Balls-into-bins games for uniform bins are widely used to model randomized load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-to-peer (P2P) networks, which are not able to perfectly balance the load over the bins. While previous evaluations try to find strategies for uniform bins under non-uniform bin selection probabilities, this paper investigates heterogeneous bins, where the "capacities" of the bins might differ significantly. We show that heterogeneous environments can even help to distribute the load more evenly, and that the load difference between bins can be bounded by 0(log log n) if each ball has two random choices, where n is the number of bins. Our analysis and simulation results show, for the first time, that the maximum load in heterogeneous balls-into-bins games is independent from the overall system capacity C and that bigger bins therefore can help to achieve good load balancing properties.
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