Splitting Poisson Process

Question

I have an arrival Poisson process $T$ representing tasks arrival in a computation system formed by two different computation node $n_1$ and $n_2$, with exponential service time $m_1$ and $m_2$. Each task has a deadline exponentially distributed, different for each task. In order to decide the computation node on which each task has to be processed, $T$ is splitted into two subprocesses $t_1$ and $t_2$ with probability $a$ and $(1-a)$, respectively. The probability $a$ is defined on the basis of an estimated distribution (Erlang distribution) of the queuing time in $n_1$, considering the number of task in the queue. I have to prove that the arrivals on $n_2$ are Poisson arrivals. I don't think it is trivial and any help would be highly appreciated.