一般负载下双星LAN数学建模的研究

【作者】 刘海光；

【导师】 逯昭义；

【作者基本信息】 青岛大学 ， 计算机软件与理论， 2006， 硕士

【摘要】 一般而言,星型计算机局域网（LAN）中心结点只有一条通道,形成所谓的单星LAN,而多星LAN的中心结点由多条通道构成。与单星LAN相比,多星LAN相当于由多个单星LAN构成。 关于多星LAN的运行机理,有关文献已经报告。人们在研究多星LAN时提出了著名的介质访问控制方式—竞争—冲突淘汰（Contention-Collision Cancellation,C-CC）访问方式。根据顾客请求服务、再次请求服务、接受服务的各种情况进行组合,区分出六类系统模型。由于该存取方式对于建立星型LAN的标准介质访问方式很有价值,引起了较大关注。目前竞争—冲突淘汰存取方式Ⅰ类、Ⅱ类、Ⅲ类、Ⅳ类、Ⅴ类系统模型的数学建模已经完成。但是,我们可以注意到,为了对C-CC进行数学建模并能够数学解析,已经发表的文献都是将多星以单星处理,也就是对C-CC访问方式的单星LAN进行了数学建模研究。这些研究进展无疑促进了星型LAN的发展,从知识创新的角度使人们认识了发展多星LAN的理论价值。然而人们至今没有报告多星LAN数学建模的研究进展,主要是数学方面存在困难。为了对C-CC访问方式进行理论创新,必须对多星LAN进行深化研究。 本文的深化研究是首先从双星LAN开始。双星LAN作为多星LAN的一种重要拓扑结构,其在重负载下的解析已经完成。本文扩展单星LAN以及重负载下双星LAN的建模研究,成功地解决了C-CC访问方式在一般负载下双星LAN的数学建模,提出了顾客转移概率P_ij、顾客平均等待时间等的数学计算式,同时进行了模拟实验,且与重负载下双星LAN的情况进行了比较。至此为双星LAN“竞争—冲突淘汰”存取方式的应用提供了理论依据。本文的结论对发展有线星型LAN和无线星型LAN有理论参考价值。更多还原

【Abstract】 Generally, there is only one channel in star-LAN named single-star LAN, while multi-star LAN has more than one channels. Multi-star LAN can be considered consisting of several single star-LANs.The working principle of Multi-star LAN has been reported in some literature. During the research in multi-star LAN, a new famous media access mode named the contention-collision cancellation access mode （abbreviated as C-CC） has been presented. According to the different situations of customers requesting for service, re-requesting for service, and being served, the system model of C-CC can be classified as six types. The C-CC mode is very useful for the establishment of the standard access mode of star-LAN, which attracts more and more contention. At present, the studies about C-CC of the Ist、 IInd、 IIIrd、 IVth、 Vth types have been finished, which undoubtedly help develop the star LAN. But we can notice that, in order to make mathematical modeling and resolution of C-CC, papers published mostly deal with multi-star LAN as single-star LAN, which means those are the mathematical modeling research of single-star LAN of C-CC. From the viewpoint of innovation we know the value of developing multi-star LAN. However, because of mathematical difficulties, no paper has made any reports of multi-star LAN. In order to make innovation for the C-CC access mode, we have to study multi-star LAN deeply.The deep research starts from double-star LAN, which is a very important topology of multi-star LAN. And the research of double-star LAN under heavy load has been finished. This paper studies on extending of single-star LAN and double-star LAN, and successfully solves the mathematical model for double-star LAN with access mode of C-CC under normal load. At the same time we get expressions for the transfer probability P_ij of the customers, the mean waiting time of the customers in the system and carry onthe simulation for them. Then we compare the result of two servers under normal load with the one that is under heavy load. So far, the theory foundation of the contention-collision cancellation access mode has been established for its application. The result of this paper can give academic reference value to wire star-LAN and wireless star-LAN.更多还原