Distributed Selfish Load Balancing with Weights and Speeds

摘要

In this paper we consider neighborhood load balancing in the context of selfish clients. We assume that a network of n processors is given, with m tasks assigned to the processors. 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, where the load of a processor is defined as the weight of its tasks divided by its speed. We investigate a concurrent probabilistic protocol 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 than the load of the task's current processor, 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 previous results for this protocol. 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.