Update draft-vpolak-bmwg-plrsearch-01->02

Change-Id: Ida23a50c9148570a6510f93a2bb731ea8b0b2b94
Signed-off-by: Maciek Konstantynowicz <mkonstan@cisco.com>

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----
-title: Probabilistic Loss Ratio Search for Packet Throughput (PLRsearch)
-# abbrev: PLRsearch
-docname: draft-vpolak-bmwg-plrsearch-00
-date: 2018-11-13
-
-ipr: trust200902
-area: ops
-wg: Benchmarking Working Group
-kw: Internet-Draft
-cat: info
-
-coding: us-ascii
-pi:    # can use array (if all yes) or hash here
-#  - toc
-#  - sortrefs
-#  - symrefs
-  toc: yes
-  sortrefs:   # defaults to yes
-  symrefs: yes
-
-author:
-      -
-        ins: M. Konstantynowicz
-        name: Maciek Konstantynowicz
-        org: Cisco Systems
-        role: editor
-        email: mkonstan@cisco.com
-      -
-        ins: V. Polak
-        name: Vratko Polak
-        org: Cisco Systems
-        role: editor
-        email: vrpolak@cisco.com
-
-normative:
-  RFC2544:
-  RFC8174:
-
-informative:
-
---- abstract
-
-This document addresses challenges while applying methodologies
-described in [RFC2544] to benchmarking NFV (Network Function
-Virtualization) over an extended period of time, sometimes referred to
-as "soak testing". More specifically to benchmarking software based
-implementations of NFV data planes. Packet throughput search approach
-proposed by this document assumes that system under test is
-probabilistic in nature, and not deterministic.
-
---- middle
-
-# Motivation
-
-Network providers are interested in throughput a device can sustain.
-
-RFC 2544 assumes loss ratio is given by a deterministic function of
-offered load. But NFV software devices are not deterministic (enough).
-This leads for deterministic algorithms (such as MLRsearch with single
-trial) to return results, which when repeated show relatively high
-standard deviation, thus making it harder to tell what "the throughput"
-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
-specify probabilities (or prior distributions) which are tied to a
-specific probabilistic model. Different models will have different
-number (and meaning) of parameters. Complicated (but more realistic)
-models have many parameters, and the math involved can be very
-complicated. It is better to start with simpler probabilistic model, and
-only change it when the output of the simpler algorithm is not stable or
-useful enough.
-
-TODO: Refer to packet forwarding terminology, such as "offered load" and
-"loss ratio".
-
-TODO: Mention that no packet duplication is expected (or is filtered
-out).
-
-TODO: Define critical load and critical region earlier.
-
-This document is focused on algorithms related to packet loss count
-only. No latency (or other information) is taken into account. For
-simplicity, only one type of measurement is considered: dynamically
-computed offered load, constant within trial measurement of
-predetermined trial duration.
-
-Also, running longer trials (in some situations) could be more efficient,
-but in order to perform trial at multiple offered loads withing critical region,
-trial durations should be kept as short as possible.
-
-# Poisson Distribution
-
-TODO: Give link to more officially published literature about Poisson
-distribution.
-
-Note-1: that the algorithm makes an assumption that packet traffic
-generator detects duplicate packets on receive detection, and reports
-this as an error.
-
-Note-2: Binomial distribution is a better fit compared to Poisson
-distribution (acknowledging that the number of packets lost cannot be
-higher than the number of packets offered), but the difference tends to
-be relevant in loads far above the critical region, so using Poisson
-distribution helps the algorithm focus on critical region better.
-
-When comparing different offered loads, the average loss per second is
-assumed to increase, but the (deterministic) function from offered load
-into average loss rate is otherwise unknown.
-
-Given a loss target (configurable, by default one packet lost per
-second), there is an unknown offered load when the average is exactly
-that. We call that the "critical load". If critical load seems higher
-than maximum offerable load, we should use the maximum offerable load to
-make search output more stable.
-
-Of course, there are great many increasing functions. The offered load
-has to be chosen for each trial, and the computed posterior distribution
-of critical load can change with each trial result.
-
-To make the space of possible functions more tractable, some other
-simplifying assumption is needed. As the algorithm will be examining
-(also) loads close to the critical load, linear approximation to the
-function (TODO: name the function) in the critical region is important.
-But as the search algorithm needs to evaluate the function also far
-away from the critical region, the approximate function has to be well-
-behaved for every positive offered load, specifically it cannot predict
-non-positive packet loss rate.
-
-Within this document, "fitting function" is the name for such well-behaved
-function which approximates the unknown function in the critical region.
-
-Results from trials far from the critical region are likely to affect
-the critical rate estimate negatively, as the fitting function does not
-need to be a good approximation there. Instead of discarding some
-results, or "suppressing" their impact with ad-hoc methods (other than
-using Poisson distribution instead of binomial) is not used, as such
-methods tend to make the overall search unstable. We rely on most of
-measurements being done (eventually) within the critical region, and
-overweighting far-off measurements (eventually) for well-behaved fitting
-functions.
-
-# Fitting Function Coefficients Distribution
-
-To accomodate systems with different behaviours, the fitting function is
-expected to have few numeric parameters affecting its shape (mainly
-affecting the linear approximation in the critical region).
-
-The general search algorithm can use whatever increasing fitting
-function, some specific functions can be described later.
-
-TODO: Describe sigmoid-based and erf-based functions.
-
-It is up to implementer to chose a fitting function and prior
-distribution of its parameters. The rest of this document assumes each
-parameter is independently and uniformly distributed over common
-interval. Implementers are to add non-linear transformations into their
-fitting functions if their prior is different.
-
-TODO: Move the following sentence into more appropriate place.
-
-Speaking about new trials, each next trial will be done at offered load
-equal to the current average of the critical load.
-
-Exit condition is either critical load stdev becoming small enough, or
-overal search time becoming long enough.
-
-The algorithm should report both avg and stdev for critical load. If the
-reported averages follow a trend (without reaching equilibrium), avg and
-stdev should refer to the equilibrium estibated based on the trend, not
-to immediate posterior values.
-
-TODO: Explicitly mention the iterative character of the search.
-
-# Algorithm Formulas
-
-## Integration
-
-The posterior distributions for fitting function parameters will not be
-integrable in general.
-
-The search algorithm utilises the fact that trial measurement takes some
-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 could take
-advantage of that.
-
-Even in the concentrated area, the likelihood can be quite small, so the
-integration algorithm should track the logarithm of the likelihood, and
-also avoid underflow errors bu ther means.
-
-# Known Implementations
-
-The only known working implementatin of Probabilistic Loss Ratio Search
-for Packet Throughput is in Linux Foundation FD.io CSIT project. https://wiki.fd.io/view/CSIT. https://git.fd.io/csit/.
-
-## FD.io CSIT Implementation Specifics
-
-In a sample implemenation in FD.io CSIT project, there is around 0.5
-second delay between trials due to restrictons imposed by packet traffic
-generator in use (T-Rex), avoiding that delay is out of scope of this
-document.
-
-TODO: Describe how the current integration algorithm finds the
-concentrated area.
-
-# IANA Considerations
-
-..
-
-# Security Considerations
-
-..
-
-# Acknowledgements
-
-..
-
---- back
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