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

在过去的十年中，一直有一个坚持不懈的追求，将网络演算-一种确定性排队系统的理论推广到它的随机对应。本研究就是为这一追求提供一个答案，并建立一个基于可能性的网络演算理论，进一步扩展这一研究线的范围。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。试点研究显示了一些显著特征，包括：1)流量和服务的对称和分解表征；Ii)去除高度非线性（min,+）卷积和反卷积算子；Iii)用随机变量的和表示单节点和串联系统的性能边界；Iv)通过动量生成函数重新获得有效带宽（容量）和大偏差特性；v)在大偏差范围内的严格界限和改进的比例因子。期望本研究将为排队理论和实践开辟一个新的前沿。提出的研究将导致排队和其他服务系统性能保证的新理论，有望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各种工程和社会系统（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）中提供性能保证的愿景是正确的；使私营机构能够创造更多增值的商业模式(例如溢价与？最好的努力吗?服务等级);并影响公共部门建设稳健的基础设施，有效地承担关键的社会责任。

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.