PME分布业务源的M/G/1排队模型研究

Research on the M/G/1 Model with PME-Distributed Source

传统的假定业务到达间隔服从负指数分布的Poisson模型或其改进形式不适用于呈现自相似性(或称为长相关性)的通信网络业务流量,但在利用M/G/1模型进行排队分析时,重尾分布服务时间的LST变换无闭合形式,从而进行排队性能分析非常困难。该文引入一类混合指数分布并证明此类分布服从Pareto重尾分布,得到相应的LST变换闭合形式及服务时间渐进级数,同时将形状参数γ=3/2时的服务时间分布及其LST变换推广到更—般的情形,从而较为有效地解决了重尾分布业务源的M/G/1模型排队等待时间分析问题。

Traditional Poisson or modulated Poisson model,which based on the assumption that traffic source arriving process is negative exponent distribution,can not be applicable to the self-similar(or long-range dependent)communication traffic.When applying the M/G/1 model to analyze the queuing performance of self-similar traffic sources with heavy tails,it is very difficult to get the explicit expressions of the Laplace-Stieltjes Transform(LST)of the service-time distribution.In this paper,a class of mixtures of exponential distribution is introduced and proved to satisfy heavy-tailed Pareto distribution.By calculating the LST and asymptotic series of the service-time distribution,the steady-state waiting-time probabilities of M/G/1 queue system are analyzed.A special case of shape parameterγ=3/2 is extended to the normal case.The results show that this extension is helpful to analyze the heavy-tailed waiting-time distribution of self-similar traffic sources.