Trade-off between fairness and efficiency in dominant alpha-fairness family

摘要

We propose dominant a-fairness including proportional fairness and dominant resource fairness and study tradeoff between fairness and efficiency over it. Decomposing a resource demand vector into two components, called the dominant resource demand vector and the normalized resource demand vector, we find that resource usage is completely decided by normalized resource demand vector and that total throughput is more influenced by dominant resource demand vector than normalized resource demand vector in dominant a-fairness. The most interesting result is the existence of explicit trade-off between fairness and resource usage for the case of two resources in the sense that a fair resource allocation leaves a big amount of unused resources. This result assures that fairness is indeed achieved at the cost of efficiency for two resources, which has not been clearly observed when throughput is used as an efficiency metric even for two different resources. We also find a counter example of the trade-off between fairness and resource usage for three resources case. Our results raise an interesting question, “Is there an efficiency metric showing trade-off between fairness and efficiency for more than two resources?”.