基于PME重尾分布服务时间的M/G/1模型排队性能研究  

Research on the Performance Analysis of M/G/1 Queue System of Service Time with PME Heavy-Tailed Distribution

作　　者：于秦[1] 毛玉明[1] 

机构地区：[1]电子科技大学通信与信息工程学院,成都610054

出　　处：《计算机学报》2005年第12期2103-2108,共6页Chinese Journal of Computers

基　　金：国家"八六三"高技术研究发展计划项目基金(2001AA123032)资助.

摘　　要：通信网络的业务源普遍存在着自相似性(或称为长相关性),传统的假定业务到达间隔服从负指数分布的Poisson模型或其改进形式已不再适用.但在利用M/G/1模型对自相似业务源进行排队分析时,由于重尾分布服务时间的LST变换无闭合形式,进行排队性能分析非常困难.该文通过引入一类混合指数分布证明此类分布服从Pareto重尾分布,并得到相应的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时的服务时间及其LST变换推广到更一般的情形,从而较为有效地解决了重尾分布的信源排队等待时间分析问题.The real network traffic is self-similar or long-range dependent （LRD）. Basing on the assumption that traffic source arriving process is negative exponent distribution, the Poisson or modulated Poisson model already can＇t be applicable to the real network traffic. When analyzing the M/G/1 queuing performance of self-similar traffic sources with heavy tails, it is very difficult to get the explicit： expressions of the Laplace-Stieltjes transform of the service-time distribution. This paper introduces a class of mixtures of exponential distribution and proofs they are heavytailed Pareto distributions. By calculating the LST and asymptotic series of the service-time distribution authors analyze the steady-state waiting-time probabilities of M/G/1 queue system. The authors also extend the special case ~y= 3/2 to the normal case. The results show that it will be helpful to analyze the heavy-tailed waiting-time distribution of self-similar traffic sources.

关 键 词：PME分布iLST变换 M/G/1模型 排队性能 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]