The Storage vs Repair Bandwidth Trade-off for Multiple Failures in Clustered Storage Networks

摘要

We study the trade-off between storage overhead and inter-cluster repairbandwidth in clustered storage systems, while recovering from multiple nodefailures within a cluster. A cluster is a collection of $m$ nodes, and thereare $n$ clusters. For data collection, we download the entire content from any$k$ clusters. For repair of $t \geq 2$ nodes within a cluster, we take helpfrom $\ell$ local nodes, as well as $d$ helper clusters. We characterize theoptimal trade-off under functional repair, and also under exact repair for theminimum storage and minimum inter-cluster bandwidth (MBR) operating points. Ourbounds show the following interesting facts: $1)$ When $t|(m-\ell)$ thetrade-off is the same as that under $t=1$, and thus there is no advantage injointly repairing multiple nodes, $2)$ When $t \nmid (m-\ell)$, the optimalfile-size at the MBR point under exact repair can be strictly less than thatunder functional repair. $3)$ Unlike the case of $t=1$, increasing the numberof local helper nodes does not necessarily increase the system capacity underfunctional repair.