Distributed Selfish Load Balancing with Weights and Speeds

In this paper we consider neighborhood load balancing in the context of selfish clients. We assume that a network of n processors and m tasks is given. The processors may have different speeds and the tasks may have different weights. Every task is controlled by a selfish user. The objective of the user is to allocate his/her task to a processor with minimum load. We revisit the concurrent probabilistic protocol introduced in [6], which works in sequential rounds. In each round every task is allowed to query the load of one randomly chosen neighboring processor. If that load is smaller the task will migrate to that processor with a suitably chosen probability. Using techniques from spectral graph theory we obtain upper bounds on the expected convergence time towards approximate and exact Nash equilibria that are significantly better than the previous results in [6]. We show results for uniform tasks on non-uniform processors and the general case where the tasks have different weights and the machines have speeds. To the best of our knowledge, these are the first results for this general setting.

💡 Research Summary

The paper studies selfish load balancing in a distributed setting where both processors and tasks may be heterogeneous: each processor i has a speed s_i (scaled so that the minimum speed is 1) and each task ℓ carries a weight w_ℓ∈(0,1]. The system is modeled as an undirected graph G=(V,E) with |V|=n processors and m tasks initially placed on the nodes. A task’s experienced load is defined as the total weight on its current processor divided by that processor’s speed. Each selfish user wants to minimize this load by possibly migrating its task to a neighboring processor.

The authors revisit a concurrent probabilistic protocol introduced in previous work