Support Materials for Dr. Gunther's CMG Presentations

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Contents

1  CMG 2008: Las Vegas, Nevada

1.1  A.A. Michelson Award

1.2  Sunday Workshop: How High Will It Fly?

1. Response times. Once we have calculated the USL model, we can easily compute the expected throughput as X(p) or X(N) and from there, it is a simple matter to calculate the response times for each load level using the formula:
   

   R(N)  =   N X(N) − Z

   (1)

   This formula applies to a closed queueing-system as is valid when the load-test data is generated by a tool like LoadRunner.
   
   
2. Brooks' Law. It turns out that the USL contains Brooks' Law as a special case. This is not obvious because the USL expresses throughput scalability, whereas Brooks' law expresses the corresponding latency picture. See this blog entry for more details.
   
   

1.3  CMG-T: Capacity Planning Boot Camp

1. Session 405: Getting Started (2.7 MB)
   
   
2. Session 415: Metrics and Management (1.3 MB)
   
   
3. Session 425: Going Guerrilla (1.8 MB)
   
   

1.4  Paper 8066: Object Measure Thyself

1.5  Paper 8143: Multidimensional Visualization of Oracle Performance Using Barry007

2  CMG 2007: San Diego

2.1  Hot Topics Session #511: Seeing It All at Once with Barry

Improving data visualization paradigms for performance management is an orphaned area of tool development. Performance tool vendors avoid investing in development if they do not see a demand, while capacity planners and performance analysts cannot demand what they have not conceived. We attempt to cut this Gordian knot with Barry: a 3D performance visualization suite based on barycentric coordinates.

Potentially thousands of active processors, servers, network segments or applications can be viewed as a moving cloud of points that produces easily comprehended visual patterns due to correlations in the workload dynamics. Barry provides an optimal impedance match between the measured computer system and the cognitive computer system (i.e., your brain).

Certainly we do not understand all the neural circuitry of the brain (which appears to be a very novel kind of non-Von Neumann parallel distributed-computer), but we do know quite a lot about certain pieces of the brain's neural circuitry and in particular the visual system. The most recent research suggests that the retina appears to form a sequence of movie-like frames containing data akin to colorized fourier transforms. A dominant feature of the brain in general, and the visual cortex in particular, is that it is an excellent differential analyzer.

Performance Metric Eye Candy
MacSpin	Barry-3	3-Simplex	Barry4

MacSpin

MacSpin is a facsimile of the program originally developed for the Macintosh computer c.1988, which applied John Tukey's concept of rotating or spinning data sets in virtual 3-space with the mouse. The 3 attributes shown here are taken from the original CRCars automobile data viz., horsepower, weight, model year. In general, the data appear as a 3-dimensional scatterplot, but as the cube rotates you will see that the otherwise random data exhibit bands at certain viewing angles. This is not at all obvious without the ability to swivel the coordinate system.

Barry-3

Barry-3 displays CPU utilization for a 72-way multiprocessor running a network-based workload on ORACLE 10g. The barry-3 axes are:

• %user time (vertical upward increasing, red)
  
  
• %system time (left-right downward increasing, yellow)
  
  
• %idle (right-left downward increasing, blue)
  
  

At 12:36:46, the workload begins to ramp up starting at the lower left corner of the triangle; maximum idleness. Most of the CPUs (shown as colored dots) gradually make their way up the blue idle axis (decreasing idleness) to cluster around the region bounded by the 25% idle line, the 25% sys line and the 50% usr line. However, 3 CPUs peel off at around 10% usr time and rapidly migrate (rightward) to the 80-90% sys location; near the tip of the yellow arrow. These CPUs are dedicated to handling network traffic and other house-keeping. At 12:53:41, the workload completes and all the CPU dots rapidly return to the tip of the blue arrow as they become idle again. Some clean up continues as some of the CPUs are seen to run back and forth along the base of the Barry3 triangle (zero usr time) between idle and system time. The frame rate of 1 second corresponds to 10 seconds of real time, as shown in the clock display. (Data supplied with permission by Time Cook of Sun Microsystems.)

Compare with the application of Barry-3 to the Apdex Alliance response time metrics in Section 2.3 below.

3-simplex

The 3-simplex is a tetrahedron. It is formed by joining the centers of close-packed uniform spheres. Notice that all the edges between the vertices are of equal length. The 4 vertices and their opposite faces provide the basis for the barycentric coordinates. The 3-simplex enables us to display 4 degrees of freedom in 3 (virtual) dimensions; Barry4. In our paper, we conjecture and demonstrate visually, that it is not possible to construct a Barry5 in 3-dimensions. In other words, there is no way to construct a geometric figure with all edges equal, out of close-packed uniform spheres.

Barry-4

Barry-4 is an application of the 3-simplex depecting 4 network performance metrics in three dimensions for 1000 network segments or cloud of points. It is very clear, even without looking closely at the visual area, that the points cluster into 3 sub-clouds along certain viewing angles. This is the barycentric analog of the MacSpin example.

2.2  Barycentric Coordinates Algorithm

    barry3Vtx = {{0, 0}, {1/Sqrt[3], 1}, {2/Sqrt[3], 0}}

• The metrics A, B and C have to be additive in order to satisfy the sum rule requirement.
  
  
• The units of A, B and C have to be of the same type, e.g., all 'apples' or all 'oranges', not 'apples' and 'oranges' mixed together.
  
  

    GetXYBarry3[Counts_List] :=
       (* Created by NJG on Thu Jun 14 14:43:19 PDT 2007 *)
       Module[
          {S, x, y, coords}, 
          (* Argument is a list of A, B, C Integer sample counts. 
          Returns x y Real plot coordinates inside Barry triangle.*)       
          If[!ListQ[Counts], Return["Error: Must be a list."]]; 
          If[Length[Counts] != 3, Return["Error: Must be 3 sample counts."]];
          If[!IntegerQ[Counts[[1]]] || !IntegerQ[Counts[[2]]] || 
              !IntegerQ[Counts[[3]]], Return["Error: Must be integers."]]; 
          A = Counts[[1]];
          B = Counts[[2]];
          C = Counts[[3]];
          S = A + B + C;
          (* A and B order swapped to position A at Barry-3 apex *)
          x = ((barry3Vtx[[1]])[[1]] * B) + ((barry3Vtx[[2]])[[1]] * A) + 
              ((barry3Vtx[[3]])[[1]] * C);
          y = ((barry3Vtx[[1]])[[2]] * B) + ((barry3Vtx[[2]])[[2]] * A) + 
              ((barry3Vtx[[3]])[[2]] * C);
          coords = {x/S, y/S};
          Return[N[coords]];(* Numeric rather than fractions *)
      ]

• Since Mathematica is a functional programming language, even IF statements become functions.
  
  
• Curly braces {..} define a list.
  
  
• The double brackets [[..]] are the Mathematica syntax for indexing into a list.
  
  

   GetXYBarry3[{132, 18, 1}] returns: {0.512351, 0.874172}

2.3  Apdex Alliance Meeting: Triangulating the Apdex Index with Barry-3

Barry-3 Animation of Apdex Measurements

• S: Samples < 4 seconds
  
  
• T: 4 seconds < Samples < 16 seconds
  
  
• F: Samples > 16 seconds
  
  

2.4  Sunday Workshop: How to Move Beyond Monitoring, Pretty Damn Quick!

3  CMG 2006: Reno, NV

3.1  Session: Virtualization: From Hyperthreads to GRIDs

3.2  NorCal CMG Meeting in San Franscisco

• Download my presentation "Scalability on a Stick" (PDF  5MB).
  
  
• The queueing theorem I discovered (that got panned by many "parallel people") can be stated thusly:

  Amdahl's law for parallel speedup is equivalent to the synchronous queueing
  bound on throughput in the repairman model of a multiprocessor.

  It was first published on arXiv in 2002. It provides the justification for applying the same Universal Scalability Law to both software and hardware systems. The Repairman queueing model is discussed in my "Perl PDQ" book. My theorem has recently been demonstrated by my colleague Prof. K. J. Christensen to be correct using simulation and is currently being written up more formally for journal publication.
  
  
• The new Guerrilla book (due out summer 2006) will contain 3 chapters on the Universal Scalability Law.
  
  
• In the meantime, check out The Guerrilla Manual online, and have some fun with you manager and colleagues.
  
  
• You might also get your manager to pay for a Guerrilla training class.
  
  
• Download an EXCEL spreadsheet containing universal scalability models for both hardware and software.
  
  
• Feel free to contact me if you have any other questions or comments.
  
  

4  CMG 2005: North East Regional Meetings

4.1  The Millennium Performance Problems

1. Performance Visualization:
   The idea here is to find ways of representing performance data that are a better impedance match for our cognitive computer (our brain). One role model is the techniques used in so-called Scientific Visualization where physicists and biologists have learned to use things like special GUIs and animation to represent complex data in ways that help them solve problems. Why should they have all the fun?
   
   
2. Self-instrumented Applications:
   Object-oriented programming has been promoted as a good thing primarily for reasons of reusability. If people are going to re-use objects, how about they come with their own instrumentation? This really should be part of the object library so that a programmer need nevre be concerned with adding such code. Then I, as the performance analyst would have the ability to turn objects on selectively and thereby trace paths through application code to find bottlenecks, even on production systems.
   
   
3. The Von Neummann Bottleneck:
   An efficient way to compute something on a machine is to do more than one thing at once. The technical term is parallelism. Unfortunately, despite a lot of intense effort over the last two decades, general-purpose parallelism remains a holy grail of performance analysis. One reason for this barrier seems to stem from the influential success of early electronic computer designers such as Alan Turing and John von Neumann. The fundamental paradigm of sequential programming and operation seem to be almost impossible to break away from in the modern digital computer. But there is an obvious role model for a non-von computer architecture: our brain. This has led to the idea neural networks as way of achieving a higher degree of parallelism. Quantum computers are another.
   
   
4. Performance Analysis of the Internet:
   The results of analyzing Internet packet traces 15 years ago at Bellcore (now Lucent) showed that long-term correlations can persist over several orders of magnitude in time. Packet arrivals are not Poisson, and service times are not constant. In other words, all the conventional queueing theory techniques near and dear to our hearts as performance analysts, are no longer valid at the packet level. How are we to model the Internet? Perhaps we need to think big. The climatologists use things like the Earth Simulator to address complex questions about global warming. Maybe we need an Internet Simulator of similar scale?
   
   
5. Performance Analysis of Quantum Computers:
   Quantum Computers are probably a long way off, but quantum communication devices are already here. The only reason you are not aware of them is because they are expensive and therefore a specialty item for institutions like banks. In the next 3 to 5 years, I believe these things will reach commodity prices and will therefore become more ubiquitous. I am also working on these technologies now. The question for us is, How will they affect performance?
   
   

5  CMG 2004: Las Vegas, NV

5.1  Session #4016: Linux Load Average Revealed

• Download the handout (PDF) (which wasn't available at the session)
  
  
• This topic is also covered in Chap. 4 of my new book Analyzing Computer System Performance wih Perl::PDQ (Springer-Verlag, 2005) which includes examples and problems as well (ISBN: 3540208658)
  
  
• Linux Load Average Reweighed Following my presentation, someone asked me over lunch how the weight factor exp(-5/60) arose in either the Linux code or my paper. The explanation turns out to be almost another paper in its own right! Soon, I will post my analysis on the Web. Watch this space for details.
  
  

6  CMG 2002: Reno, Nevada

6.1  Sunday Workshop: ASAP: Assuring Scalability for Application Performance

• Sunday schedule
  
  
• Download corrected tutorial slides
  
  
• Sample scalability (EXCEL) spreadsheet
  
  
• Attendee Comments:
  1. Jim Holtman (Convergys): Informed me that the free software package called "R" can solve my super-serial equation directly from the (uninverted) scaling measurements. "R" is a subset of the commercial (and expensive) S-PLUS programming language. Amusingly, I've had this package installed on my laptop but never found time to learn to use it.
     
     
  2. NJG: I mentioned that Mathematica can also solve my nonlinear super-serial equation directly. Another free software package called Octave (more like Matlab than Mathematica) may be able to do this but I haven't tried it.
     
     
  
  
  

6.2  Session #454: Sins of Precision-Damaging Digits in Capacity Calculations

• Invited Speaker Session
  
  
• Tools (in VBA, Perl, and Mathematica) accompanying this session.
  
  
• SAS Anyone?
  I don't do SAS but a member of the audience kindly offered to provide a SAS version of the SigFigs code. Please contact me when it becomes available. I will post it with full attribution for your work. Thank you.
  
  
• Answers to Quiz:

  Significant Figures			Rounding Problems
  Problem	Answer	Value	Problem	Answer	Value
  1	(e)	0.00030	1	(e)	0.8
  2	(e)	five	2	(d)	42.3
  3	?1	none	3	(d)	10.3

  
  
  
• Ambiguous cases that arose during the presentation:
  
  1. How many sigfigs in 3600 seconds?

     If we simply apply the rules as presented the answer would be 2 sigfigs. On the other hand, 3600 seconds (per hour) comes from the fact that 1 minute has 60 seconds (1 sigfig) and 1 hour has 60 minutes (1 sigfig). Using the "Golden Rule" requires that 60 * 60 = 3600 should be written as 4000 (i.e., rounded up to 1 sigfig; matching the multiplicand with the least significant digit).
     

     It seems that numbers like 3600 seconds per hour are defined constants, not measured values. Therefore, in any calculation, it should be written explicitly as 3600_• i.e., with the implicit decimal point made explicit. Otherwise, we might not know that it represents a defined constant with 4 sigfigs and treat it as a measured value with only 2 sigfigs.

     
     
     
  2. How many sigfigs in 0.0 ?
     

     Still undecided about this one. Is the second zero a leading or trailing zero? Certainly there are occasions when one would want to indicate that the measured value was zero to 1 decimal place (in which case it would be considered to express 1 sigfig of accuracy).

     
     
     
  
  
  

6.3  Session #681: Celebrity Boxing (and Sizing)-Alan Greenspan vs. Gene Amdahl

• Invited Paper Session
  
  
• Technical Paper accompanying this session (not published in the CMG Proceedings).
  
  
• A non-queueing interpretation of these results is discussed in Chapter 14 of The Practical Performance Analyst.
  
  

7  CMG 2001: Anaheim, California

7.1  Track: Website Scalability Day

• Agenda for Website Scalability Day
  
  

Footnotes: