (capacity) and large deviations properties defined through the momentum generating functions; and v) tight bounds and improved scaling factor in the large deviations regime. It is expected that this research will open a new frontier in queuing theory and practice.The proposed research will lead to a new theory for performance guarantees in queuing and other service systems that is expected to provide more accurate assessment of system performance and better management of system resources. Such a new theory will justify the vision of offering performance guarantees in diverse engineering and social systems such as communications networks (wireless, sensor networks and the high-speed Internet), supply chain and logistic systems, transportation and healthcare delivery systems; empowers the private sector to generate more value-adding business models (e.g. premium vs. ?best effort? service grades); and influences the public sector to construct robust infrastructures and to effectively assume its critical social responsibilities.