论CSMA/CD协议的数学原理

Demonstration of Mathematics Theory of CSMA/CD Protocol

CSMA/CD网络在长期试错中已经从单总线型网络发展到了堆叠式网络,但其不确定性本质上并未得到解决．本文从数学原理角度推导了其不确定性解决的理论依据,通过对堆叠式网络数学模型的抽象,证明了堆叠式网络结构服从幂率变换定理,在其时间敏感性上以幂率收敛方式优于单总线型网络,并从网络吞吐量和网络传输效率性能分析评价了该模型．最后,总结出了CSMA/CD的理论“究竟”,拓宽,CSMA/CD在嵌入式工业控制领域的“方便”应用．

The network based on CSMA/CD protocol has developed from single bus-type network to stacking-type network during long-time trial-and-error practice, but its uncertainty has not been solved essentially. In this paper, a theoretical foundation for resolving the uncertainty, is deduced from the angle of mathematics theory. By abstracting the mathematic model of stacking-type network, the structure of stacking-type network is proved to obey the theorem of power rate transition and to be better than the single bus-type network in that it has an exponentially convergent time-sensitivity. Furthermore, through analyzing the network capability of the network throughput and transmission efficiency, the model is evaluated. Finally the theoretical ＂however＂ of CSMA/CD is summarized and the applications of ＂convenience＂ of CSMA/CD in the embedded industrial control fields are widened.