非强占有限优先权M/G/1排队系统

针对部分数据帧有完全优先权发送的计算机网络数据服务系统存在的网络拥塞风险问题，提出了一种非强占有限优先权M/G/1排队系统模型的方法。该系统模型引入控制完全优先权的参数n，使得数据帧的完全优先权变成有限优先权，考虑了不同优先级队伍之间的公平性，降低了计算机网络数据服务系统拥塞的风险，使得网络系统在有限优先权下有较好的稳定性。在模型研究中，运用全概率拆解方法获得各级队伍平均等待时间、平均逗留时间和平均队长的理论结果。对模型采用Matlab 2010a软件实验仿真，实验得到的各级队伍平均等待时间和理论平均等待时间的平均绝对误差为0.951%。实验中，有限优先权条件下各级顾客的平均等待时间比值显著小于完全优先权条件下各级顾客的平均等待时间比值。实验结果表明对非强占有限优先权M/G/1排队系统模型研究的理论结果是正确的，该模型具有更稳定的系统特性。

M/G/1 queuing model under nonpreemptive limited-priority

Concerning the network congestion risk of computer network service system for some data frames having a full priority of transmission, a method about nonpreemptive limited-priority M/G/1 queuing system model was proposed. Firstly, as the parameter n of limited-priority was introduced into the model, the data frame with full priority was converted to the one with limited priority. Secondly, in order to lower the risk of computer network service system and stabilize the network system further, the fairness among different priorities was studied in the model. Moreover, by making use of total probability theorem, three results of the models, the average waiting time, the average dwelling time and the average queue length were obtained. Simulation under Matlab 2010a showed that, the mean absolute error between average waiting time and theoretical formula results at all levels of queue, was just 0.951%. In the experiment, the average waiting time ratio with limited-priority was significantly smaller than the average waiting time ratio with full priority at all levels of queue. The experimental results show that the theoretical results, which use the nonpreemptive limited-priority M/G/1 queuing system model, are correct; besides, the model is more stable than the others.