Abstract: Research on network measurement has shown the presence of self-similar properties in great number of network traces, but how to build self-similar queuing model and analyze it has been a problem. On the basis of hyper-erlang fitting method, M/HErd/1/K queuing model with passion arrive rate and hyper-erlang service time is proposed, and the queuing performance of the self-similar network service is derived. Compared with traditional M/M/1/K queuing model under real trace, new model effectively describes not only the quick-hang traffic attribute, but also the potential risk under heavy traffic load. So the proposed model is better, and it is instructive to the network operation and maintenance.

Key words: hyper-erlang distribution, queuing model, self-similar

摘要： 现有网络的业务流研究表明，多种通信业务中普遍存在自相似特性，但是如何对自相似业务流进行建模和分析一直是个难解问题。基于超爱尔兰拟合算法，建立了到达为泊松分布，服务时间为超爱尔兰分布的M/HErD/1/K自相似排队模型，推导得到呼叫损失概率、平均排队队长等排队性能的解析解。在实际业务环境下和传统的M/M/1/K排队模型进行了仿真对比，结果表明M/HErD/1/K模型不仅可有效表征业务流的快挂业务特性，而且能仿真出该网络在业务负荷较重时潜在的运营风险，对实际网络运营管理具有重要的指导作用。

关键词: 超爱尔兰分布, 排队模型, 自相似