TACD: A throughput allocation method based on variant of Cobb-Douglas for hybrid storage system

摘要

The development of the cloud and data centers alike has caused users to increasingly share storage systems, and storage systems have adopted SSDs to improve performance. The number of users is growing sharply and causing resource competition, so the throughput allocation of a hybrid storage system has an important effect on users' performance. A hybrid storage architect faces a challenge: sharing I/O throughput resources between SSDs and HDDs fairly with high resource utilization. Drawing on economic game-theory, many methods based on Leontief preference have been proposed to determine fair throughput allocation in a hybrid storage system with having the properties of Sharing Incentive (SI), Envy Freeness (EF) and Pareto Optimality (PO). However, users' workload characteristics vary because of the adoption of SSDs, so there is heterogeneity among the storage media. The heterogeneity of storage media and the diversity of user workloads together create more constraints on fairness, which imposes restrictions to improve the resource utilization. To improve the resource utilization, some researchers have proposed relaxing the limitation of fairness properties by adjusting users' allocations. However, when adjusting the allocation between users, some users' allocations are reduced but others' are improved, with the goal of increasing the resource utilization of the whole system, this will pose a problem because of the Leontief preference restriction: some users' performance is degraded, while other users' performance is improved.In this paper, we first propose one variant of the Cobb-Douglas preference based on users' workloads and allocations, and then present a throughput allocation model based on this variant named TACD that can capture the effects of diminishing returns and substitutability in throughput allocation for hybrid storage. By making use of these effects, TACD can improve some users' performance while providing the same performance for other users and achieving higher resource utilization in the whole system, and it can provide a fair allocation while enjoying SI, EF and PO properties. The variant of the Cobb-Douglas preference proposed in this paper has taken consideration of users' workloads, so TACD can conduct the throughput allocation based on these workloads for meeting the performance requirements of users reasonably. Extensive experiments are conducted to prove the effectiveness of TACD. The simulation results show that TACD can fit the throughput allocation of hybrid storage system very well. The Linux results show that compared with the allocation method based on Leontief preference, TACD can provide a higher resource utilization and performance for users throughout the system, it can improve some users' performance when maintaining comparable performance for other users, in contrast to the Leontief method based on weaker fairness under the same resource utilization, and its allocation result enjoys SI, EF and PO properties. (C) 2019 Elsevier Inc. All rights reserved.