$2-$ RAID

The questions that follow ask you to estimate the time taken to perform read or write operations in RAID systems. A single time unit is considered to be the time to read or write a single block on a disk. The components of those reads or writes $($i$.$e$.$ seek time, rotational delay and transfer time$)$ should not be considered.

When assessing the time taken to perform writes your answer should comply with the following rule: data disks may not be written to at the same time as writing to check or mirror disks. This means that for writes no check disk should be written to during the write of any data disk though data disks may be written to in parallel with other data disks and check disks may be written to in parallel with other check disks. This rule does not mention reads so any read may be performed in parallel with any read or write. RAID systems with distributed parity do not have dedicated check disks. For such systems if a disk is writing $($DB$)$ data it is counted as a data disk, whereas if it is writing parity $($check$)$ data it is counted as a check disk.

Each RAID system is to contain four disks worth of data. This means that each system will consist of at least four disks and, in some cases, one or more additional disks containing redundant data.

Example $1$

In the best case how many time units are required to write $4$ unrelated blocks in a single HDD$?$

Answer: $8.$ Read and write each block. In a single disk two blocks cannot be read $($or written$)$ at the same time.

Example $2$

How many time units are required to read a sequence of $16$ blocks in a $(4-$disk$)$ RAID $0$ system?

Answer: $4.$ Since the data is striped across all four disks, $4$ blocks can be read in parallel in $1$ time unit.

Questions

For each question you must give the number of time units and a brief explanation for your answer. For reads or writes of unrelated blocks assume that the block positions of the requests on the disks of the RAID systems are always different. That is$,$ any two of the unrelated blocks are never on the same block position on two different disks. For example, in a request to write two unrelated blocks on a $4-$disk RAID system, the two blocks would not be stored on the same block i on any two of the disks.

In the best case how many time units are required to read $4$ unrelated blocks in a RAID $0$ system?

In the worst case how many time units are required to read $4$ unrelated blocks in a RAID $0$ system?

In the best case how many time units are required to read $4$ unrelated blocks in a RAID $10$ system?

In the best case how many time units are required to read a sequence of $80$ blocks in a RAID $10$ system?

In the best case how many time units are required to read $5$ unrelated blocks in a RAID $4$ system?

In the best case how many time units are required to read $5$ unrelated blocks in a RAID $5$ system?

In the best case how many time units are required to write $4$ unrelated blocks in a RAID $0$ system?

In the best case how many time units are required to write $4$ unrelated blocks in a RAID $10$ system?

In the best case how many time units are required to write $4$ unrelated blocks in a RAID $4$ system?

In the best case how many time units are required to write $4$ unrelated blocks in a RAID $5$ system?

In the worst case how many time units are required to write $4$ unrelated blocks in a RAID $5$ system?

A to F: $1$ mark each, G to K: $2$ marks each.