Repair bandwidth cost of generalized regenerating codes for clustered distributed storage

When repairing storage nodes in a clustered distributed storage system (CDSS), it is crucial to distinguish the intra-cluster and inter-cluster bandwidth costs differing sharply. From this perspective, Generalized Regenerating Codes (GRCs) involving two-layer repair processes was proposed previous and proved as reaching a better trade-off between storage overhead and inter-cluster repair bandwidth. However, due to the lack of explicit expression about the GRCs' parameters for any point on the trade-off curve, it is difficult to determine the optimal GRCs' parameter configuration for reducing the total repair bandwidth cost in a practical CDSS. To address this issue, we devise a novel transmission cost model of CDSS, and initially propose two essential concepts - Cost Coefficient (CC) and Global Repair Bandwidth Cost (GRBC) to denote the unit and total transmission costs of repair bandwidths, respectively. Moreover, we parameterize the two extreme points on the optimal storage overhead versus repair bandwidth trade-off curve, termed Minimum Storage Generalized Regenerating Codes (MS-GRCs) and Minimum Inter-cluster Bandwidth Generalized Regenerating Codes (MB-GRCs), and theoretically analyze the relationships between their GRBCs and the number of local helper nodes £ (the helper nodes in the cluster with failure node). Our mathematical results provide a guidance for employing GRCs to achieve the more efficient node repairing method in CDSS