CS152
Computer Architecture and Engineering
Lecture 24
I/O and Storage Systems
April 29, 2004
John Kubiatowicz (www.cs.berkeley.edu/~kubitron)
lecture slides: http://inst.eecs.berkeley.edu/~cs152/
4/28/04
©UCB Spring 2004
CS152 / Kubiatowicz
Lec24.2
Recap: Nanolayered Disk Heads
°
Special sensitivity of Disk head comes from “Giant
MagnetoResistive effect” or (GMR)
°
IBM is leader in this technology
•
Same technology as TMJRAM breakthrough we described in
earlier class.
Coil for writing
4/28/04
©UCB Spring 2004
CS152 / Kubiatowicz
Lec24.3
Disk Latency = Queueing Time +
Controller time +
Seek Time + Rotation Time + Xfer Time
Order of magnitude times for 4K byte transfers:
Average Seek: 8 ms or less
Rotate: 4.2 ms @ 7200 rpm
Xfer: 1 ms @ 7200 rpm
Recap: Disk Device Terminology
4/28/04
©UCB Spring 2004
CS152 / Kubiatowicz
Lec24.4
Disk I/O Performance
Response time = Queue + Device Service time
100%
Response
Time (ms)
Throughput
(Utilization)
(% total BW)
0
100
200
300
0%
Proc
Queue
IOC
Device
Metrics:
Response Time
Throughput
latency goes as
T
ser
×u/(1u)
u = utilization
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4/28/04
©UCB Spring 2004
CS152 / Kubiatowicz
Lec24.5
°
Queueing Theory applies to long term, steady state
behavior
⇒
Arrival rate = Departure rate
°
Little’s Law
:
Mean number tasks in system = arrival rate x mean
reponse time
•
Observed by many, Little was first to prove
•
Simple interpretation: you should see the same number of
tasks in queue when entering as when leaving.
°
Applies to any system in equilibrium, as long as
nothing in black box is creating or destroying tasks
“Black Box”
Queueing
System
Arrivals
Departures
Introduction to Queueing Theory
4/28/04
©UCB Spring 2004
CS152 / Kubiatowicz
Lec24.6
°
Server spends a variable amount of time with customers
•
Weighted mean
m1
= (f1 x T1 + f2 x T2 +...+ fn x Tn)/F
=
Σ
p(T)xT
•
σ
2
=
(f1 x T1
2
+ f2 x T2
2
+...+ fn x Tn
2
)/F – m1
2
=
Σ
p(T)xT
2
 m1
2
•
Squared coefficient of variance
:
C =
σ
2
/m1
2

Unitless measure (100 ms
2
vs. 0.1 s
2
)
°
Exponential distribution
C = 1
: most short relative to average, few others
long; 90% < 2.3 x average, 63% < average
Hypoexponential distribution
C < 1
: most close to average,
C=0.5 => 90% < 2.0 x average, only 57% < average
Hyperexponential distribution
C > 1
: further from average
C=2.0 => 90% < 2.8 x average, 69% < average
Avg.
A Little Queuing Theory: Use of random distributions
Avg.
0
Proc
IOC
Device
Queue
server
System
4/28/04
©UCB Spring 2004
CS152 / Kubiatowicz
Lec24.7
°
Disk response times
C
≈
1.5
(majority seeks < average)
°
Yet usually pick
C = 1.0
for simplicity
•
Memoryless, exponential dist
•
Many complex systems well described
by memoryless distribution!
°
Another useful value is average time
must wait for server to complete current task:
m1(z)
•
Called “Average Residual Wait Time”
•
Not just 1/2 x m1 because doesn’t capture variance
•
Can derive
m1(z) = 1/2 x m1 x (1 + C)
•
No variance
⇒
C= 0 => m1(z) = 1/2 x m1
•
Exponential
⇒
C= 1 => m1(z) = m1
A Little Queuing Theory: Variable Service Time
Proc
IOC
Device
Queue
server
System
Avg.
0
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 Spring '04
 Kubiatowicz
 Computer Architecture, Input/output, Queueing theory, access time, Seek time, Rotational delay, Memorymapped I/O

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