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diff --git a/docs/ietf/draft-ietf-bmwg-mlrsearch-05.md b/docs/ietf/draft-ietf-bmwg-mlrsearch-05.md new file mode 100644 index 0000000000..937e632413 --- /dev/null +++ b/docs/ietf/draft-ietf-bmwg-mlrsearch-05.md @@ -0,0 +1,1460 @@ +--- +title: Multiple Loss Ratio Search +abbrev: MLRsearch +docname: draft-ietf-bmwg-mlrsearch-05 +date: 2023-10-23 + +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: yes + sortrefs: # defaults to yes + symrefs: yes + +author: + - + ins: M. Konstantynowicz + name: Maciek Konstantynowicz + org: Cisco Systems + email: mkonstan@cisco.com + - + ins: V. Polak + name: Vratko Polak + org: Cisco Systems + email: vrpolak@cisco.com + +normative: + RFC1242: + RFC2285: + RFC2544: + RFC9004: + +informative: + TST009: + target: https://www.etsi.org/deliver/etsi_gs/NFV-TST/001_099/009/03.04.01_60/gs_NFV-TST009v030401p.pdf + title: "TST 009" + FDio-CSIT-MLRsearch: + target: https://csit.fd.io/cdocs/methodology/measurements/data_plane_throughput/mlr_search/ + title: "FD.io CSIT Test Methodology - MLRsearch" + date: 2023-10 + PyPI-MLRsearch: + target: https://pypi.org/project/MLRsearch/0.4.1/ + title: "MLRsearch 0.4.1, Python Package Index" + date: 2021-07 + +--- abstract + +This document proposes extensions to [RFC2544] throughput search by +defining a new methodology called Multiple Loss Ratio search +(MLRsearch). The main objectives of MLRsearch are to minimize the +total search duration, to support searching for multiple loss ratios +and to improve results repeatability and comparability. + +The main motivation behind extending [RFC2544] is the new set of challenges +and requirements posed by evaluating and testing software based networking +systems, specifically their data planes. + +MLRsearch offers several ways to address these challenges, giving user +configuration options to select their preferred way. + +--- middle + +{::comment} + As we use kramdown to convert from markdown, + we use this way of marking comments not to be visible in rendered draft. + https://stackoverflow.com/a/42323390 + If other engine is used, convert to this way: + https://stackoverflow.com/a/20885980 +{:/comment} + +# Purpose and Scope + +The purpose of this document is to describe Multiple Loss Ratio search +(MLRsearch), a data plane throughput search methodology optimized for software +networking DUTs. + +Applying vanilla [RFC2544] throughput bisection to software DUTs +results in a number of problems: + +- Binary search takes too long as most of trials are done far from the + eventually found throughput. +- The required final trial duration and pauses between trials + prolong the overall search duration. +- Software DUTs show noisy trial results, + leading to a big spread of possible discovered throughput values. +- Throughput requires loss of exactly zero frames, but the industry + frequently allows for small but non-zero losses. +- The definition of throughput is not clear when trial results are inconsistent. + +MLRsearch library aims to address these problems by applying the following set +of enhancements: + +- Allow multiple shorter trials instead of one big trial per load. + - Optionally, tolerate a percentage of trial result with higher loss. +- Allow searching for multiple search goals, with differing loss ratios. + - Any trial result can affect each search goal in principle. +- Insert multiple coarse targets for each search goal, earlier ones need + to spend less time on trials. + - Earlier targets also aim for lesser precision. + - Use Forwarding Rate (FR) at maximum offered load + [RFC2285] (section 3.6.2) to initialize the initial targets. +- Take care when dealing with inconsistent trial results. + - Reported throughput is smaller than smallest load with high loss. + - Smaller load candidates are measured first. +- Apply several load selection heuristics to save even more time + by trying hard to avoid unnecessarily narrow bounds. + +Some of these enhancements are formalized as MLRsearch specification, +the remaining enhancements are treated as implementation details, +thus achieving high comparability without limiting future improvements. + +MLRsearch configuration options are flexible enough to +support both conservative settings and aggressive settings. +Where the conservative settings lead to results +unconditionally compliant with [RFC2544], +but longer search duration and worse repeatability. +Conversely, aggressive settings lead to shorter search duration +and better repeatability, but the results are not compliant with [RFC2544]. + +No part of [RFC2544] is intended to be obsoleted by this document. + +# Identified Problems + +This chapter describes the problems affecting usability +of various preformance testing methodologies, +mainly a binary search for [RFC2544] unconditionally compliant throughput. + +The last chapter will summarize how the problems are addressed, +the middle chapters provide explanations and definitions needed for that. + +## Long Search Duration + +Emergence of software DUTs, with frequent software updates and a +number of different frame processing modes and configurations, +has increased both the number of performance tests requred to verify DUT update +and the frequency of running those tests. +This makes the overall test execution time even more important than before. + +In the context of characterising particular DUT's network performance, +this calls for improving the time efficiency of throughput search. +A vanilla bisection (at 60sec trial duration for unconditional [RFC2544] +compliance) is slow, because most trials spend time quite far from the +eventual throughput. + +[RFC2544] does not specify any stopping condition for throughput search, +so users can trade-off between search duration and achieved precision. +But, due to logarithmic nature of bisection, even small improvement +in search duration needs relatively big sacrifice in the precision of the +discovered throughput. + +## DUT in SUT + +[RFC2285] defines: +- DUT as + - The network forwarding device to which stimulus is offered and + response measured [RFC2285] (section 3.1.1). +- SUT as + - The collective set of network devices to which stimulus is offered + as a single entity and response measured [RFC2285] (section 3.1.2). + +[RFC2544] specifies a test setup with an external tester stimulating the +networking system, treating it either as a single DUT, or as a system +of devices, an SUT. + +In case of software networking, the SUT consists nt only of the DUT +as a software program processing frames, but also of +a server hardware and operating system functions, +with server hardware resources shared across all programs +and the operating system running on the same server. + +The DUT is effectively nested within the rest of the SUT. + +Due to a shared multi-tenant nature of SUT, DUT is subject to +possible interference coming from the operating system and any other +software running on the same server. Some sources of such interference +can be to some degree eliminated, e.g. by pinning DUT program threads +to specific CPU cores and isolating those cores to avoid context switching. +But some level of adverse effects may remain even after +all such reasonable precautions are applied. +These effects affect DUT's network performance negatively. +As the effects are hard to predict in general, they have impact similar to +what other engineering disciplines define as a noise. +Thus, all such effects are called an SUT noise. + +DUT can also exhibit fluctuating performance itself, for reasons +not related to the rest of SUT, for example due to pauses in execution +as needed for internal stateful processing. In many cases this +may be an expected per-design behavior, as it would be observable even +in a hypothetical scenario where all sources of SUT noise are eliminated. +Such behavior affects trial results in a way similar to SUT noise. +As the two phenomenons are hard to destinguish, +this document uses the word noise as a shorthand covering both +this internal DUT performance fluctuations and genuine SUT noise. + +A simple model of SUT performance consists of an idealized noiseless performance, +and additional noise effects. The noiseless performance is assumed to be constant, +all observed performance variations are due to noise. +The impact of the noise can vary in time, sometimes wildly, +even within a single trial. +The noise can sometimes be negligible, but frequently +it lowers the observed SUT performance as observed in trial results. + +In this model, SUT does not have a single performance value, it has a spectrum. +One end of the spectrum is the idealized noiseless performance value, +the other end can be called a noiseful performance. In practice, trial results +close to the noiseful end of the spectrum happen only rarely. +The worse the performance value is, the more rarely it is seen in a trial. +Therefore, the extreme noiseful end of SUT spectrum is not really observable +among trial results. Also, the extreme noiseless end of SUT spectrum +is unlikely to be observable, this time because some small noise effects +are likely to occur multiple times during a trial. + +Unless specified otherwise, this document talks about potentially observable +ends of the SUT performance spectrum, not about the extreme ones. + +Focusing on DUT, the benchmarking effort should aim +at eliminating only the SUT noise from SUT measurements. +In practice that is not really possible, as based on authors experience +and available literature, there are no realistic enough models +able to distinguish SUT noise from DUT fluctuations. + +However, assuming that a well-constructed SUT has the DUT as its +performance bottleneck, the DUT ideal noiseless performance can be defined +as the noiseless end of SUT performance spectrum. At least for +throughput. For other performance quantities such as latency there may be an +additive difference. + +Note that by this definition, DUT noiseless performance +also minimizes the impact of DUT fluctuations, as much as realistically possible +for a given trial duration. + +In this document, we reduce the DUT in SUT problem to estimating +the noiseless end of SUT performance spectrum from a limited number of +trial results. + +Any improvements to throughput search algorithm, aimed for better +dealing with software networking SUT and DUT setup, should employ +strategies recognizing the presence of SUT noise, and allow discovery of +(proxies for) DUT noiseless performance +at different levels of sensitivity to SUT noise. + +## Repeatability and Comparability + +[RFC2544] does not suggest to repeat throughput search. And from just one +discovered throughput value, it cannot be determined how repeatable that value is. +In practice, poor repeatability is also the main cause of poor +comparability, that is different benchmarking teams can test the same SUT +but get throughput values differing more than expected from search precision. + +[RFC2544] throughput requirements (60 seconds trial and +no tolerance of a single frame loss) affect the throughput results +in the following way. +The SUT behavior close to the noiseful end of its performance spectrum +consists of rare occasions of significantly low performance, +but the long trial duration makes those occasions not so rare on the trial level. +Therefore, the binary search results tend to wander away from the noiseless end +of SUT performance spectrum, more frequently and more widely than shorter +trials would, thus resulting in poor throughput repeatability. + +The repeatability problem can be addressed by defining a search procedure +which reports more stable results, +even if they can no longer be called throughput in [RFC2544] sense. +According to the SUT performance spectrum model, better repeatability +will be at the noiseless end of the spectrum. +Therefore, solutions to the DUT in SUT problem +will help also with the repeatability problem. + +Conversely, any alteration to [RFC2544] throughput search +that improves repeatability should be considered +as less dependent on the SUT noise. + +An alternative option is to simply run a search multiple times, and report some +statistics (e.g. average and standard deviation). This can be used +for a subset of tests deemed more important, +but it makes the search duration problem even more pronounced. + +## Throughput with Non-Zero Loss + +[RFC1242] (section 3.17) defines throughput as: + The maximum rate at which none of the offered frames + are dropped by the device. + +Then, it says: + Since even the loss of one frame in a + data stream can cause significant delays while + waiting for the higher level protocols to time out, + it is useful to know the actual maximum data + rate that the device can support. + +Contrary to that, many benchmarking teams settle with small, non-zero +loss ratio as the goal for a their load search. + +Motivations are many: + +- Modern protocols tolerate frame loss better, + compared to the time when [RFC1242] and [RFC2544] were specified. + +- Trials nowadays send way more frames within the same duration, + increasing the chance small SUT performance fluctuatios + is enough to cause frame loss. + +- Small bursts of frame loss caused by noise have otherwise smaller impact + on the average frame loss ratio ovserved in the trial, + as during other parts of the same trial the SUT may work mroe closely + to its noiseless performance, thus perhaps lowering the trial loss ratio + below the goal loss ratio value. + +- If an approximation of the SUT noise impact on the trial loss ratio is known, + it can be set as the goal loss ratio. + +Regardless of validity of any and all similar motivations, +support for non-zero loss goals makes any search algorithm more user friendly. +[RFC2544] throughput is not user friendly in this regard. + +Assuming users are allowed to specify the goal loss ratio value, +the usefulness is enhanced even more if users can specify multiple +loss ratio values, especially when a single search can find all relevant bounds. + +Searching for multiple search goals also helps to describe the SUT performance +spectrum better than a single search goal result. +For example, repeated wide gap between zero and non-zero loss loads +indicates the noise has a large impact on the observed performance, +which is not evident from a single goal load search procedure result. + +It is easy to modify the vanilla bisection to find a lower bound +for intended load that satisfies a non-zero goal loss ratio. +But it is not that obvious how to search for multiple goals at once, +hence the support for multiple search goals remains a problem. + +## Inconsistent Trial Results + +While performing throughput search by executing a sequence of +measurement trials, there is a risk of encountering inconsistencies +between trial results. + +The plain bisection never encounters inconsistent trials. +But [RFC2544] hints about possibility of inconsistent trial results, +in two places in its text. +The first place is section 24, where full trial durations are required, +presumably because they can be inconsistent with results +from shorter trial durations. +The second place is section 26.3, where two successive zero-loss trials +are recommended, presumably because after one zero-loss trial +there can be subsequent inconsistent non-zero-loss trial. + +Examples include: + +- A trial at the same load (same or different trial duration) results + in a different trial loss ratio. +- A trial at higher load (same or different trial duration) results + in a smaller trial loss ratio. + +Any robust throughput search algorithm needs to decide how to continue +the search in presence of such inconsistencies. +Definitions of throughput in [RFC1242] and [RFC2544] are not specific enough +to imply a unique way of handling such inconsistencies. + +Ideally, there will be a definition of a new quantity which both generalizes +throughput for non-zero-loss (and other possible repeatibility enhancements), +while being precise enough to force a specific way to resolve trial result +inconsistencies. +But until such definition is agreed upon, the correct way to handle +inconsistent trial results remains an open problem. + +# MLRsearch Specification + +This chapter focuses on technical definitions needed for evaluating +whether a particular test procedure adheres to MLRsearch specification. + +For motivations, explanations, and other comments see other chapters. + +## MLRsearch Architecture + +MLRsearch architecture consists of three main components: +the manager, the controller and the measurer. +Presence of other components (mainly the SUT) is also implied. + +While the manager and the measurer can be seen a abstractions +present in any testing procedure, the behavior of the controller +is what distinguishes MLRsearch algorithms from other search procedures. + +### Measurer + +The measurer is the component which performs one trial +as described in [RFC2544] section 23, when requested by the controller. + +Specifically, one call to the measurer accepts a trial load value +and trial duration value, performs the trial, and returns +the measured trial loss ratio, and optionally a different duration value. + +It is responsibility of the measurer to uphold any requirements +and assumptions present in MLRsearch specification +(e.g. trial forwarding ratio not being larger than one). +Implementers have some freedom, for example in the way they deal with +duplicated frames, or what to return if tester sent zero frames towards SUT. +Implementations are RECOMMENDED to document their behavior +related to such freedoms in as detailed way as possible + +Implemenations MUST document any deviations from RFC documents, +for example if the wait time around traffic +is shorter than what [RFC2544] section 23 specifies. + +### Controller + +The controller is the component of MLRsearch architecture +that is called by the manager (just once), calls the measurer +(usually multiple times in succession), +and returns the result of the search to the manager. + +The only required argument in the call to the controller +is a list of search goals. For the structure of the search result, +see subsection Search Result. + +### Manager + +The manager is the component that initializes SUT, traffic generator +(tester in [RFC2544]), the measurer and the controller +with intended configurations. It then hands over the execution +to the controller and receives its result. + +Creation of reports of appropriate format can also be understood +as the responsibility of the manager. + +## Units + +The specification deals with physical quantities, so it is assumed +each numeric value is accompanied by an appropriate physical unit. + +The specification does not state which unit is appropriate, +but implementations MUST make it explicit which unit is used +for each value provided or received by the user. + +For example, load quantities (including the conditional throughput) +returned by the controller are defined to be based on single-interface +(unidirectional) loads. For bidirectional traffic, users are likely +to expect bidirectional throughput quantities, so the manager is responsible +for making its report clear. + +## SUT + +As defined in [RFC2285]: +The collective set of network devices to which stimulus is offered +as a single entity and response measured. + +## Trial + +A trial is the part of test described in [RFC2544] section 23. + +### Trial Load + +Trial load is the intended constant load for a trial. + +Load is the quantity implied by Constant Load of [RFC1242], +Data Rate of [RFC2544] and Intended Load of [RFC2285]. +All three specify this value applies to one (input or output) interface. + +### Trial Duration + +Trial duration is the intended duration of the traffic for a trial. + +In general, this general quantity does not include any preparation nor waiting +described in section 23 of [RFC2544]. + +However, the measurer MAY return a duration value different +from the intended duration. This may be useful for users +who want to control the overal search duration, not just the traffic part of it. +The manager MUST report how does the measurer computes the returned duration +values in that case. + +### Trial Forwarding Ratio + +Trial forwarding ratio is dimensionless floating point value, +assumed to be between 0.0 and 1.0, both including. +It is computed as the number of frames forwarded by SUT, divided by +the number of frames that should have been forwarded during the trial. + +Note that, contrary to load, frame counts used to compute +trial forwarding ratio are aggregates over all SUT ports. + +Questions around what is the correct number of frames +that should have been forwarded it outside of the scope of this document. +E.g. what should the measurer return when it detects +that the offered load differs significantly from the intended load. + +It is RECOMMENDED implementations return an irregular goal result +if they detect questionable (in comparability sense) trial results +affecting their goal result. + +### Trial Loss Ratio + +Trial loss ratio is equal to one minus the trial forwarding ratio. + +### Trial Forwarding Rate + +The trial forwarding rate is the trial load multiplied by +the trial forwarding ratio. + +Note that this is very similar, but not identical to Forwarding Rate +as defined in [RFC2285] section 3.6.1, as that definition +is specific to one output interface, while trial forwarding ratio +is based on frame counts aggregated over all SUT interfaces. + +## Traffic profile + +Any other specifics (besides trial load and trial duration) +the measurer needs to perform the trial are understood as a composite +called the traffic profile. +All its attributes are assumed to be constant during the search, +and the composite is configured on the measurer by the manager +before the search starts. + +Traffic profile is REQUIRED by [RFC2544] to contain some specific quantities, +for example frame size. +Several more specific quantities may be RECOMMENDED. + +Depending on SUT configuration, e.g. when testing specific protocols, +additional values need to be included in the traffic profile +and in the test report. See other IETF documents. + +## Search Goal + +A search goal is one item of the list required as an argument +when the manager calls the controller. + +Each search goal is composite consisting of several attributes, +some of them are required. +Implementations are free to add their own attributes. + +Subsections list all required attributes and one recommended attribute. + +The meaning of the attributes is formally given only by their effect +on the computation of the attributes of the goal result. +The subsections do contain a short informal description, +but see other chapters for more in-depth explanations. + +### Goal Final Trial Duration + +A threshold value for trial durations. +REQUIRED attribute, MUST be positive. + +Informally, the conditional throughput for this goal will be computed +only from trial results from trials as long as this. + +### Goal Duration Sum + +A threshold value for a particular sum of trial durations. +REQUIRED attribute, MUST be positive. + +This uses the duration values returned by the measurer, +in case it returns something else than the intended durations +for the traffic part of the search. + +Informally, even at looking only at trials done at this goal's +final trial duration, MLRsearch may spend up to this time measuring +the same load value. + +### Goal Loss Ratio + +A threshold value for trial loss ratios. +REQUIRED attribute, MUST be non-negative and smaller than one. + +Informally, if a load causes too many trials with trial results larger than this, +the conditional throughput for this goal will be smaller than that load. + +### Goal Exceed Ratio + +A threshold value for particular ratio of duration sums. +REQUIRED attribute, MUST be non-negative and smaller than one. + +This uses the duration values returned by the measurer, +in case it returns something else than the intended durations +for the traffic part of the search. + +Informally, this acts as the q-value for a quantile when selecting +the forwarding rate of which trial result becomes the conditional throughput. +For example, when the goal exceed ratio is 0.5 and MLRsearch +happened to use the whole goal duration sum when determining conditional +throughput, it means the conditional throughput is the median +of trial forwarding rates. +In practice, MLRsearch may stop measuring a load before the goal duration sum +is reached, and the conditional throughput in that case frequently +is the worst trial still not exceeding the goal loss ratio. +If the goal duration sum is no larger than the goal fina trial duration, +MLRsearch performs only one trial per load (unless other goals need more) +and the goal exceed ratio has no effect on the search result. + +### Goal Width + +A value used as a threshold for telling when two trial load values +are close enough. + +RECOMMENDED attribute, positive. Implementations without this attribute +MUST give the manager other ways to control the search exit condition. + +Absolute load difference and relative load difference are two popular choices, +but implementations may choose a different way to specify width. + +Informally, this acts as a stopping condition, controling the precision +of the search. The search stops if every goal has reached its precision. + +## Search Result + +Search result is a single composite object returned from the controller +to the manager. +It is a mapping from the search goals (see section Search Goal) into goal results +(see section Goal Result). +The mapping MUST map from all the search goals present in the controller input. + +Each search goal instance is mapped to a goal result instance. +Multiple search goal instances may map to the same goal result instance. + +## Goal Result + +Goal result is a composite object consisting of several attributes. +All attributes are related to the same search goal, the one search goal instance +the Search Result is mapping into this instance of the Goal Result. + +Some of the attributes are required, some are recommended, +implementations are free to add their own. + +The subsections define attributes for regular goal result. +Implementations are free to define their own irregular goal results, +but the manager MUST report them clearly as not regular according to this section. + +A typical irregular result is when all trials at maximum offered load +have zero loss, as the relevant upper bound does not exist in that case. + +### Relevant Upper Bound + +Relevant upper bound is the intended load value that is classified +at the end of the search as the relevant upper bound (see Appendix A) +for this goal. +This is a REQUIRED attribute. + +Informally, this is the smallest intended load that failed to uphold +all the requirements of this search goal, mainly the goal loss ratio +in combination with the goal exceed ratio. + +### Relevant Lower Bound + +Relevant lower bound is the intended load value that got classified +(after all trials) as the relevant lower bound (see Appendix A) for this goal. +This is a REQUIRED attribute. + +The distance between the relevant lower bound and the relevant upper bound +MUST NOT be larger than the goal width, for a regular goal result, +if the implementation offers width as a goal attribute. + +Informally, this is the smallest intended load that managed to uphold +all the requirements of this search goal, mainly the goal loss ratio +in combination with the goal exceed ratio, while not being larger +than the relevant upper bound. + +### Conditional Throughput + +The conditional throughput (see Appendix B) as evaluated +at the relevant lower bound. +This is a RECOMMENDED attribute. + +Informally, a typical forwarding rate expected to be seen +at the relevant lower bound. But frequently just a conservative estimate thereof, +as MLRsearch implementations tend to stop gathering more data +as soon as they confirm this estimate cannot get worse within +the goal duration sum. + +# MLRsearch Explanations + +This chapter focuses on intuitions and motivations +and skips over some important details. + +Familiarity with the MLRsearch specification is not required here, +so this chapter can act as an introduction. +For example, this chapter start talking about tightest lower bounds +before it is ready to talk about the relevant lower bound from the specification. + +## MLRsearch Versions + +The MLRsearch algorithm has been developed in a code-first approach, +a Python library has been created, debugged and used in production +before first descriptions (even informal) were published. +In fact, multiple versions of the library were used in production +over past few years, and later code was usually not compatible +with earlier descriptions. + +The code in (any version of) MLRsearch library fully determines +the search process (for given configuration parameters), +leaving no space for deviations. +MLRsearch as a name for a broad class of possible algorithms +leaves plenty of space for future improvements, at the cost +of poor comparability of results of different MLRsearch implementations. + +This document aspires to prescribe a MLRsearch specification +in a way that restricts the important parts related to comparability, +while leaving other parts vague enough so implementations can improve freely. + +## Exit Condition + +[RFC2544] prescribes that after performing one trial at a specific offered load, +the next offered load should be larger or smaller, based on frame loss. + +The usual implementation uses binary search. Here a lossy trial becomes +a new upper bound, a lossless trial becomes a new lower bound. +The span of values between the tightest lower bound and the tightest upper bound +forms an interval of possible results, +and after each trial the width of that interval halves. + +Usually the binary search implementation tracks only the two tightest bounds, +simply calling them bounds, but the old values still remain valid bounds, +just not as tight as the new ones. + +After some number of trials, the tightest lower bound becomes the throughput. +[RFC2544] does not specify when (if ever) should the search stop. + +MLRsearch library introduces a concept of goal width. The search stops +when the distance between the tightest upper bound and the tightest lower bound +is smaller than a user-configured value called goal width from now on. +In other words, interval width has to be smaller than goal width +at the end of the search. + +This goal width value therefore determines the precision of the result. +As MLRsearch specification requires a particular structure of the result, +the result itself does contain enough information to determine its precision, +thus it is not required to report the goal width value. + +This allows MLRsearch implementations to use exit conditions +different from goal width. +The MLRsearch specification only REQUIRES the search procedure +to always finish in a finite time, regardless of possible trial results. + +## Load Classification + +MLRsearch keeps the basic logic of binary search (tracking tightest bounds, +measuring at the middle), perhaps with minor technical clarifications. +The algorithm chooses an intended load (as opposed to offered load), +the interval between bounds does not need to be split exactly in two equal halves, +and the final reported structure specifies both bounds +(optionally also the conditional throughput at the lower bound, defined later). + +The biggest difference is that in order to classify a load +as an upper or lower bound, MLRsearch may need more than one trial +(depending on configuration options) to be performed at the same intended load. + +As a consequence, even if a load already does have few trial results, +it still may be classified as undecided, neither a lower bound nor an upper bound. + +Explanation of the classification logic is given in the next chatper, +as it relies heavily on other sections of this chapter. + +For repeatability and comparability reasons, it is important that +given a set of trial results, all implementations of MLRsearch +classify the load in an equivalent way. + +## Loss Ratios + +Next difference is in goals of the search. [RFC2544] has a single goal, +based on classifying full-length trials as either loss-less or lossy. + +As the name suggests, MLRsearch can seach for multiple goals, differing in their +loss ratios. Precise definition of goal loss ratio will be given later. +The [RFC2544] throughput goal then simply becomes a zero goal loss ratio. +Different goals also may have different goal width. + +A set of trial results for one specific intended load value +can classify the load as an upper bound for some goals, but a lower bound +for some other goals, and undecided for the rest of the goals. + +Therefore, the load classification depends not only on ttrial results, +but also on the goal. The overall search procedure becomes more complicated +(compared to binary search with a single goal), +but most of the complications do not affect the final result, +except for one phenomenon, loss inversion. + +## Loss Inversion + +In [RFC2544] throuhput search using bisection, any load with lossy trial +becomes a hard upper bound, meaning every subsequent trial has smaller +intended load. + +But in MLRsearch, a load that is classified as an upper bound for one goal +may still be a lower bound for another goal, and due to that other goal +MLRsearch will probably perform trials at even higher loads. +What to do when all such higher load trials happen to have zero loss? +Does it mean the earlier upper bound was not real? +Does it mean the later lossless trials are not considered a lower bound? +Surely we do not want to have an upper bound at a load smaller than a lower bound. + +MLRsearch is conservative in these situations. +The upper bound is considered real, and the lossless trials at higher loads +are considered to be a coincidence, at least when computing the final result. + +This is formalized using new notions, the relevant upper bound and +the relevant lower bound. +Load classification is still based just on the set of trial results +at a given intended load (trials at other loads are ignored), +making it possible to have a lower load classified as an upper bound +and a higher load classified as a lower bound (for the same goal). +The relevant upper bound (for a goal) is the smallest load classified +as an upper bound. But the relevant lower bound is not simply +the largest among lower bounds. It is the largest load among loads +that are lower bounds while also being smaller than the relevant upper bound. + +With these definitions, the relevant lower bound is always smaller +than the relevant upper bound (if both exist), and the two relevant bounds +are used analogously as the two tightest bounds in the binary search. +When they are less than goal width apart, the relevant bounds are used in output. + +One consequence is that every trial result can have an impact on the search result. +That means if your SUT (or your traffic generator) needs a warmup, +be sure to warm it up before starting the search. + +## Exceed Ratio + +The idea of performing multiple trials at the same load comes from +a model where some trial results (those with high loss) are affected +by infrequent effects, causing poor repeatability of [RFC2544] throughput results. +See the discussion about noiseful and noiseless ends of SUT performance spectrum. +Stable results are closer to the noiseless end of SUT preformance spectrum, +so MLRsearch may need to allow some frequency of high-loss trials +to ignore the reare but big effects near the noisefull end. + +MLRsearch is able to do such trial result filtering, but it needs +a configuration option to tell it how much frequent can the infrequent big loss be. +This option is called exceed ratio. It tells MLRsearch what ratio of trials +(more exactly what ratio of trial seconds) can have trial loss ratio +larger than goal loss ratio and still be classified as a lower bound. +Zero exceed ratio means all trials have to have trial loss ratio +equal to or smaller than the goal loss ratio. + +For explainability reasons, the RECOMMENDED value for exceed ratio is 0.5, +as it simplifies some later concepts by relating them to the concept of median. + +## Duration Sum + +When more than one trial is needed to classify a load, +MLRsearch also needs something that controlls the number of trials needed. +Therefore, each goal also has an attribute called duration sum. + +The meaning of a goal duration sum is that when a load has trials +(at full trial duration, details later) +whose trial durations when summed up give a value at least this, +the load is guaranteed to be classified as an upper bound or a lower bound +for the goal. + +As the duration sum has a big impact on the overall search duration, +and [RFC2544] prescibes wait intervals around trial traffic, +the MLRsearch algorithm may sum durations that are different +from the actual trial traffic durations. + +## Short Trials + +Section 24 of [RFC2544] already anticipates possible time savings +when short trials (shorter than full length trials) are used. + +MLRsearch requires each goal to specify its final trial duration. +Full-length trial is the short name for a trial whose intended trial duration +is equal to the goal final trial duration. + +Any MLRsearch implementation may include its own configuration options +which control when and how MLRsearch chooses to use shorter trial durations. + +For explainability reasons, when exceed ratio of 0.5 is used, +it is recommended for the goal duration sum to be an odd multiple +of the full trial durations, so conditional throughput becomes identical to +a median of a particular set of forwarding rates. + +Presence of shorter trial results complicates the load classification logic. +Full details are given later. In short, results from short trials +may cause a load to be classified as an upper bound. +This may cause loss inversion, and thus lower the relevant lower bound +(below what would classification say when considering full-length trials only). + +For explainability reasons, it is RECOMMENDED users use such configurations +that guarantee all trials have the same length. +Alas, such configurations are usually not compliant with [RFC2544] requirements, +or not time-saving enough. + +## Conditional Throughput + +As testing equipment takes intended load as input parameter +for a trial measurement, any load search algorithm needs to deal +with intended load values internally. + +But in presence of goals with non-zero loss ratio, the intended load +usually does not match the user intuition of what a throughput is. +The forwarding rate (as defined in [RFC2285] section 3.6.1) is better, +but it is not obvious how to generalize it +for loads with multiple trial results, +especially with non-zero goal exceed ratio. + +MLRsearch defines one such generalization, called the conditional throughput. +It is the forwarding rate from one of the trials performed at the load +in question. Specification of which trial exactly is quite technical. +More detailed explanations are given in the next chapter. + +Conditional throughput is partially related to load classification. +If a load is classified as a lower bound for a goal, +the conditional throughpt can be calculated, +and guaranteed to show effective loss ratio no larger than goal loss ratio. + +While the conditional throughput gives more intuitive-looking values +than the relevant lower bound, especially for non-zero goal loss ratio values, +the actual definition is more complicated than the definition of the relevant +lower bound. In future, other intuitive values may become popular, +but they are unlikely to supersede the definition of the relevant lower bound +as the most fitting value for comparability purposes, +therefore the relevant lower bound remains a required attribute +of the goal result structure. + +Note that comparing best and worst case, the same relevant lower bound value +may result in the conditional throughput differing up to the goal loss ratio. +Therefore it is rarely needed to set the goal width (if expressed +as relative difference of loads) below the goal loss ratio. +In other words, setting the goal width below the goal loss ratio +may cause the conditional throughput for a larger loss ratio to became smaller +than a conditional throughput for a goal with a smaller goal loss ratio, +which is counter-intuitive, considering they come from the same search. +Therefore it is RECOMMENDED to set the goal width to a value no smaller +than the goal loss ratio. + +## Search Time + +The main motivation for MLRsearch was to have an algorithm that spends less time +finding a throughput, either the [RFC2544] compliant one, +or some generalization thereof. The art of achieving short search times +is mainly in smart selection of intended loads (and intended durations) +for the next trial to perform. + +While there is an indirect impact of the load selection on the reported values, +in practice such impact tends to be small, +even for SUTs with quite broad performance spectrum. + +A typical example of two approaches to load selection leading to different +relevant lower bounds is when the interval is split in a very uneven way. +An implementation chosing loads very close to the current relevant lower bound +are quite likely to eventually stumble upon a trial result +with poor performance (due to SUT noise). +For an implementation chosing load very close to the current relevant upper bound +this is unlikely, as it examines more loads that can see a performance +close to the noiseless end of the SUT performance spectrum. +The reason why it is unlikely to have two MLRsearch implementation showing +this kind of preference in load selection is precisely +in the desire to have short searches. +Even splits are the best way to achive the desired precision, +so the more optimized a search algorithm is for the overall search duration, +the better the repeatability and comparability +of its results will be, assuming the user configuration remains the same. + +Therefore, this document remains quite vague on load selection +and other optimisation details, and configuration attributes related to them. +Assuming users prefer libreries that achieve short overall search time, +the definition of the relevant lower bound +should be strict enough to ensure result repeatability +and comparability between different implementations, +while not restricting future implementations much. + +Sadly, different implementations may exhibit their sweet spot of +best repeatability at given search duration at different goals attribute values, +especially with respect to optional goal attributes +such as initial trial duration. +Thus, this document does not comment much on which configurations +are good for comparability between different implementations. +For comparability between different SUTs using the same implementation, +refer to configurations recommended by that particular implementation. + +## [RFC2544] compliance + +The following search goal ensures unconditional compliance with +[RFC2544] throughput search procedure: + +- Goal loss ratio: zero. + +- Goal final trial duration: 60 seconds. + +- Goal duration sum: 60 seconds. + +- Goal exceed ratio: zero. + +Presence of other search goals does not affect compliance of this goal result. +The relevant lower bound and the conditional throughput are in this case +equal to each other, and the value is the [RFC2544] throughput. + +If the 60 second quantity is replaced by a smaller quantity in both attributes, +the conditional throughput is still conditionally compliant with +[RFC2544] throughput. + +# Selected Functional Details + +This chapter continues with explanations, +but this time more precise definitions are needed +for readers to follow the explanations. +The definitions here are wordy, implementers can look into the next chapter +for more concise definitions. + +The two areas of focus in this chapter are the load classification +and the conditional throughput, starting with the latter. + +## Performance Spectrum + +There are several equivalent ways to define the conditional throughput computation. +One of the ways relies on an object called the performance spectrum. +First, two heavy definitions are needed. + +Take an intended load value, and a finite set of trial results, all trials +measured at that load value. The performance spectrum is the function that maps +any non-negative real number into a sum of trial durations among all trials +in the set that have that number as their forwarding rate, +e.g. map to zero if no trial has that particular forwarding rate. + +A related function, defined if there is at least one trial in the set, +is the performance spectrum divided by sum of durations of all trials in the set. +That function is called the performance probability function, as it satisfies +all the requirements for probability mass function function +of a discrete probability distribution, +the one-dimensional random variable being the trial forwarding rate. + +These functions are related to the SUT performance spectrum, +as sampled by the trials in the set. + +As for any other probability function, we can talk about percentiles, +of the performance probability function, and bout other quantiles +such as the median. The conditional throughput will be +one such quantile value for a specifically chosen set of trials. + +Take a set of all full-length trials performed at the load in question. +The sum of durations of those trials may be less than goal duration sum, or not. +If it is less, add an imaginary trial result with zero forwarding rate +such that the new sum of durations is equal to the goal duration sum. +This is the set of trials to use. The q-value for the quantile +is the goal exceed ratio. If the quantile touches two trials, +the larger forwarding rate is used. + +First example. For zero exceed ratio when goal duration sum +has been reached. The conditional throughput is the smallest forwarding +rate among the trials. + +Second example. For zero exceed ratio when goal duration sum +has not been reached yet. Due to the missing duration sum, +the worst case may still happen, so the conditional througput +is zero. This is not reported to the user, as this load +cannot become the relevant lower bound yet. + +Third example. Exceed ratio 50%, goal duration sum two seconds, +one trial present with duration one second and zero loss. +An imaginary trial is added with duration one second and zero forwarding rate. +Median would touch both trials, so the conditional throughput +is the forwarding rate of the one non-imaginary trial. +As that had zero loss, the value is equal to the offered load. + +The classification does not need the whole performance spectrum, +only few duration sums. + +A trial is called bad (according to a goal) if its trial loss ratio +is larger than the goal loss ratio. Trial that is not bad is called good. + +## Single Trial Duration + +When goal attributes are chosen in such a way that every trial has the same +intended duration, the load classification is sipler. + +The following description looks technical, but it follows the motivation +of goal loss ratio, goal exceed ratio and goal duration sum. +If sum of durations of all trials (at given load) is less than the goal +duration sum, imagine best case scenario (all subsequent trials having zero loss) +and worst case scenario (all subsequent trials having 100% loss). +Here we assume there is as many subsequent trials as needed +to make the sum of all trials to become equal to the goal duration sum. +As the exceed ratio is defined just using sums of durations +(number of trials does not matter), it does not matter whether +the "subsequent trials" can consist of integer number of full-length trials. + +If even in the best case scenario the load exceed ratio would be larger +than the goal exceed ratio, the load is an upper bound. +If even in the worst case scenario the load exceed ratio would not be larger +than the goal exceed ratio, the load is a lower bound. + +Even more specifically. +Take all trials measured at a given load. +Sum of durations of all bad full-length trials is called the bad sum. +Sum of durations of all good full-length trials is called the good sum. +The result of adding bad sum plus the good sum is called the measured sum. +The larger of the measured sum and the goal duration sum is called the whole sum. +The whole sum minus the measured sum is called the missing sum. +Optimistic exceed ratio is the bad sum divided by the whole sum. +Pessimistic exceed ratio is the bad sum plus the missing sum, that divided by +the whole sum. +If optimistic exceed ratio is larger than the goal exceed ratio, +the load is classified as an upper bound. +If pessimistic exceed ratio is not larger than the goal exceed ratio, +the load is classified as a lower bound. +Else, the load is classified as undecided. + +The definition of pessimistic exceed ratio matches the logic in +the conditional throughput computation, so a load is a lower bound +if and only if the conditional throughput effective loss ratio +is not larger than the goal loss ratio. +If it is larger, the load is either an upper bound or undecided. + +## Short Trial Scenarios + +Trials with intended duration smaller than the goal final trial duration +are called short trials. +The motivation for load classification logic in presence of short trials +is based around a counter-factual case: What would the trial result be +if a short trial has been measured as a full-length trial instead? + +There are three main scenarios where human intuition guides +the intended behavior of load classification. + +Scenario one. The user had their reason for not configuring shorter goal +final trial duration. Perhaps SUT has buffers that may get full at longer +trial durations. Perhaps SUT shows periodic decreases of performance +the user does not want to treat as noise. In any case, many good short trials +may became bad full-length trial in the counter-factual case. +In extreme case, there are no bad short trials. +In this scenario, we want the load classification NOT to classify the load +as a lower bound, despite the abundance of good short trials. +Effectively, we want the good short trials to be ignored, so they +do not contribute to comparisons with the goal duration sum. + +Scenario two. When there is a frame loss in a short trial, +the counter-factual full-length trial is expected to lose at least as many +frames. And in practice, bad short trials are rarely turning into +good full-length trials. In extreme case, there are no good short trials. +In this scenario, we want the load classification +to classify the load as an upper bound just based on abundance +of short bad trials. Effectively we want the bad short trials +to contribute to comparisons with the goal duration sum, +so the load can be classified sooner. + +Scenario three. Some SUTs are quite indifferent to trial duration. +Performance probability function constructed from short trial results +is likely to be similar to performance probability function constructed +from full-length trial results (perhaps with smaller dispersion, +but overall without big impact on the median quantiles). +For moderate goal exceed ratio values, this may mean there are both +good short trials and bad short trials. +This scenario is there just to invalidate a simple heuristic +of always ignoring good short trials and never ignoring bad short trials. +That simple heuristic would be too biased. Yes, the short bad trials +are likely to turn into full-length bad trials in the counter-factual case, +but there is no information on what would the good short trials turn into. +The only way to decide is to do more trials at full length, +the same as in scenario one. + +## Short Trial Logic + +MLRsearch picks a particular logic for load classification +in presence of short trials, but it is still RECOMMENDED to use configurations +that imply no short trials, so the possible inefficiencies in that logic +do not affect the result, and the result has better explainability. + +With thas said, the logic differs from the single trial duration case +only in different definition of bad sum. +Good sum is still the sum across all good full-length trials. + +Few more notions are needed for definig the new bad sum. +Sum of durations of all bad full-length trials is called the bad long sum. +Sum of durations of all bad short trials is called the bad short sum. +Sum of durations of all good short trials is called the good short sum. +One minus the goal exceed ratio is called the inceed ratio. +The goal exceed ratio divided by the inceed ratio is called the exceed coefficient. +The good short sum multiplied by the exceed coefficient is called the balancing sum. +The bad short sum minus the balancing sum is called the excess sum. +If the excess sum is negative, the bad sum is equal to the bad long sum. +Else, the bad sum is equal to the bad long sum plus the excess sum. + +Here is how the new definition of the bad sum fares in the three scenarios, +where the load is close to what would relevant bounds be +if only full-length trials were used for the search. + +Scenario one. If duration is too short, we expect to see higher frequency +of good short trials. This could lead to negative excess sum, +which has no impact, hence the load classification is given just by +full-length trials. +Thus, MLRsearch using too short trials has no detrimental effect +on result comparability in this scenario. +But also using short trials does not help with overall search duration, +proably making it worse. + +Scenario two. Settings with small exceed ratio have small exceed coefficient, +so the impact of good short sum is small and the bad short sum +is almost wholly converted into excess sum, thus bad short trials +have almost as big impact as full-length bad trials. +The same conclusion applies for moderate exceed ratio values +when the good short sum is small. +Thus, short trials can cause a load to get classified as an upper bound earlier +bringing time savings (while not affecting comparability). + +Scenario three. Here excess sum is small in absolute value, as balancing sum +is expected to be be similar to the bad short sum. +Once again, full-length trials are needed for final load classification, +but usage of short trials probably means MLRsearch needed shorter search time +before selecting this load for measurement, bringing time savings +(while not affecting comparability). + +## Longer Trial Durations + +If there are trial results with intended duration larger +than the goal trial duration, the classification logic is intentionally undefined. + +The implementations MAY treat such longer trials as if they were full-length. +In any case, presence of such longer trials in either the relevant lower bound +or the relevant upper bound SHOULD be mentioned, as for sume SUTs +it is likely to affect comparability. + + +TODO: Here will be a chapter summarizing how MLRsearch library +adresses the problems from the Identified Problems chapter. + +{::comment} + + # Problems after MLRsearch + + Now when MLRsearch is clearly specified and explained, + it is possible to summarize how does MLRsearch specification help with problems. + + Here, "multiple trials" is a shorthand for having the goal final trial duration + significantly smaller than the goal duration sum. + This results in MLRsearch performing multiple trials at the same load, + which may not be the case with other configurations. + + ## Long Test Duration + + As shortening the overall search duration is the main motivation + of MLRsearch library development, the library implements + multiple improvements on this front, both big and small. + Most of implementation details are not part of the MLRsearch specification, + so that future implementations may keep shortening the search duration even more. + + TODO: The rest is about attributes. + + From the required goal attributes, the goal duration sum + remains the best way to get even shorter searches. + + Usage of multiple trials can also save time, + depending on wait times around trial traffic. + + The farther the goal exceed ratio is from 0.5 towards either side, + the less predictable the overal search duration becomes in practice. + + Width parameter does not change search duration much in practice + (compared to other, mainly optional goal attributes). + + ## DUT in SUT + + Practice shows big improvements when multiple trials + and moderate exceed ratios are used. Mainly when it comes to result + repeatability, as sometimes it is not easy to distinguish + SUT noise from DUT instability. + + Conditional throughput has intuitive meaning when described + using the performance spectrum, so this is an improvement, + especially when compared to search procedures which use non-zero + goal loss ratio but return only the intended load at a lower bound. + + Multiple trials can save time also when the noisy end of + the preformance spectrum needs to be examined, e.g. for [RFC9004]. + + Under some circumstances, testing the same DUT and SUT setup with different + DUT configurations can give some hints on what part of noise us SUT noise + and what part is DUT performance fluctuations. + In practice, both types of noise tend to be too complicated for that analysis. + MLRsearch does not offer additional tools in this regard, + apart of giving users ability to search for more goals, + hoping to get more insight at the cost of longer overall search time. + + ## Repeatability and Comparability + + Multiple trials improve repeatability, depending on exceed ratio. + + In practice, 1s goal final trial duration with exceed ratio 0.5 + is good enough for modern SUTs (but that usually requires + smaller wait times around the traffic part of the trial, + otherwise too much search time is wasted waiting). + + It is not clear whether exceed ratios higher than 0.5 are better + for repeatability. + The 0.5 value is still preferred due to explainability using median. + TODO: Stress single value is for comparability, which one is due explainability. + + It is possible that the conditional throughput values (with non-zero + goal loss ratio) are better for repeatability than the relevant + lower bound values, especially for implementations + which pick load from a small set of discrete values. + + Implementations focusing on shortening the overall search time + are automatically forced to avoid comparability issues + due to load selection, as they must prefer even splits wherever possible. + But this conclusion only holds when the same goals are used. + Larger adoption is needed before any further claims on comparability + between MLRsearch implementations can be made. + + ## Throughput with Non-Zero Loss + + Suported by the goal loss ratio attribute. + Improves repeatability as expected. + + ## Inconsistent Trial Results + + MLRsearch is conservative wherever possible, + this is built into the definition of conditional throughput, + and into the treatment of short trial results for load classification. + + This is consistent with [RFC2544] zero loss tolerance motivation. + + If the very best (noiseless) part of the SUT performance spectrum + is of interest, it should be enough to set small value for + the goal final trial duration, and perhaps also a large value + for the goal exceed ratio. + + Implementations may offer other (optional) configuration attributes + (and optional goal result attributes) + to become less conservative, but currently it is not clear + what impact would that have on repeatability. + +{:/comment} + +# IANA Considerations + +No requests of IANA. + +# Security Considerations + +Benchmarking activities as described in this memo are limited to +technology characterization of a DUT/SUT using controlled stimuli in a +laboratory environment, with dedicated address space and the constraints +specified in the sections above. + +The benchmarking network topology will be an independent test setup and +MUST NOT be connected to devices that may forward the test traffic into +a production network or misroute traffic to the test management network. + +Further, benchmarking is performed on a "black-box" basis, relying +solely on measurements observable external to the DUT/SUT. + +Special capabilities SHOULD NOT exist in the DUT/SUT specifically for +benchmarking purposes. Any implications for network security arising +from the DUT/SUT SHOULD be identical in the lab and in production +networks. + +# Acknowledgements + +Many thanks to Alec Hothan of OPNFV NFVbench project for thorough +review and numerous useful comments and suggestions. + +Special wholehearted gratitude and thanks to late Al Morton for his +thorough reviews filled with very specific feedback and constructive +guidelines. Thank you Al for the close collaboration over the years, +for your continuous unwavering encouragements full of empathy and +positive attitude. +Al, you are dearly missed. + +# Appendix A + +This is a specification of load classification. + +The block at the end of this appendix holds pseudocode +which computes two values, stored in variables named optimistic and pessimistic. +The pseudocode happens to be a valid Python code. + +If both values are computed to be true, the load in question +is classified as a lower bound according to the goal in question. +If both values are false, the load is classified as an upper bound. +Otherwise, the load is classifies as undecided. + +The pseudocole expects the following variables hold values as follows: + +- goal_duration_sum: The goal duration sum value. + +- goal_exceed_ratio: The goal exceed ratio value. + +- good_long_sum: Sum of durations across trials with trial duration + at least equal to the goal final trial duration and with trial loss ratio + not higher than the goal loss ratio. + +- bad_long_sum: Sum of durations across trials with trial duration + at least equal to the goal final trial duration and with trial loss ratio + higher than the goal loss ratio. + +- good_short_sum: Sum of durations across trials with trial duration + shorter than the goal final trial duration and with trial loss ratio + not higher than the goal loss ratio. + +- bad_short_sum: Sum of durations across trials with trial duration + shorter than the goal final trial duration and with trial loss ratio + higher than the goal loss ratio. + +Here the implicit set of available trial results consists of all trials +measured at given intended load at the end of search. + +The code works correctly also when there are no trial results at given load. + +``` +balancing_sum = good_short_sum * goal_exceed_ratio / (1.0 - goal_exceed_ratio) +effective_bad_sum = bad_long_sum + max(0.0, bad_short_sum - balancing_sum) +effective_whole_sum = max(good_long_sum + effective_bad_sum, goal_duration_sum) +quantile_duration_sum = effective_whole_sum * goal_exceed_ratio +optimistic = effective_bad_sum <= quantile_duration_sum +pessimistic = (effective_whole_sum - good_long_sum) <= quantile_duration_sum +``` + +# Appendix B + +This is a specification of conditional throughput. + +The block at the end of this appendix holds pseudocode +which computes a value stored as variable conditional_throughput. +The pseudocode happens to be a valid Python code. + +The pseudocole expects the following variables hold values as follows: + +- goal_duration_sum: The goal duration sum value. + +- goal_exceed_ratio: The goal exceed ratio value. + +- good_long_sum: Sum of durations across trials with trial duration + at least equal to the goal final trial duration and with trial loss ratio + not higher than the goal loss ratio. + +- bad_long_sum: Sum of durations across trials with trial duration + at least equal to the goal final trial duration and with trial loss ratio + higher than the goal loss ratio. + +- long_trials: An iterable of all trial results from trials with trial duration + at least equal to the goal final trial duration, + sorted by increasing trial loss ratio. + A trial result is a composite with the following two attributes available: + + - trial.loss_ratio: The trial loss ratio as measured for this trial. + + - trial.duration: The trial duration of this trial. + +Here the implicit set of available trial results consists of all trials +measured at given intended load at the end of search. + +The code works correctly only when there if there is at leas one +trial result measured at given load. + +``` +all_long_sum = max(goal_duration_sum, good_long_sum + bad_long_sum) +remaining = all_long_sum * (1.0 - goal_exceed_ratio) +quantile_loss_ratio = None +for trial in long_trials: + if quantile_loss_ratio is None or remaining > 0.0: + quantile_loss_ratio = trial.loss_ratio + remaining -= trial.duration + else: + break +else: + if remaining > 0.0: + quantile_loss_ratio = 1.0 + +conditional_throughput = intended_load * (1.0 - quantile_loss_ratio) +``` + +--- back |