The Probability Density Function for Network Coding with Three Input Flows

Now many researches have been studying the optimization between throughput/energy consuming and delay with a couple of independent input flows in network coding (NC). However, the implementation of network coding (NC) requires a thorough investigation of its impact on relevant queueing systems which little work focuses on. In this paper, the scenario with three independent Poisson input flows based on our previous work about the pdf with two independent Poisson input flows., and one output flow is considered. The asynchronous NC-based strategy is that a new arrival evicts a head packet holding in its queue when waiting for another packet from the other flow to encode. The three flows are divided into two parts for getting the probability density function (pdf) of the output flow. The pdf for the output flow which contains both coded and uncoded packets is derived. Besides, the statistic characteristics of this strategy are analyzed. These results are verified by numerical simulations.