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The HDFS NameNode ensures that each block is sufficiently replicated. When it detects the loss of a DataNode, it instructs remaining nodes to maintain adequate replication by creating additional block replicas.

For each lost replica, the NameNode picks a (source, destination) pair where the source is an available DataNode with another replica of the block and the destination is the target for the new replica. The re-replication work can be massively parallelized in large clusters since the replica distribution is randomized.

In this article, we estimate a lower bound for the recovery time.

Simplifying Assumptions

  1. The maximum IO bandwidth of each disk is 100MB/s (reads + writes). This is true for the vast majority of clusters that use spinning disks.
  2. The aggregate IO capacity of the cluster is limited by disk and not the network. This is not always true but helps us establish lower bounds without discussing network topologies.
  3. Block replicas are uniformly distributed across the cluster and disk usage is uniform. True if the HDFS balancer was run recently.

Theoretical Lower Bound

Let's assume the cluster has n nodes. Each each node has p disks, and the usage of each disk is c TeraBytes. The data usage of each node is thus (p ⋅ c) TB.

The amount of data data transfer needed for recovery is twice the capacity of the lost DataNode as each replica must be read once from a source disk and written once to the target disk.

Data transfer during recovery   = 2 ⋅ (Node Capacity)
                                = (2 ⋅ p ⋅ c) TB
                                = (2 ⋅ p ⋅ c ⋅ 1,000,000) MB

The re-replication rate is the limited by the available aggregate IO bandwidth in the cluster:

Cluster aggregate IO bandwidth  = (Disk IO bandwidth) ⋅ (Number of disks)
                                = (100 ⋅ n ⋅ p) MB/s

Thus

Minimum Recovery Time = (Data transfer during recovery) / (Cluster aggregate IO bandwidth)
                      = (2 ⋅ p ⋅ c ⋅ 1,000,000) / (100 ⋅ n ⋅ p)
                      = (20,000 ⋅ c/n) seconds.

where: c = Mean usage of each disk in TB.
       n = Number of DataNodes in the cluster.

This is the absolute best case with no other load, no network bandwidth limits, and a perfectly efficient scheduler.

E.g.

In a 100 node cluster where each disk has 4TB of data, recovery from the loss of a DataNode must take at least (20,000 ⋅ 4) / 100 = 800 seconds or approximately 13 minutes.

Clearly, the cluster size bounds the recovery time. Disk capacities being equal, a 1000 node cluster can recover 10x faster than a 100 node cluster.

A More Practical Lower Bound

The theoretical lower bound assumes that block re-replications can be instantaneously scheduled across the cluster. It also assumes that all cluster IO capacity is available for re-replication whereas in practice application reads and writes also consume IO capacity.

The NameNode schedules 2 outbound replication streams per DataNode, per heartbeat interval to throttle re-replication traffic. This throttle allows DataNodes to remain responsive to applications. The throttle can be adjusted via the configuration setting dfs.namenode.replication.max-streams. Let's call this m and the heartbeat interval h.

Also let's assume the mean block size in the cluster is b MB. Then:

Re-replication Rate = Blocks Replicated cluster-wide per heartbeat interval
                    = (n ⋅ m/h) Blocks/s

The total number of blocks to be re-replicated is the capacity of the lost node divided by the mean block size.

Number of Blocks Lost = (p ⋅ c) TB / b MB
                      = (p ⋅ c ⋅ 1,000,000/b).

Thus:

Recovery Time = (Number of Blocks Lost) / (Re-replication Rate)
              = (p ⋅ c ⋅ 1,000,000) / (b ⋅ n ⋅ m/h)
              = (p ⋅ c ⋅ h ⋅ 1,000,000) / (b ⋅ n ⋅ m) seconds.

where: p = Number of disks per node.
       c = Mean usage of each disk in TB.
       h = Heartbeat interval (default = 3 seconds).
       b = Mean block size in MB.
       n = Number of DataNodes in the cluster.
       m = dfs.namenode.replication.max-streams (default = 2)

Simplifying by plugging in the defaults for h and m, we get

Minimum Recovery Time (seconds) = (p ⋅ c ⋅ 1,500,000) / (b ⋅ n)

E.g. in the same cluster, assuming the mean block size is 128MB and each node has 8 disks, the practical lower bound on recovery time will be 3,750 seconds or ~1 hour.

Reducing the Recovery Time

The recovery time can be reduced by:

  1. Increasing dfs.namenode.replication.max-streams. However, setting this value too high can affect cluster performance. Note that increasing this value beyond 4 must be evaluated carefully and also requires changing the safeguard upper limit via dfs.namenode.replication.max-streams-hard-limit.
  2. Using more nodes with smaller disks. Total cluster capacity remaining the same, a cluster with more nodes and smaller disks will recover faster.
  3. Avoiding predominantly small blocks.
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