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PERF EVAL (CONT’D)

PERF EVAL (CONT’D). There are many other “tools of the trade” used in performance evaluation Only a few will be mentioned here: queueing theory verification and validation statistical analysis multi-variate analysis presentation of results. Queueing Theory.

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PERF EVAL (CONT’D)

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  1. PERF EVAL (CONT’D) • There are many other “tools of the trade” used in performance evaluation • Only a few will be mentioned here: • queueing theory • verification and validation • statistical analysis • multi-variate analysis • presentation of results

  2. Queueing Theory • A mathematical technique that specializes in the analysis of queues (e.g., customer arrivals at a bank, jobs arriving at CPU, I/O requests arriving at a disk subsystem) • General diagram: Customer Arrivals Departures Server Buffer

  3. Queueing Theory (cont’d) • The queueing system is characterized by: • Arrival process (M, G) • Service time (M, D, G) • Number of servers (1 to infinity) • Number of buffers (infinite or finite) • Example notation: M/M/1, M/D/1 • Example notation: M/M/ , M/G/1/k 8

  4. Queueing Theory (cont’d) • There are well-known mathematical results for the mean waiting time and the number of customers in the system for several simple queueing models • E.g., M/M/1, M/D/1, M/G/1 • Example: M/M/1 • q = rho/ (1 - rho) where rho = lambda/mu < 1

  5. Queueing Theory (cont’d) • These simple models can be cascaded in series and in parallel to create arbitrarily large complicated queueing network models • Two main types: • closed queueing network model (finite pop.) • open queueing network model (infinite pop.) • Software packages exist for solving these types of models to determine steady-state performance (e.g., delay, throughput, util.)

  6. Verification and Validation • An important step in any modeling work (simulation or analytical) is convincing others that the model is “correct” • Verification: develop simple test cases with known inputs; compare to expected outputs • Validation: the “reality check” to see if model predictions agree with real world • Sanity checks (e.g., Little’s Law: N = T) • This V&V process is often overlooked!!!

  7. Statistical Analysis • “Math and stats can be your friends!!!” CW • There are lots of “standard” techniques from mathematics, probability, and statistics that are of immense value in performance work: • confidence intervals, null hypotheses, F-tests, T-tests, linear regression, least-squares fit, maximum likelihood estimation, correlation, time series analysis, transforms, Q-Q, EM... • working knowledge of commonly-observed statistical distributions

  8. Multi-Variate Analysis • For in-depth and really messy data analysis, there are multi-variate techniques that can be immensely helpful • In many cases, good data visualization tools will tell you a lot (e.g., plotting graphs), but in other cases you might try things like: • multi-variate regression: find out which parameters are relevant or not for curve fitting • ANOVA: analysis of variance can show the parameters with greatest impact on results

  9. Presentation of Results • Graphs and tables are the two most common ways of illustrating and/or summarizing data • graphs can show you the trends • tables provide the details • There are good ways and bad ways to do each of these • Again, it is a bit of an “art”, but there are lots of good tips and guidelines as well

  10. Table Tips • Decide if a table is really needed; if so, should it be part of main paper, or just an appendix? • Choose formatting software with which you are familiar; easy to import data, export tables • Table caption goes at the top • Clearly delineate rows and columns (lines) • Logically organize rows and columns • Report results to several significant digits • Be consistent in formatting wherever possible

  11. Graphing Tips • Choose a good software package, preferably one with which you are familiar, and one for which it is easy to import data, export graphs • Title at top; caption below (informative) • Labels on each axis, including units • Logical step sizes along axes (10’s, 100’s…) • Make sure choice of scale is clear for each axis (linear, log-linear, log-log) • Graph should start from origin (zero) unless there is a compelling reason not to do so

  12. Graphing Tips (cont’d) • Make judicious choice of type of plot • scatter plot, line graph, bar chart, histogram • Make judicious choice of line types • solid, dashed, dotted, lines and points, colours • If multiple lines on a plot, then use a key, which should be well-placed and informative • If graph is “well-behaved”, then organize the key to match the lines on the graph (try it!) • Be consistent from one graph to the next wherever possible (size, scale, key, colours)

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