trending docs: fixed tables and maths formulas.

Change-Id: Iad93e7a57655835ee1a75664f142d3fd362f5313
Signed-off-by: Maciek Konstantynowicz <mkonstan@cisco.com>

1 files changed, 143 insertions, 118 deletions

diff --git a/docs/cpta/methodology/index.rst b/docs/cpta/methodology/index.rst
index 1b3a4c553e..35c438d8b6 100644
--- a/docs/cpta/methodology/index.rst
+++ b/docs/cpta/methodology/index.rst
@@ -1,11 +1,13 @@
+.. _trending_methodology:
+
 Trending Methodology
 ====================
 
-Continuous Trending and Analysis
---------------------------------
+Overview
+--------
 
 This document describes a high-level design of a system for continuous
-measuring, trending and performance change detection for FD.io VPP SW
+performance measuring, trending and change detection for FD.io VPP SW
 data plane. It builds upon the existing FD.io CSIT framework with
 extensions to its throughput testing methodology, CSIT data analytics
 engine (PAL – Presentation-and-Analytics-Layer) and associated Jenkins
@@ -20,23 +22,42 @@ trending dashboard and graphs with summary and drill-down views across
 all specified tests that can be reviewed and inspected regularly by
 FD.io developers and users community.
 
-Performance Trending Tests
---------------------------
+Performance Tests
+-----------------
 
 Performance trending is currently relying on the Maximum Receive Rate
-(MRR) tests. MRR tests measure the maximum forwarding rate under the
-line rate packet load over a set trial duration, regardless of packet
-loss.
+(MRR) tests. MRR tests measure the packet forwarding rate under the
+maximum load offered by traffic generator over a set trial duration,
+regardless of packet loss. Maximum load for specified Ethernet frame
+size is set to the bi-directional link rate.
 
 Current parameters for performance trending MRR tests:
 
-    - packet sizes: 64B (78B for IPv6 tests) for all tests, IMIX for
-      selected tests (vhost, memif).
-    - trial duration: 10sec.
-    - execution frequency: twice a day, every 12 hrs (02:00, 14:00 UTC).
+- **Ethernet frame sizes**: 64B (78B for IPv6 tests) for all tests, IMIX for
+  selected tests (vhost, memif); all quoted sizes include frame CRC, but
+  exclude per frame transmission overhead of 20B (preamble, inter frame
+  gap).
+- **Maximum load offered**: 10GE and 40GE link (sub-)rates depending on NIC
+  tested, with the actual packet rate depending on frame size,
+  transmission overhead and traffic generator NIC forwarding capacity.
+
+  - For 10GE NICs the maximum packet rate load is 2* 14.88 Mpps for 64B,
+    a 10GE bi-directional link rate.
+  - For 40GE NICs the maximum packet rate load is 2* 18.75 Mpps for 64B,
+    a 40GE bi-directional link sub-rate limited by TG 40GE NIC used,
+    XL710.
+
+- **Trial duration**: 10sec.
+- **Execution frequency**: twice a day, every 12 hrs (02:00, 14:00 UTC).
 
-Performance Trend Analysis
---------------------------
+Note: MRR tests should be reporting bi-directional link rate (or NIC
+rate, if lower) if tested VPP configuration can handle the packet rate
+higher than bi-directional link rate, e.g. large packet tests and/or
+multi-core tests. In other words MRR = min(VPP rate, bi-dir link rate,
+NIC rate).
+
+Trend Analysis
+--------------
 
 All measured performance trend data is treated as time-series data that
 can be modelled using normal distribution. After trimming the outliers,
@@ -44,61 +65,62 @@ the median and deviations from median are used for detecting performance
 change anomalies following the three-sigma rule of thumb (a.k.a.
 68-95-99.7 rule).
 
-Analysis Metrics
+Metrics
 ````````````````
 
-Following statistical metrics are proposed as performance trend
-indicators over the rolling window of last <N> sets of historical
-measurement data:
-
-    - Q1, Q2, Q3 : Quartiles, three points dividing a ranked data set
-      into four equal parts, Q2 is the median of the data.
-    - IQR = Q3 - Q1 : Inter Quartile Range, measure of variability, used
-      here to calculate and eliminate outliers.
-    - Outliers : extreme values that are at least (1.5 * IQR) below Q1.
-
-        - Note: extreme values that are at least (1.5 * IQR) above Q3 are not
-          considered outliers, and are likely to be classified as
-          progressions.
-
-    - TMA: Trimmed Moving Average, average across the data set of the
-      rolling window of <N> values without the outliers. Used here to
-      calculate TMSD.
-    - TMSD: Trimmed Moving Standard Deviation, standard deviation over the
-      data set of the rolling window of <N> values without the outliers,
-      requires calculating TMA. Used for anomaly detection.
-    - TMM: Trimmed Moving Median, median across the data set of the rolling
-      window of <N> values with all data points, excluding the outliers.
-      Used as a trending value and as a reference for anomaly detection.
+Following statistical metrics are used as performance trend indicators
+over the rolling window of last <N> sets of historical measurement data:
+
+- **Q1**, **Q2**, **Q3** : **Quartiles**, three points dividing a ranked
+  data set of <N> values into four equal parts, Q2 is the median of the
+  data.
+- **IQR** = Q3 - Q1 : **Inter Quartile Range**, measure of variability,
+  used here to calculate and eliminate outliers.
+- **Outliers** : extreme values that are at least (1.5 * IQR) below Q1.
+
+  - Note: extreme values that are at least (1.5 * IQR) above Q3 are not
+    considered outliers, and are likely to be classified as
+    progressions.
+
+- **TMA** : **Trimmed Moving Average**, average across the data set of
+  <N> values without the outliers. Used here to calculate TMSD.
+- **TMSD** : **Trimmed Moving Standard Deviation**, standard deviation
+  over the data set of <N> values without the outliers, requires
+  calculating TMA. Used for anomaly detection.
+- **TMM** : **Trimmed Moving Median**, median across the data set of <N>
+  values excluding the outliers. Used as a trending value and as a
+  reference for anomaly detection.
 
 Outlier Detection
 `````````````````
 
-Outlier evaluation of test result of value <X> follows the definition
-from previous section:
-
-::
+Outlier evaluation of test result of value :math:`X_n` follows the
+definition from previous section:
 
-    Outlier Evaluation Formula      Evaluation Result
-    ====================================================
-    X < (Q1 - 1.5 * IQR)            Outlier
-    X >= (Q1 - 1.5 * IQR)           Valid (For Trending)
++--------------------------------------------+----------------------+
+| Outlier Evaluation Formula                 | Evaluation Result    |
++============================================+======================+
+| :math:`X_n < \left( Q1 - 1.5 IQR \right)`  | Outlier              |
++--------------------------------------------+----------------------+
+| :math:`X_n >= \left( Q1 - 1.5 IQR \right)` | Valid (For Trending) |
++--------------------------------------------+----------------------+
 
 Anomaly Detection
 `````````````````
 
-To verify compliance of test result of value <X> against defined trend
-metrics and detect anomalies, three simple evaluation formulas are
+To verify compliance of test result of valid value <X> against defined
+trend metrics and detect anomalies, three simple evaluation formulas are
 used:
 
-::
-
-          Anomaly                                   Compliance        Evaluation
-    Evaluation Formula                            Confidence Level      Result
-    =============================================================================
-    (TMM - 3 * TMSD) <= X <= (TMM + 3 * TMSD)         99.73%            Normal
-    X < (TMM - 3 * TMSD)                              Anomaly         Regression
-    X > (TMM + 3 * TMSD)                              Anomaly         Progression
++---------------------------------------------------------------------------+-----------------------------+-------------------+
+| Anomaly Evaluation Formula                                                | Compliance Confidence Level | Evaluation Result |
++===========================================================================+=============================+===================+
+| :math:`\left( TMM - 3 TMSD \right) <= X_n <= \left( TMM + 3 TMSD \right)` | 99.73%                      | Normal            |
++---------------------------------------------------------------------------+-----------------------------+-------------------+
+| :math:`X_n < \left( TMM - 3 TMSD \right)`                                 | Anomaly                     | Regression        |
++---------------------------------------------------------------------------+-----------------------------+-------------------+
+| :math:`X_n > \left( TMM + 3 TMSD \right)`                                 | Anomaly                     | Progression       |
++---------------------------------------------------------------------------+-----------------------------+-------------------+
 
 TMM is used for the central trend reference point instead of TMA as it
 is more robust to anomalies.
@@ -113,19 +135,19 @@ ago, TMM[last - 1week] and to the maximum of trend values over last
 quarter except last week, max(TMM[(last - 3mths)..(last - 1week)]),
 respectively. This results in following trend compliance calculations:
 
-::
-
-    Trend
-    Compliance Metric     Change Formula    V(alue)      R(eference)
-    =============================================================================================
-    Short-Term Change     ((V - R) / R)     TMM[last]    TMM[last - 1week]
-    Long-Term Change      ((V - R) / R)     TMM[last]    max(TMM[(last - 3mths)..(last - 1week)])
++-------------------------+---------------------------------------------+--------------------------------+------------------------------------------------------------------------------------------------------------+
+| Trend Compliance Metric | Change Formula                              | Value                          | Reference                                                                                                  |
++=========================+=============================================+================================+============================================================================================================+
+| Short-Term Change       | :math:`\frac{Value - Reference}{Reference}` | :math:`TMM \left[ last \right] | :math:`TMM \left[ last - 1 week \right]`                                                                   |
++-------------------------+---------------------------------------------+--------------------------------+------------------------------------------------------------------------------------------------------------+
+| Long-Term Change        | :math:`\frac{Value - Reference}{Reference}` | :math:`TMM \left[ last \right] | :math:`max \left( TMM \left[ \left( last - 3 mths \right) .. \left( last - 1 week \right) \right] \right)` |
++-------------------------+---------------------------------------------+--------------------------------+------------------------------------------------------------------------------------------------------------+
 
 Trend Presentation
 ------------------
 
-Trend Dashboard
-```````````````
+Performance Dashboard
+`````````````````````
 
 Dashboard tables list a summary of per test-case VPP MRR performance
 trend and trend compliance metrics and detected number of anomalies.
@@ -134,89 +156,92 @@ Separate tables are generated for tested VPP worker-thread-core
 combinations (1t1c, 2t2c, 4t4c). Test case names are linked to
 respective trending graphs for ease of navigation thru the test data.
 
-Trend Graphs
-``````````````
+Trendline Graphs
+````````````````
 
-Trends graphs show per test case measured MRR throughput values with
+Trendline graphs show per test case measured MRR throughput values with
 associated trendlines. The graphs are constructed as follows:
 
-    - X-axis represents performance trend job build Id (csit-vpp-perf-mrr-
-      daily-master-build).
-    - Y-axis represents MRR throughput in Mpps.
-    - Markers to indicate anomaly classification:
+- X-axis represents performance trend job build Id (csit-vpp-perf-mrr-
+  daily-master-build).
+- Y-axis represents MRR throughput in Mpps.
+- Markers to indicate anomaly classification:
 
-        - Outlier - gray circle around MRR value point.
-        - Regression - red circle.
-        - Progression - green circle.
+  - Outlier - gray circle around MRR value point.
+  - Regression - red circle.
+  - Progression - green circle.
 
 In addition the graphs show dynamic labels while hovering over graph
 data points, representing (trend job build Id, MRR value) and the actual
 vpp build number (b<XXX>) tested.
 
 
-Jenkins Jobs Description
-------------------------
+Jenkins Jobs
+------------
 
 Performance Trending (PT)
 `````````````````````````
 
-CSIT PT runs regular performance test jobs finding MRR per test case. PT
-is designed as follows:
-
-    #. PT job triggers:
+CSIT PT runs regular performance test jobs measuring and collecting MRR
+data per test case. PT is designed as follows:
 
-        #. Periodic e.g. daily.
-        #. On-demand gerrit triggered.
+1. PT job triggers:
 
-    #. Measurements and calculations per test case:
+   a) Periodic e.g. daily.
+   b) On-demand gerrit triggered.
 
-        #. MRR Max Received Rate
+2. Measurements and data calculations per test case:
 
-            #. Measured: Unlimited tolerance of packet loss.
-            #. Send packets at link rate, count total received packets, divide
-               by test trial period.
+  a) Max Received Rate (MRR) - send packets at link rate over a trial
+     period, count total received packets, divide by trial period.
 
-    #. Archive MRR per test case.
-    #. Archive all counters collected at MRR.
+3. Archive MRR per test case.
+4. Archive all counters collected at MRR.
 
 Performance Analysis (PA)
 `````````````````````````
 
-CSIT PA runs performance analysis including trending and anomaly
-detection using specified trend analysis metrics over the rolling window
-of last <N> sets of historical measurement data. PA is defined as
-follows:
+CSIT PA runs performance analysis including trendline calculation, trend
+compliance and anomaly detection using specified trend analysis metrics
+over the rolling window of last <N> sets of historical measurement data.
+PA is defined as follows:
 
-    #. PA job triggers:
+1. PA job triggers:
 
-        #. By PT job at its completion.
-        #. On-demand gerrit triggered.
+   a) By PT job at its completion.
+   b) On-demand gerrit triggered.
 
-    #. Download and parse archived historical data and the new data:
+2. Download and parse archived historical data and the new data:
 
-        #. Evalute new data from latest PT job against the rolling window of
-           <N> sets of historical data.
-        #. Download RF output.xml files and compressed archived data.
-        #. Parse out the data filtering test cases listed in PA specification
-           (part of CSIT PAL specification file).
+   a) Download RF output.xml files from latest PT job and compressed
+      archived data.
+   b) Parse out the data filtering test cases listed in PA specification
+      (part of CSIT PAL specification file).
+   c) Evalute new data from latest PT job against the rolling window of
+      <N> sets of historical data for trendline calculation, anomaly
+      detection and short-term trend compliance. And against long-term
+      trendline metrics for long-term trend compliance.
 
-    #. Calculate trend metrics for the rolling window of <N> sets of
-       historical data:
+3. Calculate trend metrics for the rolling window of <N> sets of
+   historical data:
 
-        #. Calculate quartiles Q1, Q2, Q3.
-        #. Trim outliers using IQR.
-        #. Calculate TMA and TMSD.
-        #. Calculate normal trending range per test case based on TMM and TMSD.
+   a) Calculate quartiles Q1, Q2, Q3.
+   b) Trim outliers using IQR.
+   c) Calculate TMA and TMSD.
+   d) Calculate normal trending range per test case based on TMM and
+      TMSD.
 
-    #. Evaluate new test data against trend metrics:
+4. Evaluate new test data against trend metrics:
 
-        #. If within the range of (TMA +/- 3*TMSD) => Result = Pass, 
-           Reason = Normal.
-        #. If below the range => Result = Fail, Reason = Regression.
-        #. If above the range => Result = Pass, Reason = Progression.
+   a) If within the range of (TMA +/- 3*TMSD) => Result = Pass,
+      Reason = Normal. (to be updated base on the final Jenkins code).
+   b) If below the range => Result = Fail, Reason = Regression.
+   c) If above the range => Result = Pass, Reason = Progression.
 
-    #. Generate and publish results
+5. Generate and publish results
 
-        #. Relay evaluation result to job result.
-        #. Generate a new set of trend summary dashboard and graphs.
-        #. Publish trend dashboard and graphs in html format on https://docs.fd.io/.
+   a) Relay evaluation result to job result. (to be updated base on the
+      final Jenkins code).
+   b) Generate a new set of trend summary dashboard and graphs.
+   c) Publish trend dashboard and graphs in html format on
+      https://docs.fd.io/.