论文标题
使用新一代网络发现路径MTU发现的数学分析
Mathematical Analysis of Path MTU Discovery With New Generation Networks
论文作者
论文摘要
在本文中，我们介绍了IPv4＆ipv6中PATH MTU发现在数学，逻辑和图形表示中的影响。我们尝试将数学模型用于路径MTU发现的工作，并使用数据包的传输来计算其行为。我们分析了在PMTUD存在的情况下，在IPv6网络中将单个数据包从源传输到目的地的时间，并且在IPv4网络中类似地使用DF位1。根据我们的分析，我们得出结论，沟通时间随着中间节点的不同mtu而增加。此外，我们制定了数学模型，以确定网络中的通信延迟。我们的模型表明，使用PMTUD的渐近下限为$ω（n）$，渐近上限为$θ（n^2）$。我们发现，数据包下降频率遵循Bernoulli的试验，这有助于定义数据包下降频率的成功概率，这表明，对于开始路径中总节点的$ 2 \％$的数据包下降率的概率较高。我们进一步发现，$^{n} c_ {a} $可能的a组合数，而无需重复，可以为特定数量的数据包下降频率形成。每个组合的求和（在时间浪费方程中起到系数）与它们的频率之间的关系导致对称图以及数学和统计结构，以测量时间浪费及其行为。这也有助于测量可能的相对最大，最小和平均时间浪费。我们还测量了对路径中数据包下降频率和节点数量给定值的相对最大，最小值和平均值的概率。
In this paper we have presented the effects of path mtu discovery in IPv4 & IPv6 in mathematical, logical and graphical representation. We try to give a mathematical model to the working of path mtu discovery and calculated its behaviour using a transmission of a packet. We analysed the time consumed to transmit a single packet from source to destination in IPv6 network in the presence of PMTUD and similarly in IPv4 network with DF bit 1. Based on our analysis, we concluded that the communication time increases with the varying MTU of the intermediate nodes. Moreover, we formulated the mathematical model to determine the communication delay in a network. Our model shows that the asymptotic lower bound for time taken is $Ω(n)$ and the asymptotic upper bound is $Θ(n^2)$, using PMTUD. We have find that the packet drop frequency follows the Bernoulli's trials and which helps to define the success probability of the packet drop frequency, which shows that the probability is higher for packet drop rate for beginning $2\%$ of the total nodes in the path. We further found that $^{n}C_{a}$ possible number of a-combinations without repetitions that can be formed for a particular number of packet drop frequency. The relation between summation (acts as a coefficient in the time wastage equation) of each combination and their frequency resulted in symmetric graph and also mathematical and statistical structures to measure time wastage and its behaviour. This also helps in measuring the possible relative maximum, minimum and average time wastage. We also measured the probability of relative maximum, min and average summation for a given value of packet drop frequency and number of nodes in a path.
