网络流量的半马尔可夫模型

A Semi-Markov Model for Network Traffic

引入半马尔可夫模型描述网络流量特性,通过忙阈值和闲阈值的设定将网络流量划分为四种状态:忙、空闲、上升和下降,研究各状态下的网络流量特性及各状态间的相互转换关系.通过网络协议性能分析,在一定的假设条件下推出IP网络流量在处于忙状态时服从几何布朗运动,在空闲状态下服从正态分布,在上升状态或下降状态下服从指数分布.对广域网和局域网的实际流量数据的分析和检验表明,95%的数据均服从相应状态下的上述随机分布,同时根据此模型计算的系统平均利用率与实际统计结果之间的相对误差小于5%,说明引入的模型能真实反映网络流量特性.

This paper presents a Semi-Markov Model to characterize network traffic. The model divides network traffic into four states： Busy, idle, rising and falling, through setting busy and idle thresholds to network traffic. Analysis show that the average traffic transmission rate under busy state follows geometrical brown motion, that under idle state follows normal distribution, and that under rising or falling states follows exponential distribution respectively. Some practical trace data from WAN and LAN is employed to verify the model separately. 95% trace data really follows its corresponding stochastic distribution in each state. Meanwhile, taking the average network utilization as a parameter example, the theoretical result computed by the model is very consistent with the real statistical result. The relative error is within 5%, which shows how the model is well matched to real network traffic.