Performance Metrics - Computer Systems Performance Evaluation - Lecture Slides, Slides of Computer Science

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Performance

Engineering

Performance Metrics

All About Numbers

Arrivals ------> RESOURCE ------> Departures

B is the length of time that the resource was observed to be BUSY.

Note that the pictures may be equivalent; a system may have only one resource. A request

is presented to a system ( in which case it might be called a "job") or is presented to a

particular resource.

Metric Description Formula Units

Arrival Rate How many requests arrive per time.

Y = A / T (^) Requests/second

Throughput (Departure Rate)

How many requests complete per time.

X = C / T Requests/second

Utilization Fraction of time the resource is in use.

U = B / T (^) Number in range 0 - 1.

Service Requirement

Time needed by a resource to handle a request.

S = B / C Seconds

Requests in system Average number of requests in the system.

N = W / T Dimensionless

Residence time Average time a request spends in the system.

R = W / C Seconds

UTILIZATION LAW U = X S

Proof: B / T = C / T * B / C

Example:

The server of dinners in the Cafeteria keeps busy 75% of the time between 12:00 and 1:00. During this time 90 people are served a dinner. How long does it take to serve each customer?

Requests

Time ( seconds )

Y = A / T Arrival rate =

X = C / T Throughput = R = W / C Residence Time = U = B / T Utilization = S = B / C Service time/request = N = W / T Average number of =

requests in the system.

T Time interval =

A Arrivals =

C Completions =

B Time spent servicing =

requests

W Accumulated time =

within system

Example:

One day I was at the Weston Toll Booth on the Mass Pike. There were 10 collectors

working; when I joined the line, there were 8 cars ahead of me, and when my turn

came it took me 12 seconds to pay my toll.

What information can be derived from the above paragraph? What information can NOT

be deduced?

Example:

Recently in "Newsweek" it was reported that the current U.S. divorce rate is 4.6 per 1000

adults. It was also reported that half of all adults are currently married.

Develop a simple model/picture in order to make some sense of these numbers.

Some more practice problems:

Example:

Packets arrive at a gateway at a rate of 125 packets/second. The gateway takes an

average of 2 milliseconds to forward them.

What is the Throughput, Service Time, and Utilization.

Example:

A system has a CPU, Disk A, and Disk B. The throughputs of these devices are XCPU = 35.48,

XA = 15.70, X B = 19.6. We also know that the Queue lengths are QCPU = 8.88, Q A =

3.19, QB = 1.40.

What are the device response times for these devices?

Example:

On the campus, there are a number of graduate students who have varying degree and

course requirements. Build a model using duration of time until their degree, as well as

the fraction of time in school.

What is the service time, residence time, of a graduate student? What is the throughput

of the CS Graduate School?