Performance Engineering

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Performance Engineering
Performance Metrics

• Prof. Jerry Breecher

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All About Numbers
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PERFORMANCE METRICS

• In this section, a few of the metrics of
  performance are described. Along with these
  metrics are some simple equations that connect
  together the various quantities. We will
  continue to talk about metrics in a later
  section. In fact, when we get to talking about
  queues, well be spending lots of time looking at
  the interrelations of these concepts.
•  
• Arrivals ------gt SYSTEM ------gt Departures
•  
• T is the length of TIME we observed the system.
• A is the number of request ARRIVALS observed.
• C is the number of request DEPARTURES observed.
• W the ACCUMULATED TIME for all requests within
  the system - time spent both waiting for and
  using resources. It is
•  
•  S requests Tdeparture Tarrival

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PERFORMANCE METRICS

•  
•  
• Arrivals ------gt RESOURCE ------gt 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.

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PERFORMANCE METRICS
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PERFORMANCE METRICS

• Example
•  
• Requests
• 3
• 2 -----------------
  -----------------
• 1 -----------------
  ----------------- -----------------
• -----------------------------------------------
  -----------------------------
• 0 1 2 3 4 5
  6 7 8 9 10
• Time (
  seconds )
•  
• Note that requests are serviced
• simultaneously - it's a multiprocessor?
•  
•  

What are T Time interval A Arrivals C
Completions B Time spent servicing
requests   Y A / T Arrival rate X C
/ T Throughput U B / T Utilization S B /
C Service time/request
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PERFORMANCE METRICS

•  
•  
• 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 1200 and 100. During
  this time 90 people are served a dinner. How
  long does it take to serve each customer?

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PERFORMANCE METRICS

• Requests
• 3 ---------
• 3
• 2 --------------------
  ----
• 2 3
  
• 1 -----------------------------
  -----------------
• 1 2
  3
• -----------------------------------------------
  ----------------------------------
• 0 1 2 3 4 5
  6 7 8 9 10
• 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
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PERFORMANCE METRICS

•   
• LITTLES LAW N X R
•  
• Proof W / T C / T W / C
•  
•  
• Example
• On an average day in the Cafeteria, four people
  are waiting in the sandwich line. Each of the
  two sandwich makers can produce a sandwich in one
  minute. How long must the diners wait in line
  until they are handed a sandwich? How many
  sandwiches can be produced in one hour?

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PERFORMANCE METRICS

•  
• 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 it was reported that the current U.S.
  Marriage rate is 6.8 per 100 adults and the
  divorce rate is 3.6 per 1000 adults. It was also
  reported that 48 of all adults are currently
  married.
•  
• Develop a simple model/picture in order to make
  some sense of these numbers.
•  

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PERFORMANCE METRICS

•  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, XB 19.6. We also know that the Queue
  lengths are QCPU 8.88, QA 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?

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PERFORMANCE METRICS

• SUMMARY OF PERFORMANCE METRICS
•  
•  
• T is the length of TIME we observed the system.
• A is the number of request ARRIVALS observed.
• C is the number of request DEPARTURES observed.
• W is the ACCUMULATED TIME for all requests
  within the system - time spent both waiting for
  and using resources.
• B is the length of time that the resource was
  observed to be BUSY.
•  
• Arrival Rate Y A / T
• Throughput (Departure Rate) X C / T
• Utilization U B / T
• Service Requirement S B / C
• Requests in system N W / T
• Residence time R W / C

UTILIZATION LAW U X S LITTLES LAW N X R