Distributed selfish load balancing on networks

Abstract

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We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m > n selfish agents that unilaterally decide to move from one vetex to another if this improves their experienced load. We present several protocols for concurrent migration that satisfy desirable properties such as being based only on local information and computation and the absence of global coordination or cooperation of agents. Our main contribution is to show rapid convergence of the resulting migration process to states that satisfy different stability or balance criteria. In particular, the convergence time to a Nash equilibrium is only logarithmic in m and polynomial in n, where the polynomial depends on the graph structure. Using a slight modification with neutral moves, a perfectly balanced state can be reached after additional time polynomial in n. In addition, we show reduced convergence times to approximate Nash equilibria. Finally, we extend our results to networks of machines with different speeds or to agents that have different weights and show similar results for convergence to approximate and exact Nash equilibria.