分形流量通过服务器的理论

The topic of guaranteeing the end-to-end delays of packets for a specific connection or a specific class of connections not to exceed the predetermined maximum value of delay plays a role in real-time systems. Traditional approaches to assure delays not to exceed the predetermined values are based on assigning sufficient bandwidth for connections. However, bandwidth may in general be overassigned, yielding tough contradiction between guaranteed delays and bandwidth assigned properly. Consequently, to deal with that contradiction turns to be an important research issue in real-time systems.. This project proposal expects to establish a theory of fractal traffic passing through servers, aiming at solving the above issue in a considerable step. It consists of main tasks as follows towards constituting a theory for assuring end-to-end delays with significant improvement of bandwidth allocations. (1) Identifications of scale factors of real traffic of fractal type. (2) Theoretical description of accumulated multifractal traffic. (3) theory of the inverse operation of min-plus algebra system on the set of wide-sense increasing functions, including the uniqueness and closeness of the demin-plus convolution, its operation representation, and so on. (4) Novel theory of service curves based on accumulated arrival of multifractal traffic towards establishing a theory and methods of analyzing guaranteed delays with considerably increasing the utilization of bandwidth. (5) Establishing a novel theory of synthesizing service curves based on accumulated traffic of fractal type and the inverse operation of min-plus algebra system. The previous constitutes the expected theory of fractal traffic passing through servers as the proposal title implied based on the main track of guaranteed delays with significant improvement of the bandwidth utiliztion.

确保一个或一类连接上的数据包的端到端延迟不超过指定的最大值，是实时系统的重要研究内容. 为确保延迟控制在指定范围内的通常做法是为连接分配足够的带宽. 但这样的做法通常导致延迟确保与带宽过度分配的矛盾. 故解决这矛盾是实时系统领域中需进一步研究的重要课题. . 该申请项目欲建立分形流量通过服务器的理论. 主要内容有：1）分形流量的尺度因子的辨识；2）考虑广义增、大和小尺度特性及分形维数和Hurst指数的累积多分形流量表示；3）基于广义增函数集合的最小加代数系统的逆运算理论（逆的唯一性、逆运算表达式及逆运算在广义增函数集合中的封闭性等）；4）基于累积流量多分形特性，建立能显著提高带宽利用率的确保延迟计算理论和新的服务曲线理论；5）基于计及分形特性的累积流量和最小加代数系统逆运算，建立新的服务曲线综合理论. 由此，形成以确保端到端延迟及显著提高带宽利用率为主线条的分形流量通过服务器的理论.

此项目预期目标主要是发表SCI检索论文25篇。迄今已发表标注了批准号61272402的SCI检索论文42篇，其中有3篇是ESI高被引论文，1篇ESI热门论文。论文发表超出预期目标。除完成了项目主题（分形流量通过服务器的理论）的研究，项目负责人也在计算机科学、数学、统计学、统计力学、海洋科学等领域的其它43个研究问题中取得了创新性成果。此外，项目负责人于2014和2015分别列入中国高被引学者榜单。

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