高可靠性一般负载双星网络的数学建模

摘要

Contention-collision cancellation access control mode is an important access control mode in star networks .Due to the complexity of mathematical analysis for this mode in double-star networks ,so far only the study on the condition of heavy load has been reported .Furthermore ,the reliability of networking technology is dramatically improved ,so that the instance of failed ser-vice is approximately ignored .Based on the above points ,we formulate the general load double-star network combining light load and heavy load .Then we derive the expended waiting time ,which is used to evaluate the performance of double-star network .Final-ly ,we validate the mathematical result through simulation .The conclusion not only provides the theoretical foundation for the appli-cation of reliable double-star network ,but also firstly resolves non-classical queueing model LGn=2RSS ,and expands the theory of random service system .%竞争-冲突淘汰方式是一种重要的星形网访问控制方式。由于它在双星网中的数学解析十分复杂，目前见到的报告仅是在重负载条件下的研究进展。另一方面，当前网络技术可靠性已经有了大幅提升，在对计算机网络进行数学解析时可以通过近似，忽略服务失败的情况。充分考虑到以上两点，本文在一般负载（轻、重负载混合）下，对高可靠性双星网进行了数学建模和解析，求得了评价双星网性能的重要参数---扩展滞留时间，并进行了模拟实现。这一问题的解决，不仅为双星网的应用提供了理论依据，同时在运筹学中首次解析了非典型排队模型 L（二项式到达）＼D＼n＝2＼RSS ，扩展了随机服务系统理论。