宽带网络中排队系统的长尾行为：Tsallis熵框架
Long Tail Behavior of Queue Lengths in Broadband Networks: Tsallis Entropy Framework
摘要：
提出了一种基于Tsallis熵的最大熵框架来描述宽带网络中队列长度的长尾行为。以数据包数表示的队列长度表达式涉及Hurwitz-zeta函数。当Tsallis熵中的熵参数q小于1时，包的分布产生幂律行为。在q趋于1的极限下，Tsallis熵的表达式由于Shannon而简化为1，恢复了M/M/1排队系统的已知结果. Tsallis熵参数q与Hurst参数H（自相似性度量）之间的关系被假定。给出了一种基于牛顿-拉夫逊法计算拉格朗日参数b的数值方法。流量强度r和拉格朗日的参数b之间的各种关系进行检查使用的数据产生的平均数的数据包从存储模型由于诺罗斯。发现对于不同的熵参数q值，最佳拟合对应于r是b中的衰减指数和幂指数的线性组合。导出了排队长度超过某一值的概率的显式表达式，并证明了当q小于1时，排队长度超过某一值的概率渐近服从幂律。当参数r变化时，系统利用率显示出有趣的行为。当r值较小时，它的值比M/M/1系统的值低，而当r值较大时，情况相反。
英文摘要：
A maximum entropy framework based on Tsallis entropy is proposed to depict long tail behavior of queue lengths in broadband networks. Queue length expression as measured in terms of number of packets involves Hurwitz-zeta function. When the entropy parameter q in Tsallis entropy is less than unity, the distribution of packets yields power law behavior. In the limit q tending to unity, Tsallis entropy expression reduces to one due to Shannon and well-known results of M/M/1 queuing system are recovered. Relationship between Tsallis entropy parameter q and Hurst parameter H (measure of self-similarity) is postulated. A numerical procedure based on Newton-Raphson method is outlined to compute Lagrange's parameter b. Various relationships between traffic intensity r and Lagrange's parameter b are examined using data generated from mean number of packets from storage model due to Norros. It is found that best fit corresponds to r being a linear combination of decaying exponential and power exponent in b for different values of entropy parameter q. Explicit expression for the probability that queue size exceeds a certain value is derived and it is established that it asymptotically follows power law for q less than one. The system utilization shows an interesting behavior when the parameter r is varied. It attains lower values than that of M/M/1 system for smaller values of r whereas situation reverses for higher values of r.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
