# Can the traffic relation between two nodes of a communications network be governed by an exponential law?

Disclaimer: This question was initially asked in Network Engineering SE, yet got closed due to its research nature.

Assume a (hypothetical) communications network constituted by many nodes including two adjacent nodes $$u$$ and $$v$$. Let the traffic at node $$u$$ (resp., node $$v$$), denoted by $$f(u)$$ (resp., $$f(v)$$), be the difference between number of packets entering $$u$$ (resp., $$v$$) and departing it during a particular time interval. For a particular simulation to show the validity of a complicated model, I need to assume that $$f(u) = exp(f(v))$$ and $$f(v) = log(f(v))$$, where $$u$$ and $$v$$ are generally connected to many other nodes, as well. I just searched a little bit in the literature but failed to find any real-world network in which such dynamics may hold. Since I am not a network expert, it is pretty likely that I have missed something. So, does anyone know such a network? Even if there is not a real network, I am curious whether one can imagine a reasonable network in which such exponential law is (at least locally) the case.

I have already read about power graphs of social networks that might be relevant to this question. However, I am strictly interested in a potential example in the realm of communications networks (computer networks, datacenter networks, ad-hoc networks, etc.).