Leaky Buckets: Volume in a system of 2+ buckets that can be empty

Question

What is the volume of water in each bucket in a system of leaky buckets with the following conditions:

1. There are $N$ buckets with $W_i(t)$ volume of water.
2. A bucket has infinite capacity, but a finite amount of water bounded at zero: $\infty \geq W_i(t) \geq 0$.
3. There is a "source" bucket which flows into other buckets, but other buckets do not flow into it. Every non-source bucket flows into every other non-source bucket.
4. With enough volume, each bucket has a constant outflow rate, $v_i$ (units of $W/s$), of water flowing out and being equally distributed into the other buckets. You can imagine that each bucket has a pump attached to it trying to pump at a fixed rate through $N-1$ or $N-2$ pipes for the source and non-source buckets, respectively.

This figure illustrates an $N=3$ bucket system.

What are the formulae for $W_i(t)$?

This is a relatively simple problem apart from the constraint that $W_i(t) \geq 0$, since this puts a continuity-breaking constraint on the flow rate, and I'm very rusty.