2.2 Reducing Rotational Delay

  

Figure 2: Techniques for reducing rotational delay. (a) Randomly placed replicas. (b) Evenly spaced replicas. (c) Replicas placed on different tracks (either within a single disk or on different disks).

As we reduce the average seek distance, the rotational delay starts to dominate the disk access cost. To address this limitation, we replicate data at different rotational positions, and by choosing a replica that is rotationally closest to the disk head, we can reduce rotational delay. Replication for reducing rotational delay can increase seek distance by pushing data farther apart. We will discuss combining the techniques for reducing seek and rotation distance in a later section.

If the time needed to complete a rotation on a single disk is R, we observe that the average rotational delay R_r(1) is simply half of a full rotation, i.e. R_r(1)=R/2. If we replicate data D times, and spread the replicas evenly on a track (i.e. 360/D degrees apart from each other as shown in Figure 2(b)), the average read rotational latency R_r is:

$$R_{r}(D)=\frac{R}{2D}%$$ (2)

We can also show that the average read rotational latency is $R_{r}=R/\left( D+1\right)$, if we randomly place replicas (shown in Figure 2(a)) on the same track. This technique is therefore less beneficial than evenly distributing the replicas and is not used in our design.

However, having multiple replicas on one track increases average rotational latency R_w for writing all these replicas to:

$$R_{w}(D)=R-\frac{R}{2D}%$$ (3)

Of course, we could reduce the write costs by writing the closest copy synchronously and propagating other copies during idle periods. Equation (3) gives the worst case cost when we are not able to mask the replica propagation. Notice that R_r(D) + R_w(D) = R. Thus if reads are more frequent than writes, making more replicas will reduce overall latency. If reads and writes are equally frequent, varying D will not change the average overall latency. If writes are more frequent than reads, the approach with no replication is always the best. Note that this relationship is independent of the value of R and is only true for foreground replica propagation. Background propagation may make replication desirable even when writes outnumber reads.

Figures 2(a) and (b) illustrate the concept of rotational replication by making copies within the same track. Unfortunately, this decreases the bandwidth of large I/O as a result of shortening the effective track length and increasing track switch frequency. To avoid unnecessary track switches, we place the replicas on different tracks either within a cylinder of a single disk or on different disks (shown in Figure 2(c)). Track skews must be re-arranged so that large sequential I/Os that cross track boundaries do not suffer any unnecessary degradation.