In transportation systems (e.g. highways, railways, airports), traffic flows with distinct origin-destination pairs usually share common facilities and interact extensively. Such interaction is typically stochastic due to natural fluctuations in the traffic flows. In this paper, we study the interaction between multiple traffic flows and propose intuitive but provably efficient control algorithms based on modern sensing and actuating capabilities. We decompose the problem into two sub-problems: the impact of a merging junction and the impact of a diverging junction. We use a fluid model to show that (i) appropriate choice of priority at the merging junction is decisive for stability of the upstream queues and (ii) discharging priority at the diverging junction does not affect stability. We also illustrate the insights of our analysis via an example of management of multi-class traffic flows with platooning.