Delay analysis of network coding nodes and Butterfly network employing stop-and-wait automatic repeat request

The delay characteristics of network coding nodes and Butterfly network are investigated. First, the probability mass function (PMF) of delay and the average delay of general network coding nodes having multiple input links and one output link are analysed. It can be shown that the PMF and average delay can be readily evaluated from the recursive equations derived. Then, the delay performance of the Butterfly network is investigated. Specifically, the authors consider four different scenarios in the context of the packets transmitted over the Butterfly network. The PMFs of delay as well as the average delays of these four scenarios are analysed and, correspondingly, a range of formulae are obtained. Finally, the delay performance of network coding nodes and Butterfly network is investigated based on the numerical results evaluated from the formulae derived. The authors studies demonstrate that network coding nodes embedded in a network generate a big impact on the network´s delay performance. Usually, in a network including some network coding nodes, the longest path with some network coding nodes may be chosen for approximately estimating the network´s average delay.