Infinite Balanced Allocation via Finite Capacities

We analyze the following infinite load balancing process, modeled as a classical balls-into-bins game: There are $n$ bins (servers) with a limited capacity (buffer) of size $c=c(n)\in \mathbb{N}$. Given a fixed arrival rate $\lambda=\lambda(n)\in(0,1)$, in every round $\lambda n$ new balls (requests) are generated. Together with possible leftovers from p...