a note on computer system data gathering - Core

A NOTE ON COMPUTER SYSTEM DATA GATHERING

J a c k P.C.

Kleijnen

Katholieke Hogeschool Tilburg, Netherlands

Recently Orchard

(1977)

proposed

statistical

technique

in c o m p u t e r

systems.A main

use of r a n d o m traditional He

sampling,

(Boolean)

the to

sampling.

to d e r i v e

confidence

estimator.

e.g.,

time t the

is o c c u p i e d

qit = 1 ith

(or 0)

"slot"

(or e m p t y

of

respective-

ly).

author's intervals

however,

as I u n d e r s t a n d

exposE,

the d e r i v e d

observations.

is v i o l a t e d

s u c h as c o m p u t e r

confidence

This

systems

For

suppose

s y s t e m is h e a v i l y 1 for all

that

loaded,

i-values.

sampling moment,

systems

).

on q i t

are s e r i a l l y

More

generally,

then

in w h a t e v e r

if

tives

the o b s e r -

correlated!

is a t i m e

o r d e r we o b s e r v e

some of t h e s e qt' serial

qt

lightly

series, all or

we are c o n f r o n t e d w i t h

correlation. (1975,

454-468)

are d i s c u s s e d

correlation

three

alterna-

for t a c k l i n g t h e

auto-

problem:

(i) E s t i m a t e

the s e r i a l

correlation

at t=t I the

say t=t 2

t uniformly

to m a k e

distributed;

see pp.

33-34)

Suppose

slightly

larger

t h a n t I . Then the p r o b a b i -

t h a t , s a y , q l t 2 = 1 is h i g h e r

out

"sufficiently"

so t h a t the d e p e n d e n c e

m a y be

ignored. (3) m a k e o b s e r v a t i o n s

during

which

because

are

independent

Besides

"epochs"

of c e r t a i n

the v a r i a b i l i t y

estimator.

the

(Orchard

t2turns

far apart,

one s h o u l d c o n s i d e r

so t h a t Sample

the o b s e r v a t i o n s

of t h e stochastic

systems.

proposed

56

vations

"rene~-al" D r o p e r t y

(or t h e i r

simulation models

instance,

of

assumption,

in d y n a m i c

corresponding

lity

l o a d e d at t=t 1. In o t h e r w o r d s ,

(2) T a k e

the

d e p e n d on the a s s u m p t i o n

independent

next

if the s y s t e m w e r e

coefficients.

Unfortunately,

qitl

have been

In K l e i j n e n

the use of b i n a r y

variables,

if at s a m p l i n g a queue

as o p p o s e d

for the r e s u l t i n g

He a l s o p r o p o s e d

collection

idea was

fixed periodic

further proceeded

intervals

for d a t a

would

a

to be

than it

the b i a s of the

Observing

at f i x e d or u n i f o r m l y

a stochastic distributed

of time m a y c r e a t e bias, is not ~ a r k o ~ i a n services

of the e s t i m a t o r

process points

if the p r o c e s s

(Poisson arrivals

in a q u e u i n g

system).

This

and can

be seen i n t u i t i v e l y in c a s e the p r o c e s s (continued on page 62)

Performance

Prediction

(continued)

DRUM-2 Correlation Coefficient = 0.92372 STD. Error = 1.4405

ii. Smith, J. C., "Multiprogramming Under Page on Demand Strategy", CACM, i0 (1967). 12. Teorey, T. J. and T. B. Pinkerton, "A Comparitive Analysis of Disk Scheduling PoliCies", Proc. 3rd Symp. O/S Princ. (Oct. 1971).

P r e d i c t i o n Equation Z = - 3.0591 + 30.8241X 3 + 1.3222.P

A

NOTE

ON

COMPUTER

SYSTEM

....

+ 3.2817 XM - ii.5977.X

(continued

2 + 0.055026 X.M.P - 0.059479P DRUM-3 Correlation Coefficient = 0.75131

shows

periodic

unbiased

from

measurements

times"

page

behavior.

between

To

56) obtain

the"interarrival

sampling

points

should

be

STD. Error = 3.36743 Prediction Equation z = 4.8829 + 44.3342x 3 + 0.00124 X.M.C + 0.04877 x.c + 0.023718c -

exponentially

distributed:

measurement Another

Poissoln

process. issue

that

deserves

mentioning

0.003622 M 3 + 0.001363M.C

Legend:

Z = T h r o u g h p u t (no. of jobs/unit time M = M u l t i p r o g r a m m i n g Level P = No. of Pages of Memory (iK. Page Size) S = Paging Speed (in sec) X = Job Mix (Percent)

REFERENCES i. Abate, J., H. Dubner, and S. B. Weinberg, "Queuing Analysis of the IBM 2314 Disk Storage Facility", JACM, 15, 4 (1968). 2. Coffman, E. A. and T. A. Ryan, "A study of Storage P a r t i t i o n i n g Using M a t h e m a t i c a l Model of Locality," CACM, Vol. 15, No. 3, 1972. 3. Coffman, E. G. and L. C. Varian, "Further Experimental Data on the Behavior of Programs in a Paging Environment", CACM, Vol. ii, 5, 1968. 4. Denning, P. J., "The W o r k i n g Set Model for P r o g r a m Behavior", CACM, ii, 5, 1968. 5. Denning, P. J.," J. E. Savage and J. R. Spirn, "Models of Locality in Programs Behavior," TR-107, Dept. of Electrical Engineering, P r i n c e t o n u n i v e r s i t y (1972). 6. Fine, G. H., C. W. Jackson and P. V. McIssac, "Dynamic Program Behavior Under Paging", Proc. Natl. ACM, 21st, (1966). 7. Kuck, D. J. and D. H. Laurie, "The Use and Performance of Memory Hierarchies: A Survey", Software Engineering, vol. l, Julius Ton, Ed., Academic Press (1970). 8. Rodriguez-Rosell, J., "Experimental Data on H o w Programs Behavior Affects Choice of Scheduling Parameters", Proc. 3rd ACM Symp. on o/s Princ. (1971). 9. Seaman, P. H., R. A. Laird and T. L. Wilson, "On T e l e p r o c e s s i n g System Design. Pt. IV.-Analysis of A u x i l i a r y Storage Activity", IBM System J., Vol. 5, No. 3, 1966. i0. Shedler, G. S. and C. Tung, "Locality in Page Reference Strings", SIAM J. Comput. i,

is

sequential

since one

~ may

mate

in

(3~

This

Orchard's

start

s 2,

eq.

is

Kleijnen sequential

discussed

into

update

at

pp.

s 2,

also

in Note

applies

that

to

bi-

sampling

Orchard,

other

further

(1975, variance

more

see

is

briefly

analyzed

pp.

110-133).

reduction

attractive,

Kleijnen

discussed

(1975,

in However,

techniques

e.g.

control

p.p.

i05-285),

may variotes;

References: i.

Kleijnen,g.P.C.,

IN

SIMULATION.(In

Inc., 2.

New

Orchard,

computer

STATISTICAL two

York,

Marcel

Dekker

1974/1975.

R.A., system

volumes)

TECHNIQUFS

A new

methodology

data

gathering.

EVALUATION

REVIEW,

for

3 (1972).

PERFO~NCE Fall

62

etc.

several

length

479-506).

esti-

variables.

Kleijnen

be

an

approach(and

sampling

Stratified by

Unknown,

estimate

sampling,

(1975,

is

compute

this

efficient

instance, (3)

sampling,

continue

variants)

For eq.

substitute

more

nary

sampling.

1977,

pp.

27-41.

6,

no.4,