Multiple Loss Ratio Search

2.1. 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.¶

2.2. 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.¶

2.3. 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.¶

2.4. 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.¶

2.5. 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.¶

3.1. 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.¶

3.2. 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.¶

3.3. SUT

As defined in [RFC2285]: The collective set of network devices to which stimulus is offered as a single entity and response measured.¶

3.4. Trial

A trial is the part of test described in [RFC2544] section 23.¶

3.5. 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.¶

3.6. 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.¶

3.7. 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.¶

3.8. 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.¶

4.1. 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.¶

4.2. 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.¶

4.3. 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.¶

4.4. 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.¶

4.5. 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.¶

4.6. 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.¶

4.7. 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.¶

4.8. 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.¶

4.9. 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.¶

4.10. 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.¶

4.11. [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.¶

5.1. 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.¶

5.2. 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.¶

5.3. 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.¶

5.4. 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).¶

5.5. 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.¶