Multiple Loss Ratio Search

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 throughput bisection to software DUTs results in several problems: Binary search takes too long as most 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 a 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. To address the problems mentioned above, the MLRsearch test methodology specification employs the following enhancements: Allow multiple short trials instead of one big trial per load. Optionally, tolerate a percentage of trial results 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 (section 3.6.2) to initialize the initial targets. Take care when dealing with inconsistent trial results. Reported throughput is smaller than the 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. The conservative settings lead to results unconditionally compliant with , 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 . No part of is intended to be obsoleted by this document.

Identified Problems This chapter describes the problems affecting usability of various performance testing methodologies, mainly a binary search for unconditionally compliant throughput.

Long Search Duration The 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 required to verify the DUT update and the frequency of running those tests. This makes the overall test execution time even more important than before. The current throughput definition restricts the potential for time-efficiency improvements. A more generalized throughput concept could enable further enhancements while maintaining the precision of simpler methods. The bisection method, when unconditionally compliant with , is excessively slow. This is because a significant amount of time is spent on trials with loads that, in retrospect, are far from the final determined throughput. does not specify any stopping condition for throughput search, so users already have an access to a limited trade-off between search duration and achieved precision. However, each full 60-second trials doubles the precision, so not many trials can be removed without a substantial loss of precision.

DUT in SUT defines: - DUT as - The network forwarding device to which stimulus is offered and response measured (section 3.1.1). - SUT as - The collective set of network devices to which stimulus is offered as a single entity and response measured (section 3.1.2). 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 the case of software networking, the SUT consists of not only the DUT as a software program processing frames, but also of server hardware and operating system functions, with that server hardware resources shared across all programs including the operating system. Given that the SUT is a shared multi-tenant environment encompassing the DUT and other components, the DUT might inadvertently experience interference from the operating system or other software operating on the same server. Some of this interference can be mitigated. For instance, pinning DUT program threads to specific CPU cores and isolating those cores can prevent context switching. Despite taking all feasible precautions, some adverse effects may still impact the DUT's network performance. In this document, these effects are collectively referred to as SUT noise, even if the effects are not as unpredictable as what other engineering disciplines call 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 distinguish, in this document the term 'noise' is used to encompass both the internal performance fluctuations of the DUT and the genuine noise of the SUT. A simple model of SUT performance consists of an idealized noiseless performance, and additional noise effects. For a specific SUT, the noiseless performance is assumed to be constant, with all observed performance variations being attributed 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 result close to the noiseful end of the spectrum happens only rarely. The worse the performance value is, the more rarely it is seen in a trial. Therefore, the extreme noiseful end of the SUT spectrum is not observable among trial results. Also, the extreme noiseless end of the 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's focus is on the potentially observable ends of the SUT performance spectrum, as opposed to the extreme ones. When focusing on the DUT, the benchmarking effort should ideally aim to eliminate only the SUT noise from SUT measurements. However, this is currently not feasible in practice, as there are no realistic enough models available to distinguish SUT noise from DUT fluctuations, based on authors' experience and available literature. Assuming a well-constructed SUT, the DUT is likely its primary performance bottleneck. In this case, we can define the DUT's ideal noiseless performance as the noiseless end of the SUT performance spectrum, especially for throughput. However, other performance metrics, such as latency, may require additional considerations. 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. MLRsearch methodology aims to solve the DUT in SUT problem by estimating the noiseless end of the SUT performance spectrum using a limited number of trial results. Any improvements to the throughput search algorithm, aimed at better dealing with software networking SUT and DUT setup, should employ strategies recognizing the presence of SUT noise, allowing the discovery of (proxies for) DUT noiseless performance at different levels of sensitivity to SUT noise.

Repeatability and Comparability does not suggest to repeat throughput search. And from just one discovered throughput value, it cannot be determined how repeatable that value is. Poor repeatability then leads to poor comparability, as different benchmarking teams may obtain varying throughput values for the same SUT, exceeding the expected differences from search precision. 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 short trials would, thus causing poor throughput repeatability. The repeatability problem can be addressed by defining a search procedure that identifies a consistent level of performance, even if it does not meet the strict definition of throughput in . 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 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 (section 3.17 Throughput) 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. However, many benchmarking teams accept a small, non-zero loss ratio as the goal for their load search. Motivations are many: Modern protocols tolerate frame loss better, compared to the time when and were specified. Trials nowadays send way more frames within the same duration, increasing the chance of a small SUT performance fluctuation being enough to cause frame loss. Small bursts of frame loss caused by noise have otherwise smaller impact on the average frame loss ratio observed in the trial, as during other parts of the same trial the SUT may work more 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 the validity of all similar motivations, support for non-zero loss goals makes any search algorithm more user-friendly. throughput is not user-friendly in this regard. Furthermore, allowing users to specify multiple loss ratio values, and enabling a single search to find all relevant bounds, significantly enhances the usefulness of the search algorithm. Searching for multiple Search Goals also helps to describe the SUT performance spectrum better than the result of a single Search Goal. For example, the 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 the 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 hints about the 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 the results from short 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 a 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 a 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 the presence of such inconsistencies. Definitions of throughput in and 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 repeatability enhancements), while being precise enough to force a specific way to resolve trial result inconsistencies. But until such a definition is agreed upon, the correct way to handle inconsistent trial results remains an open problem.

MLRsearch Specification This section describes MLRsearch specification including all technical definitions needed for evaluating whether a particular test procedure complies with MLRsearch specification.

Overview MLRsearch specification describes a set of abstract system components, acting as functions with specified inputs and outputs. A test procedure is said to comply with MLRsearch specification if it can be conceptually divided into analogous components, each satisfying requirements for the corresponding MLRsearch component. The Measurer component is tasked to perform trials, the Controller component is tasked to select trial loads and durations, the Manager component is tasked to pre-configure everything and to produce the test report. The test report explicitly states Search Goals (as the Controller Inputs) and corresponding Goal Results (Controller Outputs). The Manager calls the Controller once, the Controller keeps calling the Measurer until all stopping conditions are met. The part where Controller calls the Measurer is called the search. Any activity done by the Manager before it calls the Controller (or after Controller returns) is not considered to be part of the search. MLRsearch specification prescribes regular search results and recommends their stopping conditions. Irregular search results are also allowed, they may have different requirements and stopping conditions. Search results are based on load classification. When measured enough, any chosen load either achieves of fails each search goal, thus becoming a lower or an upper bound for that goal. When the relevant bounds are at loads that are close enough (according to goal precision), the regular result is found. Search stops when all regular results are found (or if some goals are proven to have only irregular results).

Measurement Quantities MLRsearch specification uses a number of measurement quantities. In general, MLRsearch specification does not require particular units to be used, but it is REQUIRED for the test report to state all the units. For example, ratio quantities can be dimensionless numbers between zero and one, but may be expressed as percentages instead. For convenience, a group of quantities can be treated as a composite quantity, One constituent of a composite quantity is called an attribute, and a group of attribute values is called an instance of that composite quantity. Some attributes are not independent from others, and they can be calculated from other attributes. Such quantites are called derived quantities.

Existing Terms RFC 1242 "Benchmarking Terminology for Network Interconnect Devices" contains basic definitions, and RFC 2544 "Benchmarking Methodology for Network Interconnect Devices" contains discussions of a number of terms and additional methodology requirements. RFC 2285 adds more terms and discussions, describing some known situations in more precise way. All three documents should be consulted before attempting to make use of this document. Definitions of some central terms are copied and discussed in subsections.

SUT Defined in (section 3.1.2 System Under Test (SUT)) as follows. Definition: The collective set of network devices to which stimulus is offered as a single entity and response measured. Discussion: An SUT consisting of a single network device is also allowed.

DUT Defined in (section 3.1.1 Device Under Test (DUT)) as follows. Definition: The network forwarding device to which stimulus is offered and response measured. Discussion: DUT, as a sub-component of SUT, is only indirectly mentioned in MLRsearch specification, but is of key relevance for its motivation.

Trial A trial is the part of the test described in (section 23. Trial description). Definition: A particular test consists of multiple trials. Each trial returns one piece of information, for example the loss rate at a particular input frame rate. Each trial consists of a number of phases: a) If the DUT is a router, send the routing update to the "input" port and pause two seconds to be sure that the routing has settled. b) Send the "learning frames" to the "output" port and wait 2 seconds to be sure that the learning has settled. Bridge learning frames are frames with source addresses that are the same as the destination addresses used by the test frames. Learning frames for other protocols are used to prime the address resolution tables in the DUT. The formats of the learning frame that should be used are shown in the Test Frame Formats document. c) Run the test trial. d) Wait for two seconds for any residual frames to be received. e) Wait for at least five seconds for the DUT to restabilize. Discussion: The definition describes some traits, it is not clear whether all of them are REQUIRED, or some of them are only RECOMMENDED. For the purposes of the MLRsearch specification, it is ALLOWED for the test procedure to deviate from the description, but any such deviation MUST be made explicit in the test report. Trials are the only stimuli the SUT is expected to experience during the search. In some discussion paragraphs, it is useful to consider the traffic as sent and received by a tester, as implicitly defined in (section 6. Test set up). An example of deviation from is using shorter wait times.

Trial Terms This section defines new and redefine existing terms for quantities relevant as inputs or outputs of trial, as used by the Measurer component.

Trial Duration Definition: Trial duration is the intended duration of the traffic for a trial. Discussion: In general, this quantity does not include any preparation nor waiting described in section 23 of (section 23. Trial description). While any positive real value may be provided, some Measurer implementations MAY limit possible values, e.g. by rounding down to neared integer in seconds. In that case, it is RECOMMENDED to give such inputs to the Controller so the Controller only proposes the accepted values. Alternatively, the test report MUST present the rounded values as Search Goal attributes.

Trial Load Definition: The trial load is the intended load for a trial Discussion: For test report purposes, it is assumed that this is a constant load by default. This MAY be only an average load, e.g. when the traffic is intended to be busty, e.g. as suggested in (section 21. Bursty traffic), but the test report MUST explicitly mention how non-constant the traffic is. Trial load is the quantity defined as Constant Load of (section 3.4 Constant Load), Data Rate of (section 14. Bidirectional traffic) and Intended Load of (section 3.5.1 Intended load (Iload)). All three definitions specify that this value applies to one (input or output) interface. For test report purposes, multi-interface aggregate load MAY be reported, this is understood as the same quantity expressed using different units. From the report it MUST be clear whether a particular trial load value is per one interface, or an aggregate over all interfaces. Similarly to trial duration, some Measurers may limit the possible values of trial load. Contrary to trial duration, the test report is NOT REQUIRED to document such behavior. It is ALLOWED to combine trial load and trial duration in a way that would not be possible to achieve using any integer number of data frames.

Trial Input Definition: Trial Input is a composite quantity, consisting of two attributes: trial duration and trial load. Discussion: When talking about multiple trials, it is common to say "Trial Inputs" to denote all corresponding Trial Input instances. A Trial Input instance acts as the input for one call of the Measurer component. Contrary to other composite quantities, MLRsearch implementations are NOT ALLOWED to add optional attributes here. This improves interoperability between various implementations of the Controller and the Measurer.

Traffic Profile Definition: Traffic profile is a composite quantity containing attributes other than trial load and trial duration, needed for unique determination of the trial to be performed. Discussion: 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. This is why the traffic profile is not part of the Trial Input. As a consequence, implementations of the Manager and the Measurer must be aware of their common set of capabilities, so that the traffic profile uniquely defines the traffic during the search. The important fact is that none of those capabilities have to be known by the Controller implementations. The traffic profile SHOULD contain some specific quantities, for example (section 9. Frame sizes) governs data link frame size as defined in (section 3.5 Data link frame size). Several more specific quantities may be RECOMMENDED, depending on media type. For example, (Appendix C) lists frame formats and protocol addresses, as recommended from (section 8. Frame formats) and (section 12. Protocol addresses). Depending on SUT configuration, e.g. when testing specific protocols, additional attributes MUST be included in the traffic profile and in the test report. Example: (section 5.3. Traffic Setup) introduces traffic setups consisting of a mix of IPv4 and IPv6 traffic - the implied traffic profile therefore must include an attribute for their percentage. Other traffic properties that need to be somehow specified in Traffic Profile include: (section 14. Bidirectional traffic), (section 3.3.3 Fully meshed traffic), and (section 11. Modifiers).

Trial Forwarding Ratio Definition: The trial forwarding ratio is a dimensionless floating point value. It MUST range between 0.0 and 1.0, both inclusive. It is calculated by dividing the number of frames successfully forwarded by the SUT by the total number of frames expected to be forwarded during the trial Discussion: For most traffic profiles, "expected to be forwarded" means "intended to get transmitted from Tester towards SUT". Trial forwarding ratio MAY be expressed in other units (e.g. as a percentage) in the test report. Note that, contrary to loads, frame counts used to compute trial forwarding ratio are aggregates over all SUT output interfaces. Questions around what is the correct number of frames that should have been forwarded is generally outside of the scope of this document.

Trial Loss Ratio Definition: The Trial Loss Ratio is equal to one minus the trial forwarding ratio. Discussion: 100% minus the trial forwarding ratio, when expressed as a percentage. This is almost identical to Frame Loss Rate of (section 3.6 Frame Loss Rate), the only minor difference is that Trial Loss Ratio does not need to be expressed as a percentage.

Trial Forwarding Rate Definition: The trial forwarding rate is a derived quantity, calculated by multiplying the trial load by the trial forwarding ratio. Discussion: It is important to note that while similar, this quantity is not identical to the Forwarding Rate as defined in (section 3.6.1 Forwarding rate (FR)). The latter is specific to one output interface only, whereas the trial forwarding ratio is based on frame counts aggregated over all SUT output interfaces.

Trial Effective Duration Definition: Trial effective duration is a time quantity related to the trial, by default equal to the trial duration. Discussion: This is an optional feature. If the Measurer does not return any trial effective duration value, the Controller MUST use the trial duration value instead. Trial effective duration may be any time quantity chosen by the Measurer to be used for time-based decisions in the Controller. The test report MUST explain how the Measurer computes the returned trial effective duration values, if they are not always equal to the trial duration. This feature can be beneficial for users who wish to manage the overall search duration, rather than solely the traffic portion of it. Simply measure the duration of the whole trial (waits including) and use that as the trial effective duration. Also, this is a way for the Measurer to inform the Controller about its surprising behavior, for example when rounding the trial duration value.

Trial Output Definition: Trial Output is a composite quantity. The REQUIRED attributes are Trial Loss Ratio, trial effective duration and trial forwarding rate. Discussion: When talking about multiple trials, it is common to say "Trial Outputs" to denote all corresponding Trial Output instances. Implementations may provide additional (optional) attributes. The Controller implementations MUST ignore values of any optional attribute they are not familiar with, except when passing Trial Output instance to the Manager. Example of an optional attribute: The aggregate number of frames expected to be forwarded during the trial, especially if it is not just (a rounded-up value) implied by trial load and trial duration. While (Section 3.5.2 Offered load (Oload)) requires the offered load value to be reported for forwarding rate measurements, it is NOT REQUIRED in MLRsearch specification.

Trial Result Definition: Trial result is a composite quantity, consisting of the Trial Input and the Trial Output. Discussion: When talking about multiple trials, it is common to say "trial results" to denote all corresponding trial result instances. While implementations SHOULD NOT include additional attributes with independent values, they MAY include derived quantities.

Goal Terms This section defines new and redefine existing terms for quantities indirectly relevant for inputs or outputs of the Controller component. Several goal attributes are defined before introducing the main component quantity: the Search Goal.

Goal Final Trial Duration Definition: A threshold value for trial durations. Discussion: This attribute value MUST be positive. A trial with Trial Duration at least as long as the Goal Final Trial Duration is called a full-length trial (with respect to the given Search Goal). A trial that is not full-length is called a short trial. Informally, while MLRsearch is allowed to perform short trials, the results from such short trials have only limited impact on search results. One trial may be full-length for some Search Goals, but not for others. The full relation of this goal to Controller Output is defined later in this document in subsections of [Goal Result] (#Goal-Result). For example, the Conditional Throughput for this goal is computed only from full-length trial results.

Goal Duration Sum Definition: A threshold value for a particular sum of trial effective durations. Discussion: This attribute value MUST be positive. Informally, even when looking only at full-length trials, MLRsearch may spend up to this time measuring the same load value. If the Goal Duration Sum is larger than the Goal Final Trial Duration, multiple full-length trials may need to be performed at the same load. See [TST009 Example] (#TST009-Example) for an example where possibility of multiple full-length trials at the same load is intended. A Goal Duration Sum value lower than the Goal Final Trial Duration (of the same goal) could save some search time, but is NOT RECOMMENDED. See [Relevant Upper Bound] (#Relevant-Upper-Bound) for partial explanation.

Goal Loss Ratio Definition: A threshold value for Trial Loss Ratios. Discussion: Attribute value MUST be non-negative and smaller than one. A trial with Trial Loss Ratio larger than a Goal Loss Ratio value is called a lossy trial, with respect to given Search Goal. Informally, if a load causes too many lossy trials, the Relevant Lower Bound for this goal will be smaller than that load. If a trial is not lossy, it is called a low-loss trial, or (specifically for zero Goal Loss Ratio value) zero-loss trial.

Goal Exceed Ratio Definition: A threshold value for a particular ratio of sums of Trial Effective Durations. Discussion: Attribute value MUST be non-negative and smaller than one. See later sections for details on which sums. Specifically, the direct usage is only in [Appendix A: Load Classification] (#Appendix-A:-Load-Classification) and [Appendix B: Conditional Throughput] (#Appendix-B:-Conditional-Throughput). The impact of that usage is discussed in subsections leading to [Goal Result] (#Goal-Result). Informally, the impact of lossy trials is controlled by this value. Effectively, Goal Exceed Ratio is a percentage of full-length trials that may be lossy without the load being classified as the [Relevant Upper Bound] (#Relevant-Upper-Bound).

Goal Width Definition: A value used as a threshold for deciding whether two trial load values are close enough. Discussion: If present, the value MUST be positive. Informally, this acts as a stopping condition, controlling the precision of the search. The search stops if every goal has reached its precision. Implementations without this attribute MUST give the Controller other ways to control the search stopping conditions. Absolute load difference and relative load difference are two popular choices, but implementations may choose a different way to specify width. The test report MUST make it clear what specific quantity is used as Goal Width. It is RECOMMENDED to set the Goal Width (as relative difference) value to a value no smaller than the Goal Loss Ratio. (The reason is not obvious, see [Throughput] (#Throughput) if interested.)

Search Goal Definition: The Search Goal is a composite quantity consisting of several attributes, some of them are required. Required attributes: - Goal Final Trial Duration - Goal Duration Sum - Goal Loss Ratio - Goal Exceed Ratio Optional attribute: - Goal Width Discussion: Implementations MAY add their own attributes. Those additional attributes may be required by the implementation even if they are not required by MLRsearch specification. But it is RECOMMENDED for those implementations to support missing values by computing reasonable defaults. The meaning of listed attributes is formally given only by their indirect effect on the search results. Informally, later sections provide additional intuitions and examples of the Search Goal attribute values. An example of additional attributes required by some implementations is Goal Initial Trial Duration, together with another attribute that controls possible intermediate Trial Duration values. The reasonable default in this case is using the Goal Final Trial Duration and no intermediate values.

Controller Input Definition: Controller Input is a composite quantity required as an input for the Controller. The only REQUIRED attribute is a list of Search Goal instances. Discussion: MLRsearch implementations MAY use additional attributes. Those additional attributes may be required by the implementation even if they are not required by MLRsearch specification. Formally, the Manager does not apply any Controller configuration apart from one Controller Input instance. For example, Traffic Profile is configured on the Measurer by the Manager (without explicit assistance of the Controller). The order of Search Goal instances in a list SHOULD NOT have a big impact on Controller Output (see section [Controller Output] (#Controller-Output) , but MLRsearch implementations MAY base their behavior on the order of Search Goal instances in a list. An example of an optional attribute (outside the list of Search Goals) required by some implementations is Max Load. While this is a frequently used configuration parameter, already governed by (section 20. Maximum frame rate) and (3.5.3 Maximum offered load (MOL)), some implementations may detect or discover it instead. In MLRsearch specification, the [Relevant Upper Bound] (#Relevant-Upper-Bound) is added as a required attribute precisely because it makes the search result independent of Max Load value.

Search Goal Examples

RFC2544 Goal The following set of values makes the search result unconditionally compliant with (section 24 Trial duration) Goal Final Trial Duration = 60 seconds Goal Duration Sum = 60 seconds Goal Loss Ratio = 0% Goal Exceed Ratio = 0% The latter two attributes are enough to make the search goal conditionally compliant, adding the first attribute makes it unconditionally compliant. The second attribute (Goal Duration Sum) only prevents MLRsearch from repeating zero-loss full-length trials. Non-zero exceed ratio could prolong the search and allow loss inversion between lower-load lossy short trial and higher-load full-length zero-loss trial. From alone, it is not clear whether that higher load could be considered as compliant throughput.

TST009 Goal One of the alternatives to RFC2544 is described in (section 12.3.3 Binary search with loss verification). The idea there is to repeat lossy trials, hoping for zero loss on second try, so the results are closer to the noiseless end of performance sprectum, and more repeatable and comparable. Only the variant with "z = infinity" is achievable with MLRsearch. For example, for "r = 2" variant, the following search goal should be used: Goal Final Trial Duration = 60 seconds Goal Duration Sum = 120 seconds Goal Loss Ratio = 0% Goal Exceed Ratio = 50% If the first 60s trial has zero loss, it is enough for MLRsearch to stop measuring at that load, as even a second lossy trial would still fit within the exceed ratio. But if the first trial is lossy, MLRsearch needs to perform also the second trial to classify that load. As Goal Duration Sum is twice as long as Goal Final Trial Duration, third full-length trial is never needed.

Result Terms Before defining the output of the Controller, it is useful to define what the Goal Result is. The Goal Result is a composite quantity. Following subsections define its attribute first, before describing the Goal Result quantity. There is a correspondence between Search Goals and Goal Results. Most of the following subsections refer to a given Search Goal, when defining attributes of the Goal Result. Conversely, at the end of the search, each Search Goal has its corresponding Goal Result. Conceptually, the search can be seen as a process of load classification, where the Controller attempts to classify some loads as an Upper Bound or a Lower Bound with respect to some Search Goal. Before defining real attributes of the goal result, it is useful to define bounds in general.

Relevant Upper Bound Definition: The Relevant Upper Bound is the smallest trial load value that is classified at the end of the search as an upper bound (see [Appendix A: Load Classification] (#Appendix-A:-Load-Classification)) for the given Search Goal. Discussion: One search goal can have many different load classified as an upper bound. At the end of the search, one of those loads will be the smallest, becoming the relevant upper bound for that goal. In more detail, the set of all trial outputs (both short and full-length, enough of them according to Goal Duration Sum) performed at that smallest load failed to uphold all the requirements of the given Search Goal, mainly the Goal Loss Ratio in combination with the Goal Exceed Ratio. If Max Load does not cause enough lossy trials, the Relevant Upper Bound does not exist. Conversely, if Relevant Upper Bound exists, it is not affected by Max Load value.

Relevant Lower Bound Definition: The Relevant Lower Bound is the largest trial load value among those smaller than the Relevant Upper Bound, that got classified at the end of the search as a lower bound (see [Appendix A: Load Classification] (#Appendix-A:-Load-Classification)) for the given Search Goal. Discussion: Only among loads smaller that the relevant upper bound, the largest load becomes the relevant lower bound. With loss inversion, stricter upper bound matters. In more detail, the set of all trial outputs (both short and full-length, enough of them according to Goal Duration Sum) performed at that largest load managed to uphold all the requirements of the given Search Goal, mainly the Goal Loss Ratio in combination with the Goal Exceed Ratio. Is no load had enough low-loss trials, the relevant lower bound MAY not exist. Strictly speaking, if the Relevant Upper Bound does not exist, the Relevant Lower Bound also does not exist. In that case, Max Load is classified as a lower bound, but it is not clear whether a higher lower bound would be found if the search used a higher Max Load value. For a regular Goal Result, the distance between the Relevant Lower Bound and the Relevant Upper Bound MUST NOT be larger than the Goal Width, if the implementation offers width as a goal attribute. Searching for anther search goal may cause a loss inversion phenomenon, where a lower load is classified as an upper bound, but also a higher load is classified as a lower bound for the same search goal. The definition of the Relevant Lower Bound ignores such high lower bounds.

Conditional Throughput Definition: The Conditional Throughput (see section [Appendix B: Conditional Throughput] (#Appendix-B:-Conditional-Throughput)) as evaluated at the Relevant Lower Bound of the given Search Goal at the end of the search. Discussion: Informally, this is a typical trial forwarding rate, expected to be seen at the Relevant Lower Bound of the given Search Goal. But frequently it is only a conservative estimate thereof, as MLRsearch implementations tend to stop gathering more data as soon as they confirm the value cannot get worse than this estimate within the Goal Duration Sum. This value is RECOMMENDED to be used when evaluating repeatability and comparability if different MLRsearch implementations.

Goal Result Definition: The Goal Result is a composite quantity consisting of several attributes. Relevant Upper Bound and Relevant Lower Bound are REQUIRED attributes, Conditional Throughput is a RECOMMENDED attribute. Discussion: Depending on SUT behavior, it is possible that one or both relevant bounds do not exist. The goal result instance where the required attribute values exist is informally called a Regular Goal Result instance, so we can say some goals reached Irregular Goal Results. A typical Irregular Goal Result is when all trials at the Max Load have zero loss, as the Relevant Upper Bound does not exist in that case. It is RECOMMENDED that the test report will display such results appropriately, although MLRsearch specification does not prescibe how. Anything else regarging Irregular Goal Results, including their role in stopping conditions of the search is outside the scope of this document.

Search Result Definition: The Search Result is a single composite object that maps each Search Goal instance to a corresponding Goal Result instance. Discussion: Alternatively, the Search Result can be implemented as an ordered list of the Goal Result instances, matching the order of Search Goal instances. The Search Result (as a mapping) MUST map from all the Search Goal instances present in the Controller Input.

Controller Output Definition: The Controller Output is a composite quantity returned from the Controller to the Manager at the end of the search. The Search Result instance is its only REQUIRED attribute. Discussion: MLRsearch implementation MAY return additional data in the Controller Output.

MLRsearch Architecture MLRsearch architecture consists of three main system components: the Manager, the Controller, and the Measurer. The architecture also implies the presence of other components, such as the SUT and the Tester (as a sub-component of the Measurer). Protocols of communication between components are generally left unspecified. For example, when MLRsearch specification mentions "Controller calls Measurer", it is possible that the Controller notifies the Manager to call the Measurer indirectly instead. This way the Measurer implementations can be fully independent from the Controller implementations, e.g. programmed in different programming languages.

Measurer Definition: The Measurer is an abstract system component that when called with a [Trial Input] (#Trial-Input) instance, performs one [Trial] (#Trial), and returns a [Trial Output] (#Trial-Output) instance. Discussion: This definition assumes the Measurer is already initialized. In practice, there may be additional steps before the search, e.g. when the Manager configures the traffic profile (either on the Measurer or on its tester sub-component directly) and performs a warmup (if the tester requires one). It is the responsibility of the Measurer implementation 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 (section 10. Verifying received frames) gives some suggestions (but not requirements) related to duplicated or reordered frames. Implementations are RECOMMENDED to document their behavior related to such freedoms in as detailed a way as possible. It is RECOMMENDED to benchmark the test equipment first, e.g. connect sender and receiver directly (without any SUT in the path), find a load value that guarantees the offered load is not too far from the intended load, and use that value as the Max Load value. When testing the real SUT, it is RECOMMENDED to turn any big difference between the intended load and the offered load into increased Trial Loss Ratio. Neither of the two recommendations are made into requirements, because it is not easy to tell when the difference is big enough, in a way thay would be dis-entangled from other Measurer freedoms.

Controller Definition: The Controller is an abstract system component that when called with a Controller Input instance repeatedly computes Trial Input instance for the Measurer, obtains corresponding Trial Output instances, and eventually returns a Controller Output instance. Discussion: Informally, the Controller has big freedom in selection of Trial Inputs, and the implementations want to achieve the Search Goals in the shortest expected time. The Controller's role in optimizing the overall search time distinguishes MLRsearch algorithms from simpler search procedures. Informally, each implementation can have different stopping conditions. Goal Width is only one example. In practice, implementation details do not matter, as long as Goal Results are regular.

Manager Definition: The Manager is an abstract system component that is reponsible for configuring other components, calling the Controller component once, and for creating the test report following the reporting format as defined in (section 26. Benchmarking tests). Discussion: The Manager initializes the SUT, the Measurer (and the Tester if independent) with their intended configurations before calling the Controller. The Manager does not need to be able to tweak any Search Goal attributes, but it MUST report all applied attribute values even if not tweaked. In principle, there should be a "user" (human or CI) that "starts" or "calls" the Manager and receives the report. The Manager MAY be able to be called more than once whis way.

Implementation Compliance Any networking measurement setup where there can be logically delineated system components and there are components satisfying requirements for the Measurer, the Controller and the Manager, is considered to be compliant with MLRsearch design. These components can be seen as abstractions present in any testing procedure. For example, there can be a single component acting both as the Manager and the Controller, but as long as values of required attributes of Search Goals and Goal Results are visible in the test report, the Controller Input instance and output instance are implied. For example, any setup for conditionally (or unconditionally) compliant throughput testing can be understood as a MLRsearch architecture, assuming there is enough data to reconstruct the Relevant Upper Bound. See [RFC2544 Goal] (#RFC2544-Goal) subsection for equivalent Search Goal. Any test procedure that can be understood as (one call to the Manager of) MLRsearch architecture is said to be compliant with MLRsearch specification.

Additional Considerations This section focuses on additional considerations, intuitions and motivations pertaining to MLRsearch methodology.

MLRsearch Versions The MLRsearch algorithm has been developed in a code-first approach, a Python library has been created, debugged, used in production and published in PyPI before the first descriptions (even informal) were published. But the code (and hence the description) was evolving over time. Multiple versions of the library were used over past several years, and later code was usually not compatible with earlier descriptions. The code in (some version of) MLRsearch library fully determines the search process (for a given set of configuration parameters), leaving no space for deviations. This historic meaning of MLRsearch, as a family of search algorithm implementations, leaves plenty of space for future improvements, at the cost of poor comparability of results of search algoritm implementations. There are two competing needs. There is the need for standardization in areas critical to comparability. There is also the need to allow flexibility for implementations to innovate and improve in other areas. This document defines MLRsearch as a new specification in a manner that aims to fairly balance both needs.

Stopping Conditions 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 (including both values) 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. does not specify when, if ever, should the search stop. MLRsearch introduces a concept of [Goal Width] (#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, the interval width at the end of the search has to be no larger than the Goal Width. This Goal Width value therefore determines the precision of the result. Due to the fact that MLRsearch specification requires a particular structure of the result (see [Trial Result] (#Trial-Result) section), 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 stopping conditions different from Goal Width.

Load Classification MLRsearch keeps the basic logic of binary search (tracking tightest bounds, measuring at the middle), perhaps with minor technical differences. MLRsearch algorithm chooses an intended load (as opposed to the offered load), the interval between bounds does not need to be split exactly into two equal halves, and the final reported structure specifies both bounds. The biggest difference is that 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. In 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. An explanation of the classification logic is given in the next section [Logic of Load Classification] (#Logic-of-Load-Classification), as it heavily relies on other subsections of this section. For repeatability and comparability reasons, it is important that given a set of trial results, all implementations of MLRsearch classify the load equivalently.

Loss Ratios Another difference between MLRsearch and binary search is in the goals of the search. has a single goal, based on classifying full-length trials as either lossless or lossy. MLRsearch, as the name suggests, can search for multiple goals, differing in their loss ratios. The precise definition of the Goal Loss Ratio will be given later. The throughput goal then simply becomes a zero Goal Loss Ratio. Different goals also may have different Goal Widths. 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 trial results, but also on the goal. The overall search procedure becomes more complicated, when 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 throughput search using bisection, any load with a lossy trial becomes a hard upper bound, meaning every subsequent trial has a 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 the 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] (#Relevant-Upper-Bound) and the [Relevant Lower Bound] (#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 the Goal Width apart, the relevant bounds are used in the 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 throughput results. See the discussion about noiseful and noiseless ends of the SUT performance spectrum in section [DUT in SUT] (#DUT-in-SUT). Stable results are closer to the noiseless end of the SUT performance spectrum, so MLRsearch may need to allow some frequency of high-loss trials to ignore the rare but big effects near the noiseful end. MLRsearch can do such trial result filtering, but it needs a configuration option to tell it how frequent can the infrequent big loss be. This option is called the exceed ratio. It tells MLRsearch what ratio of trials (more exactly what ratio of trial seconds) can have a [Trial Loss Ratio] (#Trial-Loss-Ratio) larger than the Goal Loss Ratio and still be classified as a lower bound. Zero exceed ratio means all trials have to have a 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 intended to classify a load, MLRsearch also needs something that controls the number of trials needed. Therefore, each goal also has an attribute called duration sum. The meaning of a [Goal Duration Sum] (#Goal-Duration-Sum) is that when a load has (full-length) trials whose trial durations when summed up give a value at least as big as the Goal Duration Sum value, the load is guaranteed to be classified either as an upper bound or a lower bound for that goal. Due to the fact that the duration sum has a big impact on the overall search duration, and prescribes wait intervals around trial traffic, the MLRsearch algorithm is allowed to sum durations that are different from the actual trial traffic durations. In the MLRsearch specification, the different duration values are called [Trial Effective Duration] (#Trial-Effective-Duration).

Short Trials MLRsearch requires each goal to specify its final trial duration. Full-length trial is a shorter name for a trial whose intended trial duration is equal to (or longer than) the goal final trial duration. Section 24 of already anticipates possible time savings when short trials (shorter than full-length trials) are used. Full-length trials are the opposite of short trials, so they may also be called long trials. Any MLRsearch implementation may include its own configuration options which control when and how MLRsearch chooses to use short 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 trial forwarding rates. The presence of short trial results complicates the load classification logic. Full details are given later in section [Logic of Load Classification] (#Logic-of-Load-Classification). In a nutshell, 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.

Throughput Due to the fact that testing equipment takes the intended load as an input parameter for a trial measurement, any load search algorithm needs to deal with intended load values internally. But in the presence of goals with a non-zero loss ratio, the intended load usually does not match the user's intuition of what a throughput is. The forwarding rate (as defined in section 3.6.1) is better, but it is not obvious how to generalize it for loads with multiple trial results and a non-zero [Goal Loss Ratio] (#Goal-Loss-Ratio). The best example is also the main motivation: hard limit performance. Even if the medium allows higher performance, the SUT interfaces may have their additional own limitations, e.g. a specific fps limit on the NIC (a very common occurance). Ideally, those should be known and used when computing Max Load. But if Max Load is higher that what interface can receive or transmit, there will be a "hard limit" observed in trial results. Imagine the hard limit is at 100 Mfps, Max Load is higher, and the goal loss ratio is 0.5%. If DUT has no additional losses, 0.5% loss ratio will be achieved at 100.5025 Mfps (the relevant lower bound). But it is not intuitive to report SUT performance as a value that is larger than known hard limit. We need a generalization of RFC2544 throughput, different from just the relevant lower bound. MLRsearch defines one such generalization, called the Conditional Throughput. It is the trial forwarding rate from one of the trials performed at the load in question. Determining which trial exactly is defined in [MLRsearch Specification] (#MLRsearch-Specification), and in [Appendix B: Conditional Throughput] (#Appendix-B:-Conditional-Throughput). In the hard limit example, 100.5 Mfps load will still have only 100.0 Mfps forwarding rate, nicely confirming the known limitation. Conditional Throughput is partially related to load classification. If a load is classified as a lower bound for a goal, the Conditional Throughput can be calculated from trial results, and guaranteed to show an loss ratio no larger than the Goal Loss Ratio. Note that when comparing the best (all zero loss) and worst case (all loss just below Goal Loss Ratio), 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 the 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 become 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. Overall, this Conditional Throughput does behave well for comparability purposes.

Search Time MLRsearch was primarily developed to reduce the time required to determine a throughput, either the compliant one, or some generalization thereof. The art of achieving short search times is mainly in the 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 a 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. Any implementation choosing loads very close to the current Relevant Lower Bound is quite likely to eventually stumble upon a trial result with poor performance (due to SUT noise). For an implementation choosing loads 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. However, as even splits optimize search duration at give precision, MLRsearch implementations that prioritize minimizing search time are unlikely to suffer from any such bias. Therefore, this document remains quite vague on load selection and other optimization details, and configuration attributes related to them. Assuming users prefer libraries 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.

Compliance Some Search Goal instances lead to results compliant with RFC2544. See [RFC2544 Goal] (#RFC2544-Goal) for more details regarding both conditional and unconditional compliance. The presence of other Search Goals does not affect the 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 throughput.

Logic of Load Classification

Introductory Remarks This chapter continues with explanations, but this time more precise definitions are needed for readers to follow the explanations. Descriptions in this section are wordy and implementers should read [MLRsearch Specification] (#MLRsearch-Specification) section and Appendices for more concise definitions. The two areas of focus here are load classification and the Conditional Throughput. To start with [Performance Spectrum] (#Performance-Spectrum) subsection contains definitions needed to gain insight into what Conditional Throughput means. Remaining subsections discuss load classification. For load classification, it is useful to define good trials and bad trials: Bad trial: Trial is called bad (according to a goal) if its [Trial Loss Ratio] (#Trial-Loss-Ratio) is larger than the [Goal Loss Ratio] (#Goal-Loss-Ratio). Good trial: Trial that is not bad is called good.

Performance Spectrum ### Description There are several equivalent ways to explain the Conditional Throughput computation. One of the ways relies on performance spectrum. Take an intended load value, a trial duration value, and a finite set of trial results, with all trials measured at that load value and duration 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 has that number, as their trial 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 the sum of the 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 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. Take a set of all full-length trials performed at the Relevant Lower Bound, sorted by decreasing trial forwarding rate. The sum of the durations of those trials may be less than the Goal Duration Sum, or not. If it is less, add an imaginary trial result with zero trial forwarding rate, such that the new sum of durations is equal to the Goal Duration Sum. This is the set of trials to use. If the quantile touches two trials, the larger trial forwarding rate (from the trial result sorted earlier) is used. The resulting quantity is the Conditional Throughput of the goal in question. A set of examples follows.

First Example [Goal Exceed Ratio] (#Goal-Exceed-Ratio) = 0 and [Goal Duration Sum] (#Goal-Duration-Sum) has been reached. Conditional Throughput is the smallest trial forwarding rate among the trials.

Second Example Goal Exceed Ratio = 0 and Goal Duration Sum has not been reached yet. Due to the missing duration sum, the worst case may still happen, so the Conditional Throughput is zero. This is not reported to the user, as this load cannot become the Relevant Lower Bound yet.

Third Example Goal Exceed Ratio = 50% and Goal Duration Sum is two seconds. One trial is present with the duration of one second and zero loss. The imaginary trial is added with the duration of one second and zero trial forwarding rate. The median would touch both trials, so the Conditional Throughput is the trial forwarding rate of the one non-imaginary trial. As that had zero loss, the value is equal to the offered load.

Summary While the Conditional Throughput is a generalization of the trial forwarding rate, its definition is not an obvious one. Other than the trial forwarding rate, the other source of intuition is the quantile in general, and the median the recommended case.

Trials with Single Duration When goal attributes are chosen in such a way that every trial has the same intended duration, the load classification is simpler. The following description follows the motivation of Goal Loss Ratio, Goal Exceed Ratio, and Goal Duration Sum. If the sum of the durations of all trials (at the given load) is less than the Goal Duration Sum, imagine two scenarios: best case scenario: all subsequent trials having zero loss, and worst case scenario: all subsequent trials having 100% loss. Here we assume there are as many subsequent trials as needed to make the sum of all trials equal to the Goal Duration Sum. The exceed ratio is defined using sums of durations (and number of trials does not matter), so it does not matter whether the "subsequent trials" can consist of an integer number of full-length trials. In any of the two scenarios, best case and worst case, we can compute the load exceed ratio, as the duration sum of good trials divided by the duration sum of all trials, in both cases including the assumed trials. Even if, in the best case scenario, the load exceed ratio is larger than the Goal Exceed Ratio, the load is an upper bound. MKP2 Even if, in the worst case scenario, the load exceed ratio is not larger than the Goal Exceed Ratio, the load is a lower bound. More specifically: Take all trials measured at a given load. The sum of the durations of all bad full-length trials is called the bad sum. The sum of the durations of all good full-length trials is called the good sum. The result of adding the 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. The optimistic exceed ratio is the bad sum divided by the whole sum. The pessimistic exceed ratio is the bad sum plus the missing sum, that divided by the whole sum. If the optimistic exceed ratio is larger than the Goal Exceed Ratio, the load is classified as an upper bound. If the 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 is compatible with the logic in the Conditional Throughput computation, so in this single trial duration case, a load is a lower bound if and only if the Conditional Throughput loss ratio is not larger than the Goal Loss Ratio. If it is larger, the load is either an upper bound or undecided.

Trials with Short Duration

Scenarios Trials with intended duration smaller than the goal final trial duration are called short trials. The motivation for load classification logic in the 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.

False Good Scenario The user had their reason for not configuring a shorter goal final trial duration. Perhaps SUT has buffers that may get full at longer trial durations. Perhaps SUT shows periodic decreases in performance the user does not want to be treated as noise. In any case, many good short trials may become bad full-length trials in the counter-factual case. In extreme cases, there are plenty of good short trials and 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.

True Bad Scenario 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. In practice, bad short trials are rarely turning into good full-length trials. In extreme cases, 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 the 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.

Balanced Scenario Some SUTs are quite indifferent to trial duration. Performance probability function constructed from short trial results is likely to be similar to the performance probability function constructed from full-length trial results (perhaps with larger dispersion, but without a big impact on the median quantiles overall). For a moderate Goal Exceed Ratio value, 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, as 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 safely is to do more trials at full length, the same as in False Good Scenario.

Classification Logic MLRsearch picks a particular logic for load classification in the 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 that said, the logic differs from the single trial duration case only in different definition of the bad sum. The good sum is still the sum across all good full-length trials. Few more notions are needed for defining the new bad sum: The sum of durations of all bad full-length trials is called the bad long sum. The sum of durations of all bad short trials is called the bad short sum. The sum of durations of all good short trials is called the good short sum. One minus the Goal Exceed Ratio is called the subceed ratio. The Goal Exceed Ratio divided by the subceed 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. Otherwise, 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 the relevant bounds be if only full-length trials were used for the search.

False Good Scenario If the duration is too short, we expect to see a higher frequency of good short trials. This could lead to a 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, probably making it worse.

True Bad Scenario Settings with a small exceed ratio have a small exceed coefficient, so the impact of the 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 an impact as full-length bad trials. The same conclusion applies to 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).

Balanced Scenario Here excess sum is small in absolute value, as the balancing sum is expected to 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 a shorter overall search time before selecting this load for measurement, thus bringing time savings (while not affecting comparability). Note that in presence of short trial results, the comparibility between the load classification and the Conditional Throughput is only partial. The Conditional Throughput still comes from a good long trial, but a load higher than the Relevant Lower Bound may also compute to a good value.

Trials with Longer Duration If there are trial results with an intended duration larger than the goal trial duration, the precise definitions in Appendix A and Appendix B treat them in exactly the same way as trials with duration equal to the goal trial duration. But in configurations with moderate (including 0.5) or small Goal Exceed Ratio and small Goal Loss Ratio (especially zero), bad trials with longer than goal durations may bias the search towards the lower load values, as the noiseful end of the spectrum gets a larger probability of causing the loss within the longer trials.

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 Some phrases and statements in this document were created with help of Mistral AI (mistral.ai). Many thanks to Alec Hothan of the OPNFV NFVbench project for thorough review and numerous useful comments and suggestions in the earlier versions of this document. Special wholehearted gratitude and thanks to the 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 encouragement full of empathy and positive attitude. Al, you are dearly missed.

Appendix A: Load Classification This section specifies how to perform the load classification. Any intended load value can be classified, according to a given [Search Goal] (#Search-Goal). The algorithm uses (some subsets of) the set of all available trial results from trials measured at a given intended load at the end of the search. All durations are those returned by the Measurer. 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 values of both variables are computed to be true, the load in question is classified as a lower bound according to the given Search Goal. If values of both variables are false, the load is classified as an upper bound. Otherwise, the load is classified as undecided. The pseudocode expects the following variables to hold values as follows: goal_duration_sum: The duration sum value of the given Search Goal. goal_exceed_ratio: The exceed ratio value of the given Search Goal. good_long_sum: Sum of durations across trials with trial duration at least equal to the goal final trial duration and with a 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 a 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 a 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 a Trial Loss Ratio higher than the Goal Loss Ratio. The code works correctly also when there are no trial results at a given load.

Appendix B: Conditional Throughput This section specifies how to compute Conditional Throughput, as referred to in section [Conditional Throughput] (#Conditional-Throughput). Any intended load value can be used as the basis for the following computation, but only the Relevant Lower Bound (at the end of the search) leads to the value called the Conditional Throughput for a given Search Goal. The algorithm uses (some subsets of) the set of all available trial results from trials measured at a given intended load at the end of the search. All durations are those returned by the Measurer. 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 pseudocode expects the following variables to hold values as follows: goal_duration_sum: The duration sum value of the given Search Goal. goal_exceed_ratio: The exceed ratio value of the given Search Goal. good_long_sum: Sum of durations across trials with trial duration at least equal to the goal final trial duration and with a 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 a 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 the 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. The code works correctly only when there if there is at least one trial result measured at a given load.

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) ]]>