Ishfaq Hussain | Searcharxiv

arXiv2022

Mathematical Analysis of Path MTU Discovery With New Generation Networks

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.

cs.NI↗

arXiv2020

Dynamic MTU : Technique to reduce packet drops in IPv6 network resulted due to smaller path mtu size

With an increase in the number of internet users and the need to secure internet traffic, the unreliable IPv4 protocol has been replaced by a more secure protocol, called IPv6 for Internet system. The IPv6 protocol does not allow intermediate routers to fragment the on-going IPv6 packet. Moreover, due to IP tunneling, some extra headers are added to the IPv6 packet, exceeding the packet size higher than the maximum transmission unit (MTU), resulting in increase in packet drops. One probable solution is to find the MTU of every link in advance using the Internet Control Message Protocol (ICMP) packets and accordingly fragment the packets at the source itself. However, most of the intermediate routers and the network firewalls do not allow ICMP packets to traverse through their network, resulting in network black holes, where we cannot know the MTU of some links in advance. This method tries to handle the packet drops in IPv6 network by proposing a DMTU scheme where we dynamically adjust the MTU of each link depending upon the original size of the IPv6 packet, thereby reducing the number of packet drops by a significant amount. Using mathematical and graphical analysis, our scheme proves to be much more efficient than the state-of-the-art PMTUD scheme. In this paper the method, mathematical and graphical representations are focusing solely in IPv6 Internet communication.

cs.NI↗