  We consider congestion control in peer-to-peer distributed systems. The
problem can be reduced to the following scenario: Consider a set $V$ of $n$
peers (called clients in this paper) that want to send messages to a fixed
common peer (called server in this paper). We assume that each client $v \in V$
sends a message with probability $p(v) \in [0,1)$ and the server has a capacity
of $\sigma \in \mathbb{N}$, i.e., it can recieve at most $\sigma$ messages per
round and excess messages are dropped. The server can modify these
probabilities when clients send messages. Ideally, we wish to converge to a
state with $\sum p(v) = \sigma$ and $p(v) = p(w)$ for all $v,w \in V$. We
propose a loosely self-stabilizing protocol with a slightly relaxed legimate
state. Our protocol lets the system converge from any initial state to a state
where $\sum p(v) \in \left[\sigma \pm \epsilon\right]$ and $|p(v)-p(w)| \in
O(\frac{1}{n})$. This property is then maintained for
$\Omega(n^{\mathfrak{c}})$ rounds in expectation. In particular, the initial
client probabilities and server variables are not necessarily well-defined,
i.e., they may have arbitrary values. Our protocol uses only $O(W + \log n)$
bits of memory where $W$ is length of node identifers, making it very
lightweight. Finally we state a lower bound on the convergence time an see that
our protocol performs asymptotically optimal (up to some polylogarithmic
factor).
