SLIDE 1
1
2
1 2 Single Disk (a) Side view of a magnetic disk. (b) Top view - - PowerPoint PPT Presentation
1 2 Single Disk (a) Side view of a magnetic disk. (b) Top view - - PowerPoint PPT Presentation
1 2 Single Disk (a) Side view of a magnetic disk. (b) Top view of a magnetic disk. 3 Computing Disk Service Time Architecture of a typical I/O subsystem 4 Nomenclature 5 Computing Disk Service Time 6 Computing Disk Service Time Types
SLIDE 2
SLIDE 3
Single Disk
(a) Side view of a magnetic disk. (b) Top view of a magnetic disk.
3
SLIDE 4
Computing Disk Service Time
Architecture of a typical I/O subsystem
4
SLIDE 5
Nomenclature
5
SLIDE 6
Computing Disk Service Time
6
SLIDE 7
Computing Disk Service Time
Types of workloads
7
SLIDE 8
Computing Disk Service Time
8
SLIDE 9
Computing Disk Service Time
9
SLIDE 10
Computing Disk Service Time
10
SLIDE 11
Disk service times equations
11
SLIDE 12
Example: a DB Server
Arrival rate: 20 req/sec Workload: 20% random 80% sequential avarege run length = 24 Block size: 2,048 bytes Disk Revolution Time: 7,200 RPM Seek Time: 9 msec Transfer Rate: 20 MB/sec Controller Time: 0.1 msec ⇒ Latency = ½ x 60/7,200 x 1,000 = 4.17 msec
12
SLIDE 13
⇒ TransferTime = 2,048/(106 x 20) x 1,000 = 0.1 msec ⇒ Average Service Time (Random Request) = 0.1+ 9 +4.17 + 0.1 =13.4 msec Ud = ArrivalRate x (RandomSeek + AverageLatency + AverageTransferTime) ⇒ Ud = 0.020 x (9+4.17+0.1) = 0.27 ⇒ Pmiss = 1/24 = 4.2 % ⇒ AverageSeekTime = 9/24 = 0.38 msec ⇒ AverageRotationalLatency = ½+23(1+0.27)/2 x 60x1,000 = 5.25 msec 24 7,200
13
SLIDE 14
⇒ Average Service Time (Sequential Request) = 0.1+ 0.38 +5.25 + 0.042x0.1 =5.73 msec ⇒ Average Service Time = 7.25 msec
14
SLIDE 15
Disk Arrays
Disk array
15
SLIDE 16
16
SLIDE 17
17
SLIDE 18
18
SLIDE 19
19
SLIDE 20
20
SLIDE 21
Nomenclature
- nr : number of stripe units reads by a read request
- nw : number of stripe units modified by a write request
- λr
array: arrival rate of read requests to the disk array
- λw
array: arrival rate of write requests to the disk array
- λr
disk: arrival rate of read requests to any of the disk in the array
- λw
disk: arrival rate of write requests to any of the disk in the array
- N: number of physical disks in the array
- Sr
array: average service time at a disk array for read
- Sw
array: average service time at a disk array for write
21
SLIDE 22
- Fraction of read requests to the array that goes to any of the disks
(uniform distribution to all disks):
N nr
- Arrival rate of disk requests at a disk:
w array w r array r r disk
N n rw N n λ λ λ ⋅ + ⋅ = ) (
where
) (
w
n rw
is the number of read request to a disk as a result of
w
n write
requests
- Arrival rate of write requests to any disk in the array:
w array w w disk
N n λ λ ⋅ + = 1
⇒ Average service time of read request at disk array:
{ }
r i disk n i r array
R S
r
1
max = = 22
SLIDE 23
where Rr
disk i is the average response time of read requests at disk i :
⇒ Average service time of write request at disk array:
{ } { }
w i disk n i r i disk n rw i w array
R R S
w w
1 1 ) ( 1
max max
+ = =
+ =
where Rw
disk i is the average response time of write requests at disk i.
23