diff options
Diffstat (limited to 'docs/report/introduction')
| -rw-r--r-- | docs/report/introduction/PLRsearch.svg | 2015 | ||||
| -rw-r--r-- | docs/report/introduction/methodology_plrsearch.rst | 47 |
2 files changed, 2042 insertions, 20 deletions
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Motivation ----------- +`````````` Network providers are interested in throughput a device can sustain. @@ -27,7 +27,7 @@ actually is. We need another algorithm, which takes this indeterminism into account. Model ------ +````` Each algorithm searches for an answer to a precisely formulated question. When the question involves indeterministic systems, it has to @@ -55,7 +55,7 @@ generator detects duplicate packets on receive detection, and reports this as an error. Poisson distribution --------------------- +```````````````````` For given offered load, number of packets lost during trial measurement is assumed to come from `Poisson distribution`_, @@ -112,7 +112,7 @@ in an attempt to speed up convergence, but such methods tend to be scpecific for a particular system under tests. Fitting function coefficients distribution ------------------------------------------- +`````````````````````````````````````````` To accomodate systems with different behaviours, the fitting function is expected to have few numeric parameters affecting its shape (mainly @@ -136,7 +136,7 @@ stdev should refer to the equilibrium estimates based on the trend, not to immediate posterior values. Integration ------------ +``````````` The posterior distributions for fitting function parameters will not be integrable in general. @@ -146,7 +146,7 @@ time, so this time can be used for numeric integration (using suitable method, such as Monte Carlo) to achieve sufficient precision. Optimizations -------------- +````````````` After enough trials, the posterior distribution will be concentrated in a narrow area of parameter space. The integration method should take @@ -169,7 +169,7 @@ it only cares about overall counts of packets sent and packets lost), but debug output from traffic generator lists unidirectional values. Measurement delay ------------------ +````````````````` In a sample implemenation in FD.io CSIT project, there is roughly 0.5 second delay between trials due to restrictons imposed by packet traffic @@ -191,7 +191,7 @@ trial durations with configurable coefficients each subsequent trial being 0.2 second longer). Rounding errors and underflows ------------------------------- +`````````````````````````````` In order to avoid them, the current implementation tracks natural logarithm (instead of the original quantity) for any quantity which is never negative. @@ -202,7 +202,7 @@ Specific functions for frequent operations are defined to handle None correctly. Fitting functions ------------------ +````````````````` Current implementation uses two fitting functions. In general, their estimates for critical rate differ, @@ -257,7 +257,7 @@ During each measurement, two estimates are computed, even though only one (in alternating order) is used for next offered load. Stretch function -________________ +---------------- The original function (before applying logarithm) is primitive function to `logistic function`_. @@ -265,13 +265,13 @@ The name "stretch" is used for related function in context of neural networks with sigmoid activation function. Erf function -____________ +------------ The original function is double primitive function to `Gaussian function`_. The name "erf" comes from error function, the first primitive to Gaussian. Prior distributions -------------------- +``````````````````` The numeric integrator expects all the parameters to be distributed (independently and) uniformly on an interval (-1, 1). @@ -288,7 +288,7 @@ raised to a random power between zero and one; thus it follows a `reciprocal distribution`_. Integrator ----------- +`````````` After few measurements, the posterior distribution of fitting function arguments gets quite concentrated into a small area. @@ -314,17 +314,17 @@ is concentrated at. The second phase (dominated by whole sample population) is actually relevant for the critical rate estimation. Caveats -------- +``````` Current implementation does not constrict the critical rate (as computed for every sample) to the min_rate, max_rate interval. Earlier implementations were targeting loss rate (as opposed to loss ratio). -The chosen fitting functions do not even allow arbitrarily low loss ratios, -especially if the "spread" value is high enough (relative to "mrr" value). +The chosen fitting functions do allow arbitrarily low loss ratios, +but may suffer from rounding errors in corresponding parameter regions. Internal loss rate target is computed from given loss ratio -using the current trial offered load, which increases search instability -if measurements with surprisingly high loss count appear. +using the current trial offered load, which increases search instability, +especially if measurements with surprisingly high loss count appear. As high loss count measurements add many bits of information, they need a large amount of small loss count measurements to balance them, @@ -338,9 +338,16 @@ as the observed trends have varied characteristics. Probably, using a more realistic fitting functions will give better estimates than trend analysis. -.. TODO: Add a 1901 result section when results are available. +Graphical example +````````````````` + +The following picture shows the estimated average of the critical rate +computed by the two fitting functions after each trial measurement +within the 30 minute duration of a PLRsearch test run. -.. TODO: Add a graph of time evolution when 1901 run is available. +.. image:: PLRsearch.svg + +.. TODO: Add a 1901 result section when results are available. .. _plrsearch draft: https://tools.ietf.org/html/draft-vpolak-bmwg-plrsearch-00 .. _RFC 2544: https://tools.ietf.org/html/rfc2544 |
