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

SGER：勒让德变换下随机和可能网络演算的排队系统性能保证

• 批准号: 0738605
• 负责人: Xiaoyue Jiang
• 金额: $ 3万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-15 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0738605&HistoricalAwards=false
• 关键词: SGER; Queuing; System; Performance; Guarantees

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.

在过去的十年里，人们一直在不懈地追求将网络演算-确定性排队系统理论推广到随机排队系统。本研究的目的是为这一问题提供一个答案，并建立一个基于可能性的网络演算理论，进一步扩展了这一研究路线的范围。这种发展背后的关键方法是在样本路径级应用勒让德变换。初步研究显示了一些突出的特点，包括：i）对称和分解的流量和服务的特征; ii）删除高度非线性（min，+）卷积和去卷积算子; iii）通过随机变量的总和表示单节点和串联系统的性能界限; iv）重新捕获有效带宽（容量）和通过动量生成函数定义的大偏差性质;以及v）在大偏差状态中的紧边界和改进的比例因子。预计这项研究将在排队理论和实践中开辟一个新的前沿，提出的研究将导致排队和其他服务系统的性能保证的新理论，预计将提供更准确的系统性能评估和更好的系统资源管理。这种新的理论将证明在不同的工程和社会系统，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提供性能保证的愿景;授权私营部门产生更多的增值业务模式（例如溢价与？尽最大努力？服务等级）;并影响公共部门建设强大的基础设施，有效地承担其重要的社会责任。