Multiple Loss Ratio Search

Multiple Loss Ratio Search Cisco Systems

mkonstan@cisco.com

Cisco Systems

vrpolak@cisco.com

OPS bmwg benchmarking performance evaluation testing measurement trial network device network function network interconnect device This document describes an alternative to throughput in "Benchmarking Methodology for Network Interconnect Devices" (RFC 2544) by defining a new methodology called Multiple Loss Ratio Search (MLRsearch). MLRsearch aims to minimize Search Duration, support multiple loss ratio goals, and improve result repeatability and comparability. MLRsearch is motivated by the pressing need to address the challenges of evaluating and testing the various data plane solutions, especially in software-based networking systems based on Commercial Off-the-Shelf (COTS) CPU hardware vs. purpose-built Application-Specific Integrated Circuit (ASIC) / Network Processing Unit (NPU) / Field-Programmable Gate Array (FPGA) hardware.

Introduction This document describes the Multiple Loss Ratio Search (MLRsearch) methodology, optimized for determining data plane throughput in software-based networking functions running on commodity systems with generic CPUs (vs. purpose-built ASICs, NPUs, and FPGAs). Such network functions can be deployed on a dedicated physical appliance (e.g., a standalone hardware device) or as virtual appliance (e.g., a Virtual Network Function running on shared servers in the compute cloud). This document tightly couples terminology and methodology aspects. Instead of a separate terminology section, the subsections of "MLRsearch Specification" act as a list of newly defined terms. If a term appears with the first letter capitalized, it likely refers to a specific term defined in an eponymous subsection of MLRsearch Specification. For first-time readers, the information in MLRsearch Specification might feel dense and lacking motivation. Subsequent sections provide explanations, making MLRsearch Specification more approachable on repeated reads.

Purpose The purpose of this document is to describe the Multiple Loss Ratio Search (MLRsearch) methodology, optimized for determining data plane throughput in software-based networking devices and functions. Applying the "Binary Search" to software Devices Under Test (DUTs) results in several problems:

Binary Search takes a long time, 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 Throughput values that could be discovered.
Throughput requires a loss of exactly zero frames, but the industry best practices frequently allow for tolerance of low but non-zero losses (see and test-equipment manuals for more information).
The definition of Throughput is not clear when Trial Results are inconsistent (e.g., when a successive Trial at a higher Load yields a smaller Trial Loss Ratio, Throughput can no longer be pinned to a single, unambiguous value.)

To address these problems, early MLRsearch implementations employed the following enhancements:

Allow multiple Short Trials instead of one long Trial per Load.
- Optionally, tolerate a percentage of Trial Results with higher Trial Loss Ratios.
Allow searching for multiple Search Goals, with differing Goal 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 at Maximum Offered Load (FRMOL), as defined in , to initialize bounds.
Clarify handling of Inconsistent Trial Results.
- Reported Throughput should be smaller than the smallest Load with high loss.
- Measure smaller Load candidates first.
Apply several time-saving Load selection heuristics that deliberately prevent the bounds from narrowing unnecessarily.

Enhancements 1, 2, and partly 4 are formalized as the MLRsearch Specification within this document. The remaining enhancements are treated as implementation details and out of scope for this document. This achieves high comparability without limiting future improvements. MLRsearch configuration supports both conservative settings and aggressive settings. Results unconditionally compliant with are possible with conservative enough settings but without much improvement on Search Duration and repeatability, see "MLRsearch Compliant with RFC 2544". Conversely, aggressive settings lead to shorter Search Durations and better repeatability, but the results are not compliant with . This document offers only soft recommendations for settings, but see the discussion in "Overview of RFC 2544 Problems" for the impact of different settings on result quality. This document does not change or obsolete any part of .

Positioning Within BMWG Methodologies The Benchmarking Methodology Working Group (BMWG) produces recommendations (RFCs) that describe various benchmarking methodologies for use in a controlled laboratory environment. A large number of these benchmarks are based on the terminology from and the foundational methodology from . A common pattern has emerged where BMWG documents reference the methodology of and augment it with specific requirements for testing particular network systems or protocols, without modifying the core benchmark definitions. While BMWG documents are formal recommendations, they are widely treated as industry norms to ensure the comparability of results between different labs. The set of benchmarks defined in , in particular, became a de facto standard for performance testing. In this context, the MLRsearch Specification formally defines a new class of benchmarks that fits within the wider framework of ; see "Scope". A primary consideration in the design of MLRsearch is the trade-off between configurability and comparability. The methodology's flexibility, especially the ability to define various sets of Search Goals, in supporting both single-goal and multi-goal benchmarks in a unified way is powerful for detailed characterization and internal testing. However, this same flexibility is detrimental to inter-lab comparability unless a specific, common set of Search Goals is agreed upon. Therefore, MLRsearch should not be seen as a direct extension nor a replacement for the Throughput benchmark. Instead, this document provides a foundational methodology that future BMWG documents can use to define new, specific, and comparable benchmarks by mandating particular Search Goal configurations. For operators of existing test procedures, it is worth noting that many test setups measuring Throughput can be adapted to produce results compliant with the MLRsearch Specification, often without affecting Trials, merely by augmenting the content of the final Test Report.

Overview of RFC 2544 Problems This section describes the problems affecting usability of various performance testing methodologies, mainly the Binary Search for unconditionally compliant Throughput.

Binary Search While offers some flexibility when searching for Throughput, a particular algorithm is frequently used as a starting point, as it is the simplest one among those that offer reasonable effectivity. This algorithm is based on (balanced) binary search over sorted arrays but does not have a specific name when searching for Throughput. "Trial duration" () mentions binary search only in quotes, without providing specifics. In this document, we call that algorithm the Binary Search, as that is the title of Section 12.3.2 of , which describes a variant of it. Here is a simplified description of the algorithm:

Initialize the lower-bound variable to a line-rate Load.
Initialize the upper-bound variable to a loss-free Load.
Compute a midpoint, the arithmetic mean of current bounds.
Run a single 60-second Trial at the midpoint (for unconditional compliance).
If loss is zero, set the lower-bound to the midpoint; else, set the upper bound to the midpoint.
Repeat (computing new midpoint) until the gap between the bounds meets the desired precision.
Return the final lower-bound as the Throughput.

The description in has two more requirements (stopping condition and rounding, both based on the Offered Load Step Size Parameter), but those are not required in this document. Small modifications related to initial bounds are also allowed. The Loads currently held in the two variables are called tightest bounds, especially when discussing older Trial Results (logically still bounds).

Long Search Duration The proliferation 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 definition of Throughput test methodology per restricts the potential for time-efficiency improvements. The Binary Search, when used in a manner unconditionally compliant with Throughput methodology, is excessively slow due to two main factors. First, a significant amount of time is spent on Trials with Loads that, in retrospect, are far from the final determined Throughput. Second, does not specify any stopping condition for Throughput search, so users of testing equipment implementing the procedure already have access to a limited trade-off between Search Duration and achieved precision, as each one of the full 60-second Trials halves the interval of possible results. As such, not many Trials can be removed without a substantial loss of precision.

DUT in SUT specifies a test setup with an external tester stimulating the networking system, treating it either as a single Device Under Test (DUT) or as a system of devices, a System Under Test (SUT). defines these terms as follows.

DUT:: The network frame forwarding device to which stimulus is offered and response measured ().
SUT:: The collective set of network devices to which stimulus is offered as a single entity and response measured ().

For software-based data plane forwarding running on commodity x86/ARM CPUs, the SUT comprises not only the forwarding application itself, the DUT, but also the entire execution environment: host hardware, firmware and kernel/hypervisor services, as well as any other software workloads that share the same CPUs, memory, and I/O resources. Given that a SUT is a shared multi-tenant environment, the DUT might inadvertently experience interference from the operating system or from other software operating on the same server. Some of this interference can be mitigated. For instance, in multi-core CPU systems, 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. A DUT can also exhibit fluctuating performance itself, for reasons not related to the rest of SUT. For example, this can be 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 phenomena 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 it frequently lowers the observed SUT performance as observed in Trial Results. In this simple model, a SUT does not have a single performance value; it has a spectrum. One end of the spectrum is the idealized noiseless performance, and 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 a possible performance 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. Furthermore, the extreme noiseless end of the SUT spectrum is unlikely to be observable, this time because minor noise events almost always occur during each Trial, nudging the measured performance slightly below the theoretical maximum. 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 that would be capable to distinguish SUT noise from DUT fluctuations (based on the available literature at the time of writing). If the SUT execution environments and any co-resident workloads place only negligible demands on SUT shared resources, so that the DUT remains the principal performance limiter, the DUT's ideal noiseless performance is defined as the noiseless end of the SUT performance spectrum. 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. The 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. Improvements to the Throughput search algorithm, aimed at better dealing with software networking SUT and DUT setups, should adopt methods that explicitly model SUT-generated noise, deriving surrogate metrics that approximate the (proxies for) DUT noiseless performance across a range of SUT noise-tolerance levels.

Repeatability and Comparability does not suggest repeating Throughput search. Also, note that from simply one discovered Throughput, it cannot be determined how repeatable that value is. Unsatisfactory repeatability then leads to unacceptable comparability, as different benchmarking teams may obtain varying Throughput values for the same SUT, exceeding the expected differences from search precision. Repeatability is also important when the test procedure is kept the same, but SUT is varied in small ways. For example, during development of software-based DUTs, repeatability is needed to detect small regressions. Throughput requirements (60-second Trial and no tolerance of a single frame loss) affect the Throughput result as follows. 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 spread away from the noiseless end of SUT performance spectrum more frequently and more widely than shorter Trials would, thus causing unacceptable Throughput repeatability. The repeatability problem can be better addressed by defining a search procedure that identifies a consistent level of performance, even if it does not meet the strict definition of Throughput test methodology 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 also help 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 and/or percentiles like p95). 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 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 low, non-zero Goal Loss Ratio for their Load search. There are many motivations:

Networking protocols tolerate frame loss better, compared to the time when and were specified.
Increased link speeds require Trials sending more frames within the same duration, increasing the chance of a small SUT performance fluctuation being enough to cause frame loss.
Because noise-related drops usually arrive in small bursts, their impact on the Trial Loss Ratio is diluted by the longer intervals in which the SUT operates close to its noiseless performance; consequently, the Trial Loss Ratio as an average over the Trial can still end up below the specified Goal Loss Ratio.
If an approximation of the SUT noise impact on the Trial Loss Ratio is known, it can be set as the Goal Loss Ratio.

For more information, see (and the references there) for a few synthetic examples, confirming that each protocol and application can have different realistic Goal Loss Ratios. Regardless of the validity of all similar motivations, support for non-zero Goal Loss Ratios makes a search algorithm applicable for a wider range of use cases than the approach defined in . Furthermore, allowing users to specify multiple Goal Loss Ratios, 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 the result of a single goal Load search procedure. It is easy to modify the Binary Search to find a Lower Bound for the Load that satisfies a single non-zero Goal Loss Ratio. But how to search for multiple goals at once is not that obvious; hence, the support for multiple Search Goals remains a problem. At the time of writing, there does not seem to be a consensus in the industry on which Goal Loss Ratio is the best. For users, performance of higher protocol layers is important, for example, goodput of TCP connection (TCP throughput ), but the relationship between goodput and Trial Loss Ratio is not simple. Refer to for examples of various corner cases, for Goal Loss Ratios acceptable for an accurate measurement of TCP throughput, and for models and computations of TCP performance in presence of packet loss.

Inconsistent Trial Results While performing Throughput search by executing a sequence of measurement Trials, there is a risk of encountering inconsistencies between Trial Results. Examples include but are not limited to:

A Trial at the same Load (same or different Trial Duration) results in a different Trial Loss Ratio.
A Trial at a larger Load (same or different Trial Duration) results in a lower Trial Loss Ratio.

The Binary Search never encounters inconsistent Trials. But hints about the possibility of Inconsistent Trial Results in two places in its text. The first place is , where full Trial Durations are required, presumably because they can be inconsistent with the Trial Results from shorter Trial Durations. The second place is , where two successive zero-loss Trials are recommended, presumably because after one zero-loss Trial Result, there can be a subsequent inconsistent non-zero-loss Trial Result. A robust Throughput search algorithm needs to decide how to continue the search in the presence of such inconsistencies. Definitions of Throughput and its test methodology in and are not specific enough to imply a unique way of handling such inconsistencies. Ideally, there will be a definition of a new metric that both generalizes Throughput for non-zero Goal Loss Ratio (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. Relevant Lower Bound is the MLRsearch term that addresses this problem.

Requirements Language The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here. This document is categorized as an Informational RFC. While it does not mandate the adoption of the MLRsearch methodology, it uses the normative language of BCP 14 to provide an unambiguous specification. This ensures that if a test procedure or Test Report claims compliance with the MLRsearch Specification, it MUST adhere to all the absolute requirements defined herein. The use of normative language is intended to promote repeatable and comparable results among those who choose to implement this methodology.

MLRsearch Specification This section provides all technical definitions needed for evaluating whether a particular test procedure complies with the MLRsearch Specification. Some terms used in the specification are capitalized. This is a stylistic choice for this document, reminding the reader that the term is introduced, defined, or explained elsewhere in the document. Lowercase variants are equally valid; capitalization was already applied in earlier sections where required. This document does not separate terminology from methodology. Terms are fully specified and discussed in their own subsections, under sections with the word "Terms" in their titles. This way, the list of terms is visible in the table of contents. Each term-defining subsection contains a short Definition paragraph containing a minimal definition and all strict requirements, followed by Discussion paragraphs focusing on important consequences and recommendations. Requirements about how other components can use the defined term are also included in the discussion.

Scope This document specifies the Multiple Loss Ratio Search (MLRsearch) methodology. The MLRsearch Specification details a new class of benchmarks by listing all terminology definitions and methodology requirements. The definitions support multi-goal benchmarks, with single-goal ones as a subset. The normative scope of this specification includes:

The terminology for all required quantities and their attributes.
An abstract architecture consisting of functional components (Manager, Controller, and Measurer) and the requirements for their inputs and outputs.
The required structure and attributes of the Controller Input, including one or more Search Goals.
The required logic for Load Classification, which determines whether a given Load qualifies as a Lower Bound or an Upper Bound for a Search Goal.
The required structure and attributes of the Controller Output, including a Goal Result for each Search Goal.

Relationship to RFC 2544 The MLRsearch Specification is an independent methodology and does not change nor obsolete any part of . This specification permits deviations from the Trial procedure as described in . Any deviation from the procedure in must be documented explicitly in the Test Report, and such variations remain outside the scope of the original benchmarks in . A specific single-goal MLRsearch benchmark can be configured to be compliant with Throughput, and most procedures reporting Throughput can be adapted to also satisfy MLRsearch requirements for a specific Search Goal.

Applicability of Other Specifications Methodology extensions from other BMWG documents that specify details for testing particular DUTs, configurations, or protocols (e.g., by defining a particular Traffic Profile) are considered orthogonal to MLRsearch and are applicable to a benchmark conducted using MLRsearch methodology.

Out of Scope The following aspects are explicitly out of the normative scope of this document:

The internal heuristics or algorithms used by the Controller to select Trial Inputs are implementation specific.
Treatment of situations where Offered Load is found to differ noticeably from Intended Load is not prescribed, only the "use smaller Max Load" recommendation is mentioned.
The potential for, and the effects of, interference between different Search Goals within a multi-goal search are considered outside the normative scope of this specification.
This specification does not mandate any single, universal Search Goal configuration for all use cases. The selection of Search Goal parameters is left to the operator of the test procedure or may be recommended in future publications.

Several weak recommendations related to Search Goal possibilities are included, but they are conditional on specific intents (for example, compatibility with other methodologies) and are not considered universal enough yet.

Architecture Overview Although the normative text only references terminology that has already been introduced, explanatory passages sometimes profit from terms that are defined later in the document. To keep the initial read-through clear, this informative section offers a concise, top-down sketch of the complete MLRsearch architecture. The architecture is modelled as a set of abstract, interacting components. Information exchange between components is expressed in an imperative-programming style: One component calls another, supplying inputs (arguments) and receiving outputs (return values). This notation is purely conceptual, actual implementations need not exchange explicit messages. When the text contrasts alternative behaviors, it refers to the different implementations of the same component. A test procedure is considered compliant with the MLRsearch Specification if it can be conceptually decomposed into the abstract components defined herein, and if each component satisfies the requirements defined for its corresponding MLRsearch Specification section. The Measurer component is tasked to perform Trials, the Controller component is tasked to select Trial Durations and Loads, and the Manager component is tasked to preconfigure involved entities and to produce the Test Report. The Test Report explicitly states Search Goals (as Controller Input) and corresponding Goal Results (Controller Output). This constitutes one benchmark (single-goal or multi-goal). Repeated or slightly differing benchmarks are realized by calling the Controller once for each benchmark.

Search For one benchmark, the Manager calls a Controller once, and the Controller then invokes the Measurer repeatedly until the Controller decides it has enough information to return its outputs. The part during which the Controller invokes the Measurer is termed the Search. Any work the Manager performs, either before invoking the Controller or after Controller returns, falls outside the scope of the Search. The MLRsearch Specification prescribes Regular Goal Results and recommends corresponding Search completion conditions. Irregular Goal Results are also allowed, they have different requirements and their corresponding stopping conditions are out of scope. The Search Result is the combination of regular or irregular results, one for each Search Goal. Search Results are based on Load Classification. When measured enough, a chosen Load can either achieve or fail each Search Goal (separately), thus becoming a Lower Bound or an Upper Bound for that Search Goal. When the Relevant Lower Bound is close enough to the Relevant Upper Bound according to Goal Width, the Regular Goal Result is found. Search stops when all Regular Goal Results are found or when all remaining Search Goals are proven to have only Irregular Goal Results.

Search Duration Even if the time it takes the Controller to compute Trial Input attributes for next Trial is negligible; Trials themselves take some time to finish, and SUT behavior affects how quickly stopping conditions can be satisfied. For large scale tests where many SUT configurations and Traffic Profiles need benchmarking, it is important to optimize the overall duration of one Search, while the time cost of initial configuration tends to be constant. There are three considerations worth discussing for such Search Duration optimization. Firstly, as SUT behavior can be probabilistic, so can be the Search Duration of each benchmark. The quantity to optimize is the expected value of Search Duration, it should be as short as possible within the intended reliability. Secondly, Search Duration probability distributions with smaller standard deviations are preferred, as it makes it easier to plan execution of multiple benchmarks one-by-one on the same SUT. Thirdly, any prior knowledge about SUT behavior can be leveraged into average time gains if the Controller implementation supports corresponding heuristics. Without such knowledge, implementations should focus on worst possible results, as lowering Search Duration for those helps with standard deviation, if not also the expected value. Most of optimization heuristics are outside of the scope of this document, but many design decisions were affected by generic optimizations found in practice so far.

Test Report A primary responsibility of the Manager is to produce a Test Report, which serves as the final and formal output of the test procedure. This document does not provide a single, complete, normative definition for the structure of the Test Report. For example, the Test Report may contain results for a single benchmark, or it could aggregate results of many benchmarks. Instead, normative requirements for the content of the Test Report are specified throughout this document in conjunction with the definitions of the quantities and procedures to which they apply. Readers should note that any clause requiring a quantity to be "reported" or "stated in the Test Report" constitutes a normative requirement on the content of this final artifact. Even where not stated explicitly, the "Reporting format" paragraphs in are still requirements on Test Reports if they apply to an MLRsearch benchmark.

Behavior Correctness The MLRsearch Specification by itself does not guarantee that the Search ends in finite time, as the freedom the Controller has for Load selection also allows for clearly deficient choices. For deeper insights on these matters, refer to . The primary MLRsearch implementation, used as the prototype for this specification, is .

Quantities The MLRsearch Specification relies on several specific quantities. In physics, a single magnitude can be expressed in multiple ways as a product of a unit and a value. This document uses the computer science vocabulary, where the term "quantity" can describe multiple variables or constants at once. One instance of a scalar quantity is called a value, with the corresponding unit only mentioned when needed. Where the context allows, a shorter phrase is used, for example, "Load" instead of "value of the Load quantity". In general, the MLRsearch Specification does not prescribe 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. In rare cases, a primary unit is mentioned, usually when comparison across different Traffic Profiles would be otherwise ambiguous. Some units MAY be preferred by some implementations, for example, when they round the values to integers. For convenience, a group of quantities can be treated as a composite quantity. One constituent of a composite quantity is called an attribute. A group of attribute values is called an instance of that composite quantity. Some attributes may depend on others and can be computed from other attributes. Such quantities are called derived quantities.

Current and Final Values Some quantities are defined in a way that makes it possible to compute their values in the middle of a Search. Other quantities are specified so that their values can be computed only after the Search ends. Some quantities are important only after a Search ends, but their values are also computable before a Search ends. For a quantity that is computable before a Search ends, the adjective current is used to mark a value of that quantity available before the Search ends. When such value is relevant for the Search Result, the adjective final is used to denote the value of that quantity at the end of the Search. If a time evolution of such a dynamic quantity is guided by configuration quantities, those adjectives can be used to distinguish such quantities. For example, if the current value of "duration" (a dynamic quantity) increases from "initial duration" to "final duration" (configuration quantities), all the quoted names denote separate but related quantities. As the naming suggests, the final value of the duration quantity is expected to be equal to the "final duration" value.

Existing Terms This specification relies on the following three documents that should be consulted before attempting to make use of this document:

"Benchmarking Terminology for Network Interconnection Devices" contains basic term definitions.
"Benchmarking Terminology for LAN Switching Devices" includes more terms and discussions, and it describes some known network benchmarking situations in a more precise way.
"Benchmarking Methodology for Network Interconnect Devices" contains discussions about terms and additional methodology requirements.

References to several central terms from the above documents are given in the following subsections. Some of those terms need no further discussion, but some require some elaboration to put into proper context.

SUT SUT is defined in as follows.

Definition:: The collective set of network devices to which stimulus is offered as a single entity and response measured.
Discussion:: A SUT consisting of a single network device is allowed by this definition. In software-based networking, SUT may comprise a multitude of networking applications and the entire host hardware and software execution environment. SUT is the only entity that can be benchmarked directly, even though only the performance of some sub-components are of interest. For example, describes a single SUT consisting of DUT 1, DUT 2, and a WAN link between them.

DUT DUT is defined in as follows.

Definition:: The network forwarding device to which stimulus is offered and response measured.
Discussion:: Contrary to SUT, the DUT stimulus and response are frequently initiated and observed only indirectly, on different parts of SUT. DUT, as a sub-component of SUT, is only indirectly mentioned in the MLRsearch Specification but is of key relevance for its motivation. The device can represent a software-based networking function running on commodity x86/ARM CPUs (vs. purpose-built ASICs, NPUs, and FPGAs). When the MLRsearch Specification mentions SUT configuration, it implies adequate configuration of constituent DUTs, subjected to requirements from . A well-designed SUT SHOULD have the primary DUT as their performance bottleneck. The ways to achieve and verify that are outside the scope of the MLRsearch Specification. A typical exception to this rule is when DUT has a surprisingly good performance. For example, achieving the line rate does not make the SUT badly designed. This situation is quite common in practice, when the DUT is the bottleneck for a traffic consisting of small frames, but achieves the line rate with large frames.

Trial A trial is the part of the test described in .

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:

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.
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.
Run the test trial.
Wait for two seconds for any residual frames to be received.
Wait for at least five seconds for the DUT to restabilize.

Discussion:

The traffic is sent only in phase c) and received in phases c) and d). Trials are the only stimuli the SUT is expected to experience during the Search. It is useful to consider the traffic as sent and received by a tester, as implicitly defined in . The definition above describes some traits but does not use key words as defined in BCP 14 to signify the strength of the requirements. For the purposes of the MLRsearch Specification, the test procedure MAY deviate from the description in , but any such deviation MUST be described explicitly in the Test Report. It is still RECOMMENDED to not deviate from the description, as any deviation weakens comparability. An example of deviation from is using shorter wait times, compared to those described in phases a), b), d), and e). seems to treat phase b) as any type of configuration that cannot be configured only once (by the Manager, before the Search starts), as some crucial SUT state could time out during the Search. It is RECOMMENDED to interpret the "learning frames" to mean any such time-sensitive per-Trial configuration method, with bridge Media Access Control (MAC) address learning being only one possible example. lists another example: ARP with a wait time of 5 seconds. Some methodologies describe recurring tests. If those are based on Trials, they are treated as multiple independent Trials. That means there are no "recurring trials" treated as a single measurement in MLRsearch, but the Controller MAY repeat the same Trial Inputs to get multiple independent Trial Outputs.

Load Quantities Several existing quantities describe the intensity of the traffic entering a SUT. MLRsearch needs a quantity useful not only as an input for a Trial, but also as a basis for several related quantities not tied to a single Trial. The following subsections refer to existing terms before introducing their combination used as such a base quantity in this document.

Intended Load Defined in "Intended load (Iload)" ().

Offered Load Defined in "Offered load (Oload)" ().

Constant Load Defined in "Constant Load" ().

Load

Definition:: Load is a global per-interface Intended Load usable for a Trial.
Discussion:: For specification purposes, Load is also assumed to be Constant Load. Similarly to existing definitions, this quantity is related to one (input or output) SUT interface. In the common case of bidirectional traffic, as described in "Bidirectional traffic" (), Load is the "data rate" per each direction, half of the "sum of data rates". The Test Report MAY present the aggregate Load across multiple interfaces, treating it as the same magnitude expressed using different units. Each reported Load MUST unambiguously state whether it refers to (i) a single interface, (ii) a specified subset of interfaces (such as all logical interfaces mapped to one physical port), or (iii) the total across every interface. For any aggregate Load value, the report MUST also give the fixed conversion factor that links the per-interface and multi-interface Load values. The per-interface Load remains the primary unit, consistent with the prevailing practice described in , , and . The previous paragraph also applies to other terms related to Load. For example, tests with symmetric bidirectional traffic MAY report Load-related values as "bidirectional load" (double of "unidirectional load" if that is distinguished in the same Test Report).

Besides Trial Load, the Relevant Lower Bound will be another example of a newly defined quantity based on Load.

Forwarding Rate Quantities Similar to Load as a main quantity acting as an input for a Trial, Forwarding Rate is an existing quantity describing an output from a Trial. Besides Trial Forwarding Rate, the Conditional Throughput will be another example of a newly defined quantity based on Forwarding Rate.

Forwarding Rate Defined in "Forwarding rate (FR)" (Section 3.6.1 of ).

Throughput Defined in "Throughput" (). The methodology of measuring Throughput is codified in "Throughput" (). This document frequently uses the phrase Throughput when referring not only to the Throughput quantity itself, but also to the methodology requirements for benchmarking it.

Trial Terms This section defines new terms and redefines existing terms for quantities relevant as inputs or outputs of a Trial, as handled by the Measurer component. This also includes any derived quantities related to results of one Trial.

Trial Duration

Definition:: Trial Duration is the intended duration of phase c) of a Trial.
Discussion:: The value MUST be positive. While any positive real value may be provided, some Measurer implementations MAY limit possible values, e.g., by rounding down to the nearest integer in seconds. In that case, it is RECOMMENDED to give such inputs to the Controller so that the Controller implementation only generates the accepted values.

Trial Load

Definition:: Trial Load is the Load used in a specific Trial.
Discussion:: This is a Load-related quantity that is tied to a single Trial, to distinguish it from later derived quantities that are not tied that way. For specification purposes, it is assumed that this is a Constant Load by default. Informally, Trial Load is a single number that can "scale" any traffic pattern as long as the intuition of a load intended against a single interface can be applied. It MAY be possible to use a Trial Load to describe non-constant traffic (using average load when the traffic consists of repeated bursts of frames, e.g., as suggested in ). In the case of a non-constant load, the Test Report MUST explicitly mention exactly how non-constant the traffic is and how it reacts to the Trial Load value. But the rest of the MLRsearch Specification assumes that is not the case, to avoid discussing corner cases (e.g., which values are possible within medium limitations). Similarly, traffic patterns where different interfaces are subject to different loads MAY be described by a single Trial Load value (e.g., using the largest Intended Load among interfaces), but again, the Test Report MUST explicitly describe how the traffic pattern reacts to the Trial Load value, and this specification does not discuss all the implications of that approach. Traffic patterns where a single Trial Load does not describe their scaling cannot be used for MLRsearch benchmarks. Similarly to Trial Duration, some Measurers MAY limit the possible values of Trial Load. Contrary to Trial Duration, documenting such behavior in the Test Report is OPTIONAL. This is because the load differences are negligible (and frequently undocumented) in practice. The Controller MAY select the Trial Load and Trial Duration values in a way that would not be possible to achieve using any integer number of data frames. Given that the Trial Load is a quantity based on Load, Test Report MAY express this quantity using multi-interface values, as the sum of Intended Loads over input interfaces.

Trial Input

Definition:: Trial Input is a composite quantity, consisting of exactly two attributes: Trial Duration and Trial Load.
Discussion:: When talking about a set of Trials, it is common to say Trial Inputs to denote all corresponding Trial Input instances. One Trial Input instance acts as the input for one call of the Measurer component. Contrary to other composite quantities, MLRsearch implementations MUST NOT add optional attributes into Trial Input. This improves interoperability between various implementations of a Controller and a Measurer. Note that both attributes are intended quantities, as only those can be fully controlled by the Controller. The actual offered quantities, as realized by the Measurer, can be different (and must be different if not multiplying into an integer number of frames), but questions around those offered quantities are generally outside of the scope of this document.

Traffic Profile

Definition:

Traffic Profile is a composite quantity containing all attributes other than Trial Load and Trial Duration that are needed for the unique determination of the Trial to be performed.

Discussion:

All the attributes MUST be constant during the Search, and the composite is conceptually configured on the Measurer by the Manager before the Search starts. This is why the Traffic Profile is not part of the Trial Input. Specification of traffic properties included in the Traffic Profile is the responsibility of the Manager, but the specific configuration mechanisms are outside of the scope of this document. Implementations are allowed to include this data in Controller calls to the Measurer, as long as its impact is functionally constant. Implementations of the Manager and the Measurer should be aware of their common set of capabilities well enough to ensure that the Traffic Profile instance uniquely defines the traffic during the Search. Typically, Manager and Measurer implementations are tightly integrated. Integration efforts between independent Manager and Measurer implementations are outside of the scope of this document. An example standardization effort is described in . Examples of common traffic properties include:

Data link frame size:
- Fixed sizes as listed in and in
- "Internet Mix" (IMIX) mixed frame sizes as defined in
Frame formats and protocol addresses:
- Sections and of and

Other traffic properties that need to somehow be specified in Traffic Profile, and MUST be mentioned in Test Report if they apply to the benchmark, include:

symmetric bidirectional traffic from ,
fully meshed traffic from ,
modifiers from , and
IP version mixing from .

Trial Forwarding Ratio

Definition:: The Trial Forwarding Ratio is a dimensionless floating point quantity. Its value MUST range between 0.0 and 1.0, both inclusive. It is computed 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 received by a SUT from the tester". This SHOULD be the default interpretation. However, if this is not the case, the Test Report MUST describe the Traffic Profile in sufficient enough detail to imply how the Trial Forwarding Ratio should be computed. The Trial Forwarding Ratio MAY be expressed in other units (e.g., as a percentage) in the Test Report. Note that, contrary to Load terms, frame counts used to compute the Trial Forwarding Ratio are generally aggregates over all SUT output interfaces, as most test procedures verify all outgoing frames. The procedure for Throughput counts received frames, so it implies bidirectional counts for bidirectional traffic, even though the final value is the "rate" that is still per-interface. For example, in a test with symmetric bidirectional traffic, if one direction is forwarded without any losses, but the opposite direction does not forward at all, the Trial Forwarding Ratio would be 0.5 (50%). In future extensions, more general ways to compute the Trial Forwarding Ratio may be allowed, but the current MLRsearch Specification relies on this specific averaged counters approach.

Trial Loss Ratio

Definition:: The Trial Loss Ratio is equal to one minus the Trial Forwarding Ratio.
Discussion:: When expressing ratio values as percentages, the Trial Loss Ratio is equal to 100% minus the Trial Forwarding Ratio. This is almost identical to Frame Loss Rate in . The only minor differences are that Trial Loss Ratio does not need to be expressed as a percentage, and Trial Loss Ratio is explicitly based on averaged frame counts when more than one traffic direction is present.

Trial Forwarding Rate

Definition:: The Trial Forwarding Rate is a derived quantity, computed by multiplying the Trial Load by the Trial Forwarding Ratio.
Discussion:: Despite the similar name, this quantity differs substantially from Forwarding Rate.

Under the method described in , each output interface is measured separately, so every interface may report a different Forwarding Rate. The Trial Forwarding Rate, by contrast, uses a single set of frame counts and therefore yields one value that represents the whole system while still preserving the direct relation to the per-interface Load. When the Traffic Profile is symmetric and bidirectional, as defined in , the Trial Forwarding Rate is numerically equal to the arithmetic average of the individual per-interface Forwarding Rates. For more complex traffic patterns, such as many-to-one, as mentioned in "Partially meshed traffic" (), the meaning of Trial Forwarding Rate is less straightforward. For example, if two input interfaces receive one million frames per second (fps) each, and a single interface outputs 1.4 million fps, the Trial Load is 1 million fps, the Trial Loss Ratio is 30%, and the Trial Forwarding Rate is 0.7 million fps. Because Trial Forwarding Rate is anchored to the Load defined for one interface, a Test Report MAY show it either as the single averaged figure just described or as the sum of the separate per-interface Forwarding Rates. For the example above, the aggregate Trial Forwarding Rate is 1.4 million fps.

Trial Effective Duration

Definition:: The Trial Effective Duration is a time quantity related to a Trial. By default, it is 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 from its Trial Input instead. The Trial Effective Duration MAY be any positive 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 time-critical benchmarks designed to manage the overall Search Duration, rather than solely the traffic portion of it. An approach is to measure the duration of the whole Trial (including all wait times) and use that as the Trial Effective Duration. This is also 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 consisting of several attributes. The REQUIRED attributes are Trial Loss Ratio, Trial Effective Duration, and Trial Forwarding Rate.
Discussion:: When referring to more than one Trial, the plural term Trial Outputs is used to collectively describe multiple Trial Output instances. Measurer implementations MAY provide additional attributes. The Controller implementations SHOULD ignore any such optional attribute they are not familiar with. If a Controller implementation passes selected Trial Outputs to the Manager, the instances SHOULD contain all such additional attributes. An example of an optional attribute is the aggregate count of frames expected to be forwarded during the Trial, especially if it is not (a rounded-down value) implied by Trial Load and Trial Duration. While requires the Offered Load to be reported for Forwarding Rate measurements, it is not required in the MLRsearch Specification, as Search Results do not depend on it, and technically the Measurer is not performing a direct Forwarding Rate measurement.

Trial Result

Definition:: Trial Result is a composite quantity, consisting of the Trial Input and the Trial Output as REQUIRED attributes.
Discussion:: When referring to more than one Trial, the plural term Trial Results is used to collectively describe multiple Trial Result instances.

Goal Terms This section defines new terms for quantities relevant (directly or indirectly) for inputs and outputs of the Controller component. Several goal attributes are defined before introducing the main composite quantity: the Search Goal. Contrary to other sections, definitions in subsections of this section are necessarily vague, as their fundamental meaning is to act as coefficients in formulas for Controller Output attributes, which are not defined yet. The discussions in this section relate the attributes to concepts mentioned in "Overview of RFC 2544 Problems", but these discussion paragraphs are short and informal, and they mostly reference later sections, where the impact on Search Results is discussed after introducing the complete set of Auxiliary Terms.

Goal Final Trial Duration

Definition:: This is the minimal value for Trial Duration that should be reached. The value MUST be positive.
Discussion:: Certain Trials must reach this minimum Trial Duration before a Load can be classified as a Lower Bound. The Controller MAY choose shorter Trial Durations, and those Trial Results can be enough for classification as an Upper Bound. If such shorter Trials prove no Lower Bound exists, this Trial Duration value may never be reached, thus shortening Search Duration. It is RECOMMENDED for all Search Goals to share the same Goal Final Trial Duration value. Otherwise, Trial Durations larger than the Goal Final Trial Duration may occur, weakening the assumptions the "Load Classification Logic" is based on. Note that this is a soft limitation for the Trial Duration values selected by the Controller. The Measurer may keep returning different Effective Trial Durations in Trial Results, so Controller implementations MUST be ready to handle such situations.

Goal Duration Sum

Definition:: This is a threshold value for a particular sum of Trial Effective Duration values. The value MUST be positive.
Discussion:: Informally, this prescribes the sufficient number of Trials performed at a specific Trial Load and Goal Final Trial Duration during the Search. If the Goal Duration Sum is larger than the Goal Final Trial Duration, multiple Trials may be needed to be performed at the same Load. Refer to "MLRsearch Compliant with TST009" for an example where the possibility of multiple Trials at the same Load is intended. A Goal Duration Sum shorter than the Goal Final Trial Duration (of the same Search Goal) could reduce Search time but is NOT RECOMMENDED, as the time savings come at the cost of decreased repeatability. In practice, the Search can spend less than the Goal Duration Sum measuring a Load when the Trial Results are particularly one-sided, but also, the Search can spend more than the Goal Duration Sum measuring a Load when the Trial Results are balanced and include Trials shorter than the Goal Final Trial Duration.

Goal Loss Ratio

Definition:: This is a threshold value for Trial Loss Ratio values. The value MUST be non-negative and smaller than one.
Discussion:: A Trial with the Trial Loss Ratio larger than this value signals the SUT may be unable to process this Load well enough. See "Throughput with Non-Zero Loss" for reasons why users may want to set this value above zero. Since multiple Trials might be needed for one Load, the Load Classification might be more complicated than the mere comparison of one Trial Loss Ratio to the Goal Loss Ratio.

Goal Exceed Ratio

Definition:: This is a threshold value for a particular ratio of sums of Trial Effective Durations. The value MUST be non-negative and smaller than one.
Discussion:: Informally, this controls the ratio of Trial Results exceeding Goal Loss Ratio. More specifically, up to this proportion of the Trial Results with the Trial Loss Ratio above the Goal Loss Ratio is tolerated at a Lower Bound. This is the full impact if every Trial is measured at Goal Final Trial Duration. The actual full logic is more complicated, as shorter Trials are allowed. For explainability reasons, the RECOMMENDED value for the Goal Exceed Ratio is 0.5 (50%), and in practice that also leads to the smallest variation in overall Search Duration. Refer to "Exceed Ratio and Multiple Trials" for more details.

Goal Width

Definition:: This is a threshold value for deciding whether two Load values are close enough. This is an OPTIONAL attribute. If present, the value MUST be positive.
Discussion:: Informally, this acts as a stopping condition, controlling the precision of the Goal Result. The Search stops if every Search Goal has reached its precision. Implementations without this attribute MUST provide the Controller with other means to control the Search stopping conditions. Absolute Load difference (in fps) and relative Load difference (in percents) are two popular choices, but implementations MAY choose different ways to specify Goal Width. The Test Report MUST make it clear what specific quantity is used as the Goal Width. It is RECOMMENDED to express the Goal Width as a relative difference and set it to a value not lower than the Goal Loss Ratio. Refer to "Performance Variability" for more elaboration on the reasoning.

Goal Initial Trial Duration

Definition:: This is the minimal value for the Trial Duration suggested to be used for this goal. This is an OPTIONAL attribute. If present, this value MUST be positive.
Discussion:: This is an example of an optional Search Goal attribute. A typical default value is equal to the Goal Final Trial Duration value. Informally, this is the shortest Trial Duration the Controller should select when focusing on this Search Goal. Note that shorter Trial Durations might still be selected by the Controller, for example, when focusing on a different Search Goal. The Goal Initial Trial Duration is a mechanism for a user to discourage Trials with Trial Durations deemed as too small to be reliable for a particular SUT and a given Search Goal. As with Goal Final Trial Duration, the Controller implementation MUST be able to handle possibly lower Effective Trial Duration values returned by the Measurer.

Search Goal

Definition:: The Search Goal is a composite quantity consisting of several attributes, some of which are required. The REQUIRED attributes are Goal Final Trial Duration, Goal Duration Sum, Goal Loss Ratio, and Goal Exceed Ratio.
Discussion:: Typical optional attributes are Goal Initial Trial Duration and Goal Width. Implementations MAY add their own attributes. Those additional attributes may be required by an implementation even if they are not required by the MLRsearch Specification. However, it is RECOMMENDED for those implementations to support missing attributes by providing typical default values. For example, implementations with Goal Initial Trial Durations might also require users to specify "how quickly" Trial Durations should increase. Refer to "Compliance" for important Search Goals.

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 Goals.
Discussion:: MLRsearch implementations MAY use additional attributes. Those additional attributes may be required by an implementation even if they are not required by the MLRsearch Specification. Formally, the Manager does not apply any Controller configuration apart from one Controller Input instance. For example, Traffic Profile is conceptually configured on the Measurer by the Manager, without explicit assistance of the Controller. The order of Search Goals in a list SHOULD NOT have a big impact on Controller Output, but MLRsearch implementations MAY base their behavior on the order of Search Goals in a list.

Max Load

Definition:: Max Load is an OPTIONAL attribute of Controller Input. It is the maximal value the Controller is allowed to select for Trial Loads.
Discussion:: Max Load is an example of an optional attribute (outside the list of Search Goals) required by some implementations of MLRsearch. If the Max Load is provided, the Controller MUST NOT select Trial Loads larger than that value. In theory, each Search Goal could have its own Max Load, but as all Trial Results are possibly affecting all Search Goals, it makes more sense for a single Max Load to apply to all Search Goals. While Max Load is a frequently used configuration parameter, already governed (as Maximum Frame Rate) by and (as Maximum Offered Load) by , some implementations MAY detect or discover it, instead of requiring a user-supplied value. In the MLRsearch Specification, one reason for listing the Relevant Upper Bound as a required attribute is that it makes the Search Result independent of the Max Load value. Given that Max Load is a quantity based on Load, Test Report MAY express this quantity using multi-interface values, as the sum of per-interface maximal Loads.

Min Load

Definition:: Min Load is an OPTIONAL attribute of Controller Input. It is the minimal value the Controller is allowed to use for Trial Loads.
Discussion:: Min Load is another example of an optional attribute required by some implementations of MLRsearch. Similarly to Max Load, it makes more sense to prescribe one common value, as opposed to using a different value for each Search Goal. If the Min Load is provided, the Controller MUST NOT select Trial Loads smaller than that value. Min Load is mainly useful for saving time by failing early, arriving at an Irregular Goal Result when Min Load gets classified as an Upper Bound. For implementations, it is RECOMMENDED to require Min Load to be non-zero and large enough to allow at least one frame to be forwarded even at the shortest allowed Trial Duration, so that the Trial Loss Ratio is always well-defined and the implementation can apply a relative Goal Width safely. Given that Min Load is a quantity based on Load, Test Report MAY express this quantity using multi-interface values, as the sum of per-interface minimal Loads.

Auxiliary Terms While the terms defined in this section are not strictly needed when formulating MLRsearch requirements, they simplify the language used in discussion paragraphs and explanation sections.

Trial Classification When one Trial Result instance is compared to one Search Goal instance, several relations can be named using short adjectives. As Trial Results do not affect each other, this Trial Classification does not change during a Search.

High-Loss Trial A Trial with a Trial Loss Ratio larger than a Goal Loss Ratio is called a High-Loss Trial, with respect to the given Search Goal (or lossy Trial, if the Goal Loss Ratio is zero).

Low-Loss Trial If a Trial is not a High-Loss Trial, it is called a Low-Loss Trial (or zero-loss Trial, if the Goal Loss Ratio is zero).

Short Trial A Trial with a Trial Duration shorter than the Goal Final Trial Duration is called a Short Trial with respect to the given Search Goal.

Full-Length Trial A Trial that is not a Short Trial is called a Full-Length Trial. Note that this includes Trial Durations larger than the Goal Final Trial Duration.

Long Trial A Trial with a Trial Duration longer than the Goal Final Trial Duration is called a Long Trial.

Load Classification When a set of all Trial Result instances, performed so far at one Load, is compared to one Search Goal instance, their relation can be named using the concept of a bound. In general, such bounds are a current quantity, even though cases of a Load changing its classification more than once during the Search is rare in practice.

Upper Bound

Definition:: A Load is called an Upper Bound if and only if it is classified as such by a "Load Classification Code" algorithm for the given Search Goal at the current moment of the Search.
Discussion:: In more detail, the set of all Trial Results performed so far at the Load (and any Trial Duration) is certain to fail to uphold all the requirements of the given Search Goal, mainly the Goal Loss Ratio in combination with the Goal Exceed Ratio. In this context, "certain to fail" relates to any possible Trial Results within the time remaining till the Goal Duration Sum is reached. One Search Goal can have multiple different Loads classified as its Upper Bounds. While Search progresses and more Trials are measured, any Load can become an Upper Bound in principle. Moreover, a Load can stop being an Upper Bound, but that can only happen when more than a Goal Duration Sum of Trials are measured (e.g., because another Search Goal needs more Trials at this Load). Informally, the previous Upper Bound got invalidated. In practice, the Load frequently becomes a Lower Bound instead.

Lower Bound

Definition:: A Load is called a Lower Bound if and only if it is classified as such by a "Load Classification Code" algorithm for the given Search Goal at the current moment of the Search.
Discussion:: In more detail, the set of all Trial Results performed so far at the Load (and any Trial Duration) is certain to uphold all the requirements of the given Search Goal, mainly the Goal Loss Ratio in combination with the Goal Exceed Ratio. Here, "certain to uphold" relates to any possible Trial Results within the time remaining till the Goal Duration Sum is reached. One Search Goal can have multiple different Loads classified as its Lower Bounds. As Search progresses and more Trials are measured, any Load value can become a Lower Bound in principle. No Load can be both an Upper Bound and a Lower Bound for the same Search Goal at the same time, but it is possible for a larger Load to be a Lower Bound while a smaller Load is an Upper Bound at the same time. Moreover, a Load can stop being a Lower Bound, but that can only happen when more than a Goal Duration Sum of Trials are measured (e.g., because another Search Goal needs more Trials at this Load). Informally, the previous Lower Bound got invalidated. In practice, the Load frequently becomes an Upper Bound instead.

Undecided

Definition:: A Load is called Undecided if it is currently neither an Upper Bound nor a Lower Bound for the give Search Goal.
Discussion:: Any Load that has not been measured so far is Undecided. It is possible for a Load to transition from an Upper Bound to Undecided by adding Short Low-Loss Trials. That is yet another reason for users to avoid using Search Goals with different Goal Final Trial Durations.

Result Terms Before defining the full structure of a Controller Output, it is useful to define the composite quantity, called Goal Result. The 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 their terms. Conversely, at the end of the Search, each Search Goal instance has its corresponding Goal Result instance.

Relevant Upper Bound

Definition:: The Relevant Upper Bound is the smallest Load classified as an Upper Bound for a given Search Goal at the end of the Search.
Discussion:: If no measured Load had enough High-Loss Trials, the Relevant Upper Bound MAY be non-existent, for example, when Max Load is classified as a Lower Bound. Conversely, when the Relevant Upper Bound does exist, it is not affected by the Max Load value. Given that the Relevant Upper Bound is a quantity based on Load, Test Report MAY express this quantity using multi-interface values, as the sum of Intended Loads over input interfaces.

Relevant Lower Bound

Definition:: The Relevant Lower Bound is the largest Load among those smaller than the Relevant Upper Bound that got classified as a Lower Bound for a given Search Goal at the end of the Search.
Discussion:: If no Load had enough Low-Loss Full-Length Trials, the Relevant Lower Bound MAY be non-existent. Strictly speaking, if the Relevant Upper Bound does not exist, the Relevant Lower Bound also does not exist. In a typical case, Max Load is classified as a Lower Bound, making it impossible to increase the Load to continue the Search for an actual Upper Bound. Thus, it is not clear whether a larger value would be found for a Relevant Lower Bound if larger Loads were available for selection. Given that the Relevant Lower Bound is a quantity based on Load, Test Report MAY express this quantity using multi-interface values, as the sum of Intended Loads over input interfaces.

Conditional Throughput

Definition:: Conditional Throughput is a value computed at the Relevant Lower Bound according to the algorithm defined in "Conditional Throughput Code".
Discussion:: The Relevant Lower Bound is defined only at the end of the Search, and so is the Conditional Throughput. But the algorithm can be applied at any time on any current Lower Bound, so the final Conditional Throughput value may appear sooner than at the end of a Search. Informally, the Conditional Throughput should be a typical Trial Forwarding Rate, expected to be seen at the Relevant Lower Bound of a given Search Goal. But frequently, it is only a conservative estimate thereof, as MLRsearch implementations tend to stop measuring more Trials as soon as they confirm the value cannot get worse than this estimate within the Goal Duration Sum. This quantity is RECOMMENDED to be used when evaluating repeatability and comparability of different MLRsearch implementations. Refer to "Generalized Throughput" for more details. Given that Conditional Throughput is a quantity based on Load, Test Report MAY express this quantity using multi-interface values, as the sum of per-interface Forwarding Rates.

Goal Results The MLRsearch Specification is based on a set of requirements for a regular result. But in practice, it is not always possible for such a result instance to exist, so irregular results also need to be supported.

Regular Goal Result

Definition:: Regular 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:: Implementations MAY add their own attributes. Test Report MUST display the Relevant Lower Bound. Displaying the Relevant Upper Bound is RECOMMENDED, especially if the implementation does not use Goal Width. In general, stopping conditions for the corresponding Search Goal MUST be satisfied to produce a Regular Goal Result. Specifically, if an implementation offers Goal Width as a Search Goal attribute, the distance between the Relevant Lower Bound and the Relevant Upper Bound MUST NOT be larger than the Goal Width. For stopping conditions, refer to "Goal Width" and "Stopping Conditions and Precision".

Irregular Goal Result

Definition:: Irregular Goal Result is a composite quantity. All attributes are OPTIONAL.
Discussion:: It is RECOMMENDED to report any useful quantity even if it does not satisfy all the requirements. For example, if Max Load is classified as a Lower Bound, it is fine to report it as an "effective" Relevant Lower Bound (although not a real one, as that requires a Relevant Upper Bound, which does not exist in this case) and compute Conditional Throughput for it. In this case, only the missing Relevant Upper Bound signals this instance is irregular. Similarly, if both Relevant Bounds exist, it is RECOMMENDED to include them as Irregular Goal Result attributes and let the Manager decide if they are too far apart for Test Report purposes. If Test Report displays some Irregular Goal Result attribute values, they MUST be clearly marked as coming from irregular results. The implementation MAY define additional attributes, for example, explicit flags for expected situations, so the Manager logic can be simpler.

Goal Result

Definition:: Goal Result is a composite quantity. Each instance is either a Regular Goal Result or an Irregular Goal Result.
Discussion:: The Manager MUST be able of distinguishing whether the instance is regular or not, without accessing data outside the instance.

Search Result

Definition:: The Search Result is a single composite object that maps each Search Goal instance to a corresponding Goal Result instance.
Discussion:: As an alternative to mapping, the Search Result MAY be represented as an ordered list of Goal Results that in that case MUST appear in the exact same order as the list of their corresponding Search Goals as specified in the Controller Input instance. When the Search Result is expressed as a mapping, it MUST contain an entry for every Search Goal supplied in the Controller Input. Identical Goal Result instances MAY be listed for different Search Goals, but their status as regular or irregular MAY be different, for example, if two Search Goals differ only in the Goal Width, and the Relevant Lower Bound is close enough to the Relevant Upper Bound according to only one of them.

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:: The MLRsearch implementation MAY return additional data in the Controller Output, for example, the number of Trials performed and the total Search Duration.

Architecture Terms The MLRsearch architecture consists of three main system components: the Manager, the Controller, and the Measurer. The components were introduced in "Architecture Overview", and the following sections finalize their definitions using terms from previous sections. Note that the architecture also implies the presence of other components, such as the SUT and the tester (as a sub-component of the Measurer). Communication protocols and interfaces between components are left unspecified. For example, when the MLRsearch Specification uses the verb "to call" when describing how the Controller interacts with the Measurer, it is possible that the Controller notifies the Manager to call the Measurer indirectly instead. In doing so, the Measurer implementations can be fully independent from the Controller implementations, for example, developed in different programming languages.

Measurer

Definition:: The Measurer is a functional element that, when called with a Trial Input instance, performs one Trial and returns a 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 warm-up (if the tester or the test procedure requires one). It is the responsibility of the Measurer implementation to uphold any requirements and assumptions present in the MLRsearch Specification, e.g., the Trial Forwarding Ratio not being larger than one. Implementers have some freedom. For example, 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 the sender and receiver directly (without any SUT in the path), find a Load that guarantees the Offered Load is not too far from the Intended Load, and use that value as the Max Load. When measuring the real SUT, it is RECOMMENDED to turn any severe deviation between the Intended Load and the Offered Load into the increased Trial Loss Ratio. Neither of these two recommendations are made into mandatory requirements, because it is not easy to provide guidance about when the difference is severe enough in a way that would be disentangled from other Measurer freedoms.

For a sample situation where the Offered Load cannot keep up with the Intended Load, and the consequences on the Search Result, refer to "Hard Performance Limit".

Controller

Definition:: The Controller is a functional element that, upon receiving a Controller Input instance, repeatedly generates Trial Input instances for the Measurer and collects the corresponding Trial Output instances. This cycle continues until the stopping conditions are met, at which point, the Controller produces a final Controller Output instance and terminates.
Discussion:: Informally, the Controller has considerable freedom in selection of Trial Inputs, and the implementations want to achieve all the Search Goals in the shortest average Search Duration. The Controller's role in optimizing the overall Search Duration 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 affect comparability that much, as long as the Goal Result instances compared are regular.

Manager

Definition:: The Manager is a functional element that is responsible for provisioning other components, calling a Controller component once, and for creating the Test Report following the reporting format as defined in .
Discussion:: The Manager MUST initialize the SUT (including constituent DUTs) and the Measurer (and the tester if independent from Measurer) with their intended configurations before calling the Controller. Note that already puts requirements on DUT setups:
It is expected that all of the tests will be run without changing the configuration or setup of the DUT in any way other than that required to do the specific test. For example, it is not acceptable to change the size of frame handling buffers between tests of frame handling rates or to disable all but one transport protocol when testing the throughput of that protocol.
It is REQUIRED for the Test Report to encompass all the SUT configuration details, including the description of a default DUT configuration common for most tests and configuration changes if required by a specific test. For example, recommends testing jumbo frames if SUT can forward them, even though they are outside the scope of the 802.3 IEEE standard . In this case, it is acceptable for the SUT default configuration to not support jumbo frames and only enable this support when testing jumbo Traffic Profiles, as the handling of jumbo frames typically has different packet buffer requirements and potentially higher processing overhead. Non-jumbo frame sizes should also be tested on the jumbo-enabled setup. The Manager does not need to be able to tweak any Search Goal attributes, but it MUST report all applied attributes even if not tweaked. A human or automated user invokes the Manager once to launch a single Search and receive its Test Report. Every new invocation is treated as a fresh, independent Search; how the system behaves across multiple calls (for example, combining or comparing their Search Results) is explicitly out of scope for this document.

Compliance This section discusses compliance relations between MLRsearch and other test procedures.

Test Procedure Compliant with MLRsearch Any networking measurement setup that could be understood as consisting of functional elements satisfying all requirements for the Measurer, the Controller, and the Manager is compliant with the MLRsearch Specification. These components can be seen as abstractions present in any testing procedure. For example, there may be a single component acting as both the Manager and the Controller, but if values of all required attributes of Search Goals and Goal Results are visible in the Test Report, the Controller Input and Controller Output instances are implied. For example, any setup for conditionally (or unconditionally) compliant Throughput testing can be understood as an MLRsearch architecture if there is enough data to reconstruct the Relevant Upper Bound. Refer to "MLRsearch Compliant with RFC 2544" for an equivalent Search Goal. Any test procedure that can be understood as one call to the Manager of the MLRsearch architecture is said to be compliant with the MLRsearch Specification.

MLRsearch Compliant with RFC 2544 Compliance with RFC 2544 is governed by ; rules of MLRsearch Specification cannot change that, but they can give recommendations to improve comparability. The following Search Goal instance is RECOMMENDED to make the corresponding Search Result unconditionally compliant with .

Goal Final Trial Duration = 60 seconds
Goal Duration Sum = 60 seconds
Goal Loss Ratio = 0%
Goal Exceed Ratio = 0%

The presence of other Search Goals does not affect the compliance of this Goal Result. In this case, the Relevant Lower Bound and the Conditional Throughput are equal to each other, and the value is the Throughput. Goal Duration Sum smaller than Goal Final Trial Duration should have no effect on the results. A non-zero Goal Exceed Ratio would needlessly prolong the Search when Short Trials of both loss types are present. The Goal Loss Ratio and Goal Exceed Ratio are enough to make the Search Goal conditionally compliant. Adding Goal Final Trial Duration makes the Search Goal unconditionally compliant. Small enough Goal Duration Sum prevents MLRsearch from repeating zero-loss Full-Length Trials. Allowing those would make it less clear whether the result is compliant with or whether it is a new, stricter methodology.

MLRsearch Compliant with TST009 One of the alternatives to is Binary Search With Loss Verification, as described in Section 12.3.3 of . The rationale of such a Search is to repeat High-Loss Trials, hoping for zero loss on the second try, so the Goal Results are closer to the noiseless end of the performance spectrum, thus more repeatable and comparable. Only the variant with "z = infinity" is achievable with MLRsearch. For example, for the "max(r) = 2" variant, the following Search Goal instance is RECOMMENDED (for comparability reasons) to get a compatible Search Result:

Goal Final Trial Duration = 60 seconds
Goal Duration Sum = 120 seconds
Goal Loss Ratio = 0%
Goal Exceed Ratio = 50%

If the first 60-second Trial has zero loss, it is enough for MLRsearch to stop measuring at that Load, as even a second High-Loss Trial would still fit within the Goal Exceed Ratio of 50%. But if the first Trial is High-Loss, MLRsearch also needs to perform the second Trial to classify that Load. The Goal Duration Sum is twice as long as the Goal Final Trial Duration, so a third Full-Length Trial is never needed.

Methodology Rationale and Design Considerations This section explains the "why" behind MLRsearch. Building on the normative specification in MLRsearch Specification, it contrasts MLRsearch with the classic single-ratio Binary Search in and walks through the key design choices: search mechanics, stopping-rule precision, Loss Inversion for multiple goals, Goal Exceed Ratio handling, Short Trial strategies, and the generalized throughput concept. Together, these considerations show how the methodology reduces test time, supports multiple Goal Loss Ratios, and improves repeatability.

Binary Search Commonalities A typical search implementation for , such as Binary Search, tracks only the two tightest bounds (in variables lower-bound and upper-bound). To start, the search needs both Max Load and Min Load values. Then, one Trial is used to confirm Max Load is an Upper Bound, and one Trial is used to confirm Min Load is a Lower Bound. Then, Trial Load is chosen as the mean of the current tightest upper bound and the current tightest lower bound and becomes a new tightest bound depending on the Trial Loss Ratio. After some number of Trials, the tightest lower bound becomes the Throughput, but does not specify when, if ever, the search should stop. In practice, the search stops either at some distance between the tightest upper bound and the tightest lower bound or after some number of Trials. For a given pair of Max Load and Min Load values, there is a one-to-one correspondence between the number of Trials and the final distance between the tightest bounds. Thus, the search always takes the same time, assuming initial bounds are confirmed.

Stopping Conditions and Precision The MLRsearch Specification requires listing both Relevant Upper Bound and Relevant Lower Bound for each Search Goal, and the difference between the bounds implies whether the precision needed for Regular Goal Result is achieved. Therefore, it is not necessary to report the specific stopping condition used. MLRsearch implementations may use Goal Width to allow direct control of Regular Goal Result precision and indirect control of the Search Duration. Other MLRsearch implementations may use different stopping conditions, for example, based on the Search Duration, trading off precision control for Search Duration control. Due to various possible time optimizations, there is no strict correspondence between the Search Duration and Goal Width values. In practice, noisy SUT performance increases both average Search Duration and its variance.

Loss Ratios and Loss Inversion The biggest difference between MLRsearch and Binary Search is in the goals of the search. has a single goal, based on classifying a single Full-Length Trial as either zero loss or non-zero loss. MLRsearch supports searching for multiple Search Goals at once, usually differing in their Goal Loss Ratios.

Single Goal and Hard Bounds Each bound in Binary Search is "hard", in the sense that all further Trial Loads are smaller than any current upper bound and larger than any current lower bound. This is also possible for MLRsearch implementations when the Search is started with only one Search Goal.

Loss Inversion The MLRsearch Specification supports multiple Search Goals, making the Search procedure more complicated compared to Binary Search with a single goal, but most of the complications do not affect the final Search Results much, except for one phenomenon: Loss Inversion. Depending on Search Goal attributes, Load Classification results may be resistant to small amounts of Inconsistent Trial Results. However, for larger amounts, a Load that is classified as an Upper Bound for one Search Goal may still be a Lower Bound for another Search Goal. Due to this other Search Goal, MLRsearch will probably perform subsequent Trials at Loads even larger than the original value. This introduces questions any multi-goal search algorithm has to address, such as: What to do when all such Trials at larger Loads happen to have zero loss? Does it mean the earlier Upper Bound was not real? Does it mean the later Low-Loss Trials do not count toward a Lower Bound? The situation where a smaller Load is classified as an Upper Bound, while a larger Load is classified as a Lower Bound (for the same Search Goal), is called Loss Inversion. Conversely, only single-goal search algorithms can have hard bounds that shield them from Loss Inversion.

Conservativeness and Relevant Bounds MLRsearch is conservative when dealing with Loss Inversion: The Upper Bound is considered real, and the Lower Bound is considered to be a fluke, at least when computing the Goal Result. This is formalized using the definitions of "Relevant Upper Bound" and "Relevant Lower Bound". The Relevant Upper Bound (for a specific Search 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 meet the stopping conditions, the Relevant Upper Bound and the Relevant Lower Bound are used in the Goal Result.

Consequences The consequence of the way the Relevant Upper Bound and Relevant Lower Bound are defined is that every Trial Result can have an impact on any current Relevant Upper Bound or Relevant Lower Bound larger than that Trial Load, namely by becoming a new Relevant Upper Bound. This also applies when that Load is measured before another Load gets enough measurements to become a current Relevant Lower Bound or Relevant Upper Bound. This also implies that if the SUT tested (or the Traffic Generator used) needs a warm-up, it should be warmed up before starting the Search; otherwise, the first few measurements could become unjustly limiting. For MLRsearch implementations, this means that it is better to measure at smaller Loads first, so any Lower Bounds found earlier are less likely to get invalidated later.

Exceed Ratio and Multiple Trials The idea of performing multiple Trials at the same Trial Load comes from a model where some Trial Results (those with a high Trial Loss Ratio) are affected by infrequent effects, causing unsatisfactory repeatability of Throughput results. Refer to "DUT in SUT" for a discussion about noiseful and noiseless ends of the SUT performance spectrum. 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. For MLRsearch to perform such Trial Result filtering, it needs a configuration option to tell how frequent the "infrequent" big Trial Loss Ratio can be. This option is called the Goal Exceed Ratio. It tells MLRsearch what ratio of Trials (more specifically, what ratio of Trial Effective Duration seconds) can have a Trial Loss Ratio larger than the Goal Loss Ratio and still be classified as a Lower Bound. A zero Goal Exceed Ratio means all Trials must have a Trial Loss Ratio equal to or lower than the Goal Loss Ratio. When more than one Trial is intended to classify a Load, MLRsearch also needs something that controls the number of Trials needed. Therefore, each Search Goal also has an attribute called Goal Duration Sum. The meaning of a Goal Duration Sum is that when a Load has Full-Length Trials whose Trial Effective Durations when summed up give a value at least as big as the Goal Duration Sum, the Load is guaranteed to be classified as either an Upper Bound or a Lower Bound for that Search Goal.

Short Trials and Duration Selection MLRsearch requires each Search Goal to specify its Goal Final Trial Duration. already anticipates possible time savings when Short Trials are used. An MLRsearch implementation MAY expose configuration parameters that decide whether, when, and how Short Trials are used. The exact heuristics and controls are left to the discretion of the implementer. While MLRsearch implementations are free to use any logic to select Trial Inputs, comparability between MLRsearch implementations is only assured when the Load Classification Logic handles any possible set of Trial Results in the same way. The presence of Short Trial Results complicates the Load Classification Logic; see more details in "Load Classification Logic". While the Load Classification algorithm is designed to avoid any unneeded Trials, for explainability reasons, it is recommended for users to use such Controller Inputs that lead to all Trial Durations selected by the Controller to be the same, e.g., by setting any Goal Initial Trial Duration to be a single value also used for all Goal Final Trial Durations.

Generalized Throughput Because 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 Search Goals with a non-zero Goal Loss Ratio, the Load usually does not match the user's intuition of what a throughput is. The Trial Forwarding Rate is better, but it is not obvious how to generalize it for Loads with multiple Trials and a non-zero Goal Loss Ratio. The clearest illustration for adopting a generalized throughput definition is the presence of a hard performance limit.

Hard Performance Limit Even if the bandwidth of a medium allows higher traffic forwarding performance, the SUT interfaces may have their own additional limitations, e.g., a specific frames-per-second limit on the Network Interface Card (NIC), a common occurrence. Those limitations should be known and provided as Max Load. But if Max Load is set larger than what the interface can receive or transmit, there will be a hard limit behavior observed in Trial Results. Consider that the hard limit is at one hundred million frames per second (100 Mfps), Max Load is larger, and the Goal Loss Ratio is 0.5%. If DUT introduces no additional losses, 0.5% Trial Loss Ratio will be achieved at the Relevant Lower Bound of 100.5025 Mfps. Reporting a throughput that exceeds the SUT's verified hard limit would be counterintuitive. Therefore, the Throughput metric should be generalized to reflect realistic, limit-aware performance. MLRsearch defines one such generalization, the "Conditional Throughput". It is the Trial Forwarding Rate from one of the Full-Length Trials performed at the Relevant Lower Bound. For the algorithm to determine exactly which Trial, see "Conditional Throughput Code". In the hard limit example, a 100.5025 Mfps Load will still have only a 100.0 Mfps Trial Forwarding Rate, nicely confirming the known limitation.

Performance Variability With a non-zero Goal Loss Ratio, and without hard performance limits, Low-Loss Trials at the same Load may achieve different Trial Forwarding Rate values simply due to DUT performance variability. By comparing the best case (all Relevant Lower Bound Trials have zero loss) and the worst case (all Trial Loss Ratios at the Relevant Lower Bound are equal to the Goal Loss Ratio), one can prove that Conditional Throughput values may have a relative difference up to the Goal Loss Ratio. Setting the Goal Width below the Goal Loss Ratio may cause the Conditional Throughput for a larger Goal Loss Ratio to become smaller than a Conditional Throughput for a Search Goal with a lower Goal Loss Ratio, which is counterintuitive, considering they come from the same Search. Therefore, it is RECOMMENDED to set the Goal Width to a value no lower than the Goal Loss Ratio of the next higher loss Search Goal. Although Conditional Throughput can fluctuate from one run to the next, it still offers a more nuanced basis for comparison than the Relevant Lower Bound, particularly when deterministic Load selection yields the same Relevant Lower Bound value across multiple runs.

MLRsearch Logic This section uses informal language to describe two aspects of MLRsearch logic: Load Classification and Conditional Throughput, reflecting formal pseudocode representation provided in "Load Classification Code" and "Conditional Throughput Code". The logic is equivalent but not identical to the pseudocode in the appendices. The pseudocode is designed to be short and frequently combines multiple operations into one expression. The logic, as described in this section, lists each operation separately and uses more intuitive names for the intermediate values. A detailed description of an example Search is in "Example Search".

Load Classification Logic For clarity of explanation, variables are tagged as (I)nput, (T)emporary, and (O)utput.

Collect Trial Results:
- Take all Trial Results (I) measured at a given Load.
Aggregate Trial Durations:
- Full-Length High-Loss sum (T) is the sum of Trial Effective Duration values of all Full-Length High-Loss Trials (I).
- Full-Length Low-Loss sum (T) is the sum of Trial Effective Duration values of all Full-Length Low-Loss Trials (I).
- Short High-Loss sum is the sum (T) of Trial Effective Duration values of all Short High-Loss Trials (I).
- Short Low-Loss sum is the sum (T) of Trial Effective Duration values of all Short Low-Loss Trials (I).
Derive goal-based ratios:
- Subceed ratio (T) is one minus the Goal Exceed Ratio (I).
- Exceed coefficient (T) is the Goal Exceed Ratio divided by the subceed ratio.
Balance Short Trial effects:
- Balancing sum (T) is the Short Low-Loss sum multiplied by the exceed coefficient.
- Excess sum (T) is the Short High-Loss sum minus the balancing sum.
- Positive excess sum (T) is the maximum of zero and the excess sum.
Compute effective duration totals:
- Effective High-Loss sum (T) is the Full-Length High-Loss sum plus the positive excess sum.
- Effective full sum (T) is the effective High-Loss sum plus the Full-Length Low-Loss sum.
- Effective whole sum (T) is the larger of the effective full sum and the Goal Duration Sum.
- Missing sum (T) is the effective whole sum minus the effective full sum.
Estimate exceed ratios:
- Pessimistic High-Loss sum (T) is the effective High-Loss sum plus the missing sum.
- Optimistic exceed ratio (T) is the effective High-Loss sum divided by the effective whole sum.
- Pessimistic exceed ratio (T) is the pessimistic High-Loss sum divided by the effective whole sum.
Classify the Load:
- The Load is classified as an Upper Bound (O) if the optimistic exceed ratio is larger than the Goal Exceed Ratio.
- The Load is classified as a Lower Bound (O) if the pessimistic exceed ratio is not larger than the Goal Exceed Ratio.
- The Load is classified as Undecided (O) otherwise.

Conditional Throughput Logic

Collect Trial Results:
- Take all Trial Results (I) measured at a given Load.
Sum of Full-Length Durations:
- Full-Length High-Loss sum (T) is the sum of Trial Effective Duration values of all Full-Length High-Loss Trials (I).
- Full-Length Low-Loss sum (T) is the sum of Trial Effective Duration values of all Full-Length Low-Loss Trials (I).
- Full-Length sum (T) is the Full-Length High-Loss sum (I) plus the Full-Length Low-Loss sum (I).
Derive initial thresholds:
- Subceed ratio (T) is one minus the Goal Exceed Ratio (I).
- Remaining sum (T) is initially the Full-Length sum multiplied by the subceed ratio.
- Current loss ratio (T) is initially 100%.
Iterate through ordered Trials:
- For each Full-Length Trial Result, sorted in increasing order by Trial Loss Ratio:
  - If the remaining sum is not larger than zero, exit the loop.
  - Set the current loss ratio to this Trial's Trial Loss Ratio (I).
  - Decrease the remaining sum by this Trial's Trial Effective Duration (I).
Compute Conditional Throughput:
- Current forwarding ratio (T) is one minus the current loss ratio.
- Conditional Throughput (T) is the current forwarding ratio multiplied by the Load value.

Conditional Throughput and Load Classification Conditional Throughput and results of Load Classification overlap but are not identical.

When a Load is marked as a Relevant Lower Bound, its Conditional Throughput is taken from a Trial whose Trial Loss Ratio is not larger than the Goal Loss Ratio.
The reverse is not guaranteed: If the Goal Width is narrower than the Goal Loss Ratio, Conditional Throughput can still end up higher than the Relevant Upper Bound.

SUT Behaviors In "DUT in SUT", the notion of noise is introduced. This section uses new terms to describe possible SUT behaviors more precisely. From a measurement point of view, noise is visible as Inconsistent Trial Results. See "Inconsistent Trial Results" for general points and "Loss Inversion" for specifics when comparing different Load values. Load Classification and Conditional Throughput apply to a single Load value, but even the set of Trial Results measured at that Trial Load value may appear inconsistent. As MLRsearch aims to save time, it executes only a small number of Trials, getting only a limited amount of information about SUT behavior. It is useful to introduce a SUT expert point of view to contrast with that limited information.

Expert Predictions Imagine that before the Search starts, a human expert had unlimited time to measure SUT and obtain all reliable information about it. The information is not perfect, as there is still random noise influencing SUT. But the expert is familiar with possible noise events, even the rare ones, and thus, the expert can do probabilistic predictions about future Trial Outputs. When several outcomes are possible, the expert can assess the probability of each outcome.

Exceed Probability When the Controller selects a new Trial Duration and Trial Load, and just before the Measurer starts performing the Trial, the SUT expert can envision possible Trial Results. With respect to a particular Search Goal, the possibilities can be summarized into a single number: Exceed Probability. It is the probability (according to the expert) that the measured Trial Loss Ratio will be higher than the Goal Loss Ratio.

Trial Duration Dependence When comparing Exceed Probability values for the same Trial Load value but different Trial Duration values, there are several patterns that commonly occur in practice.

Strong Increase Exceed Probability is very low for Short Trials but very high for Full-Length Trials. This SUT behavior is undesirable and may hint at a faulty SUT, e.g., SUT leaks resources and is unable to sustain the desired performance. But this behavior is also seen when SUT uses large amount of buffers. This is the main reason users may want to set a large Goal Final Trial Duration.

Mild Increase Short Trials are slightly less likely to become High-Loss according to the Goal Loss Ratio, but the slope is modest. This mild increase is typical when noise is dominated by rare, large loss spikes: During a Full-Length Trial, the good-performing periods cannot fully offset the heavy frame loss that occurs in the brief low-performing bursts.

Independence Short Trials have basically the same Exceed Probability as Full-Length Trials. This is possible only if loss spikes are small (so other parts can compensate) and if the Goal Loss Ratio is more than zero (otherwise, other parts cannot compensate at all).

Decrease Short Trials have a larger Exceed Probability than Full-Length Trials. This can only be possible for a non-zero Goal Loss Ratio, for example, if the SUT needs to "warm up" to the best performance within each Trial, which is not commonly seen in practice.

IANA Considerations This document has no IANA actions.

Security Considerations Benchmarking activities as described in this document are limited to the 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 an "opaque" basis, relying solely on measurements observable external to the DUT/SUT. The DUT/SUT SHOULD NOT include features that serve only to boost benchmark scores, such as a dedicated "fast-track" test mode that is never used in normal operation. Any implications for network security arising from the DUT/SUT SHOULD be identical in the lab and in production networks.

References Normative References Informative References Network Functions Virtualisation (NFV) Release 3; Testing; Specification of Networking Benchmarks and Measurement Methods for NFVI ETSI ETSI GS NFV-TST 009 V3.4.1 Ethernet service activation test methodology ITU-T FD.io CSIT Test Methodology - MLRsearch MLRsearch 1.2.1 Python Package Index Gaming with the Throughput and the Latency Benchmarking Measurement Procedures of RFC 2544 The Macroscopic Behavior of the TCP Congestion Avoidance Algorithm Pittsburgh Supercomputing Center, Teunis Ott, Bellcore Pittsburgh Supercomputing Center, Teunis Ott, Bellcore Pittsburgh Supercomputing Center, Teunis Ott, Bellcore Bellcore ACM SIGCOMM Computer Communication Review, vol. 27, no. 3, pp. 67-82 IEEE Standard for Ethernet Amendment 9: Media Access Control Parameters for 800 Gb/s and Physical Layers and Management Parameters for 400 Gb/s and 800 Gb/s Operation IEEE

Load Classification Code This appendix specifies how to perform the Load Classification. Any Load value can be classified, according to a given Search Goal. The algorithm uses (some subsets of) the set of all available Trial Results from Trials measured at a given Load at the end of the Search. The block at the end of this appendix holds pseudocode that computes two values, stored in variables named optimistic_is_lower and pessimistic_is_lower. Although presented as pseudocode, the listing is syntactically valid Python and can be executed without modification. 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. Some variable names are shortened to fit expressions in one line. Namely, variables holding sum quantities end in "_s" instead of "_sum", and variables holding effective quantities start with "effect_" instead of "effective_". The pseudocode expects the following variables to hold the following values:

goal_duration_s: The Goal Duration Sum value of the given Search Goal.
goal_exceed_ratio: The Goal Exceed Ratio value of the given Search Goal.
full_length_low_loss_s: Sum of Trial Effective Durations across Trials with the Trial Duration at least equal to the Goal Final Trial Duration and with the Trial Loss Ratio not higher than the Goal Loss Ratio (across Full-Length Low-Loss Trials).
full_length_high_loss_s: Sum of Trial Effective Durations across Trials with the Trial Duration at least equal to the Goal Final Trial Duration and with the Trial Loss Ratio higher than the Goal Loss Ratio (across Full-Length High-Loss Trials).
short_low_loss_s: Sum of Trial Effective Durations across Trials with the Trial Duration shorter than the Goal Final Trial Duration and with the Trial Loss Ratio not higher than the Goal Loss Ratio (across Short Low-Loss Trials).
short_high_loss_s: Sum of Trial Effective Durations across Trials with the Trial Duration shorter than the Goal Final Trial Duration and with the Trial Loss Ratio higher than the Goal Loss Ratio (across Short High-Loss Trials).

The code also works correctly when there are no Trial Results at the given Load.

Conditional Throughput Code This section specifies an example of how to compute Conditional Throughput. Any 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 Load at the end of the Search. The block at the end of this appendix holds pseudocode that computes a value stored as the conditional_throughput variable. Although presented as pseudocode, the listing is syntactically valid Python and can be executed without modification. Some variable names are shortened in order to fit expressions in one line. Namely, variables holding sum quantities end in "_s" instead of "_sum", and variables holding effective quantities start with "effect_" instead of "effective_". The pseudocode expects the following variables to hold the following values:

goal_duration_s: The Goal Duration Sum value of the given Search Goal.
goal_exceed_ratio: The Goal Exceed Ratio value of the given Search Goal.
full_length_low_loss_s: Sum of Trial Effective Durations across Trials with the Trial Duration at least equal to the Goal Final Trial Duration and with the Trial Loss Ratio not higher than the Goal Loss Ratio (across Full-Length Low-Loss Trials).
full_length_high_loss_s: Sum of Trial Effective Durations across Trials with the Trial Duration at least equal to the Goal Final Trial Duration and with the Trial Loss Ratio higher than the Goal Loss Ratio (across Full-Length High-Loss Trials).
full_length_trials: An iterable of all Trial Results from Trials with the Trial Duration at least equal to the Goal Final Trial Duration (all Full-Length Trials), sorted by increasing the Trial Loss Ratio. One item trial is a composite with the following two attributes available:
- trial.loss_ratio: The Trial Loss Ratio as measured for this Trial.
- trial.effect_duration: The Trial Effective Duration of this Trial.

The code works correctly only when there is at least one Trial Result measured at a given Load. 0.0: quantile_loss_ratio = trial.loss_ratio remaining -= trial.effect_duration else: break else: if remaining > 0.0: quantile_loss_ratio = 1.0 conditional_throughput = intended_load * (1.0 - quantile_loss_ratio)]]>

Example Search The following example Search is related to one hypothetical run of the Search part of the MLRsearch test procedure that has been started with multiple Search Goals. Several points in time are chosen, to show how the logic works, with specific sets of Trial Results available. The Trial Results themselves are not very realistic, as the intention is to show several corner cases of the logic. In all Trials, the Trial Effective Duration is equal to the Trial Duration. Only one Load is in focus, its value is one million frames per second (1 Mfps). Trial Results at other Loads are not mentioned, as the parts of logic present here do not depend on those. In practice, Trial Results at other Load values would be present, e.g., MLRsearch will look for a Lower Bound smaller than any Upper Bound found. At any given moment, exactly one Search Goal is designated as in focus. This designation affects only the Trial Duration chosen for new Trials; it does not alter the rest of the decision logic. An MLRsearch implementation is free to evaluate several Search Goals simultaneously, the focus mechanism is optional and appears here only to show that a Load can still be classified against Search Goals that are not currently in focus.

Example Goals The following four Search Goal instances are selected for the example Search. Each Search Goal has a readable name and dense code; the code is useful to show Search Goal attribute values. As the variable exceed coefficient does not depend on Trial Results, it is also precomputed here.

Goal 1:

name:: RFC2544
Goal Final Trial Duration:: 60s
Goal Duration Sum:: 60s
Goal Loss Ratio:: 0%
Goal Exceed Ratio:: 0%
exceed coefficient:: 0% / (100% / 0%) = 0.0
code:: 60f60d0l0e

Goal 2:

name:: TST009
Goal Final Trial Duration:: 60s
Goal Duration Sum:: 120s
Goal Loss Ratio:: 0%
Goal Exceed Ratio:: 50%
exceed coefficient:: 50% / (100% - 50%) = 1.0
code:: 60f120d0l50e

Goal 3:

name:: 1s final
Goal Final Trial Duration:: 1s
Goal Duration Sum:: 120s
Goal Loss Ratio:: 0.5%
Goal Exceed Ratio:: 50%
exceed coefficient:: 50% / (100% - 50%) = 1.0
code:: 1f120d.5l50e

Goal 4:

name:: 20% exceed
Goal Final Trial Duration:: 60s
Goal Duration Sum:: 60s
Goal Loss Ratio:: 0.5%
Goal Exceed Ratio:: 20%
exceed coefficient:: 20% / (100% - 20%) = 0.25
code:: 60f60d0.5l20e

The first two goals are important for compliance reasons; the other two cover less frequent cases.

Example Trial Results The following six sets of Trial Results are selected for the example Search. The sets are defined as points in time, describing which Trial Results were added since the previous point. Each point has a readable name and dense code; the code is useful to show Trial Output attribute values and the number of times identical Trial Results were added.

Point 1:

name:: first short good
goal in focus:: 1s final (1f120d.5l50e)
added Trial Results:: 59 Trials, each 1 second and 0% loss
code:: 59x1s0l

Point 2:

name:: first short bad
goal in focus:: 1s final (1f120d.5l50e)
added Trial Result:: one Trial, 1 second, 1% loss
code:: 59x1s0l+1x1s1l

Point 3:

name:: last short bad
goal in focus:: 1s final (1f120d.5l50e)
added Trial Results:: 59 Trials, 1 second each, 1% loss each
code:: 59x1s0l+60x1s1l

Point 4:

name:: last short good
goal in focus:: 1s final (1f120d.5l50e)
added Trial Results:: one Trial, 1 second, 0% loss
code:: 60x1s0l+60x1s1l

Point 5:

name:: first long bad
goal in focus:: TST009 (60f120d0l50e)
added Trial Results:: one Trial, 60 seconds, 0.1% loss
code:: 60x1s0l+60x1s1l+1x60s.1l

Point 6:

name:: first long good
goal in focus:: TST009 (60f120d0l50e)
added Trial Results:: one Trial, 60 seconds, 0% loss
code:: 60x1s0l+60x1s1l+1x60s.1l+1x60s0l

Comments on point in time naming:

When a name contains "short", it means the added Trial had a Trial Duration of 1 second, which is a Short Trial for 3 of the Search Goals, but it is a Full-Length Trial for the "1s final" goal.
Similarly, when a name contains "long", it means the added Trial had a Trial Duration of 60 seconds, which is a Full-Length Trial for 3 Search Goals but a Long Trial for the "1s final" goal.
When a name contains "good", it means the added Trial is a Low-Loss Trial for all the Search Goals.
When a name contains "short bad", it means the added Trial is a High-Loss Trial for all the Search Goals.
When a name contains "long bad", it means the added Trial is a High-Loss Trial for goals "RFC2544" and "TST009", but it is a Low-Loss Trial for the two other Search Goals.

Load Classification Computations This section shows how Load Classification Logic is applied by listing all temporary values at the specific time point.

Point 1 This is the "first short good" point. The code for available Trial Results is: 59x1s0l.

Goal name	RFC2544	TST009	1s final	20% exceed
Goal code	60f60d0l0e	60f120d0l50e	1f120d.5l50e	60f60d0.5l20e
Full-Length High-Loss sum	0s	0s	0s	0s
Full-Length Low-Loss sum	0s	0s	59s	0s
Short High-Loss sum	0s	0s	0s	0s
Short Low-Loss sum	59s	59s	0s	59s
Balancing sum	0s	59s	0s	14.75s
Excess sum	0s	-59s	0s	-14.75s
Positive excess sum	0s	0s	0s	0s
Effective High-Loss sum	0s	0s	0s	0s
Effective full sum	0s	0s	59s	0s
Effective whole sum	60s	120s	120s	60s
Missing sum	60s	120s	61s	60s
Pessimistic High-Loss sum	60s	120s	61s	60s
Optimistic exceed ratio	0%	0%	0%	0%
Pessimistic exceed ratio	100%	100%	50.833%	100%
Classification result	Undecided	Undecided	Undecided	Undecided

This is the last point in time where all Search Goals have this Load as Undecided.

Point 2 This is the "first short bad" point. The code for available Trial Results is: 59x1s0l+1x1s1l.

Goal name	RFC2544	TST009	1s final	20% exceed
Goal code	60f60d0l0e	60f120d0l50e	1f120d.5l50e	60f60d0.5l20e
Full-Length High-Loss sum	0s	0s	1s	0s
Full-Length Low-Loss sum	0s	0s	59s	0s
Short High-Loss sum	1s	1s	0s	1s
Short Low-Loss sum	59s	59s	0s	59s
Balancing sum	0s	59s	0s	14.75s
Excess sum	1s	-58s	0s	-13.75s
Positive excess sum	1s	0s	0s	0s
Effective High-Loss sum	1s	0s	1s	0s
Effective full sum	1s	0s	60s	0s
Effective whole sum	60s	120s	120s	60s
Missing sum	59s	120s	60s	60s
Pessimistic High-Loss sum	60s	120s	61s	60s
Optimistic exceed ratio	1.667%	0%	0.833%	0%
Pessimistic exceed ratio	100%	100%	50.833%	100%
Classification result	Upper Bound	Undecided	Undecided	Undecided

Due to zero Goal Loss Ratio, the "RFC2544" goal must have a mild or strong increase of Exceed Probability, so the one lossy Trial would be lossy even if measured at a 60-second Trial Duration. Due to zero Goal Exceed Ratio, one High-Loss Trial is enough to preclude this Load from becoming a Lower Bound for the "RFC2544" goal. That is why this Load is classified as an Upper Bound for the "RFC2544" goal this early. This is an example of how significant time can be saved, compared to 60-second Trials.

Point 3 This is the "last short bad" point. The code for available Trial Results is: 59x1s0l+60x1s1l.

Goal name	RFC2544	TST009	1s final	20% exceed
Goal code	60f60d0l0e	60f120d0l50e	1f120d.5l50e	60f60d0.5l20e
Full-Length High-Loss sum	0s	0s	60s	0s
Full-Length Low-Loss sum	0s	0s	59s	0s
Short High-Loss sum	60s	60s	0s	60s
Short Low-Loss sum	59s	59s	0s	59s
Balancing sum	0s	59s	0s	14.75s
Excess sum	60s	1s	0s	45.25s
Positive excess sum	60s	1s	0s	45.25s
Effective High-Loss sum	60s	1s	60s	45.25s
Effective full sum	60s	1s	119s	45.25s
Effective whole sum	60s	120s	120s	60s
Missing sum	0s	119s	1s	14.75s
Pessimistic High-Loss sum	60s	120s	61s	60s
Optimistic exceed ratio	100%	0.833%	50%	75.417%
Pessimistic exceed ratio	100%	100%	50.833%	100%
Classification result	Upper Bound	Undecided	Undecided	Upper Bound

This is the last point for the "1s final" goal to have this Load still Undecided. Only one 1-second Trial is missing within the 120-second Goal Duration Sum, but its Trial Result will decide the classification result. The "20% exceed" goal started to classify this Load as an Upper Bound somewhere between points 2 and 3.

Point 4 This is the "last short good" point. The code for available Trial Results is: 60x1s0l+60x1s1l.

Goal name	RFC2544	TST009	1s final	20% exceed
Goal code	60f60d0l0e	60f120d0l50e	1f120d.5l50e	60f60d0.5l20e
Full-Length High-Loss sum	0s	0s	60s	0s
Full-Length Low-Loss sum	0s	0s	60s	0s
Short High-Loss sum	60s	60s	0s	60s
Short Low-Loss sum	60s	60s	0s	60s
Balancing sum	0s	60s	0s	15s
Excess sum	60s	0s	0s	45s
Positive excess sum	60s	0s	0s	45s
Effective High-Loss sum	60s	0s	60s	45s
Effective full sum	60s	0s	120s	45s
Effective whole sum	60s	120s	120s	60s
Missing sum	0s	120s	0s	15s
Pessimistic High-Loss sum	60s	120s	60s	60s
Optimistic exceed ratio	100%	0%	50%	75%
Pessimistic exceed ratio	100%	100%	50%	100%
Classification result	Upper Bound	Undecided	Lower Bound	Upper Bound

The one missing Trial for "1s final" was Low-Loss; half of Trial Results are Low-Loss, which exactly matches the 50% Goal Exceed Ratio. This shows time savings are not guaranteed.

Point 5 This is the "first long bad" point. The code for available Trial Results is: 60x1s0l+60x1s1l+1x60s.1l.

Goal name	RFC2544	TST009	1s final	20% exceed
Goal code	60f60d0l0e	60f120d0l50e	1f120d.5l50e	60f60d0.5l20e
Full-Length High-Loss sum	60s	60s	60s	0s
Full-Length Low-Loss sum	0s	0s	120s	60s
Short High-Loss sum	60s	60s	0s	60s
Short Low-Loss sum	60s	60s	0s	60s
Balancing sum	0s	60s	0s	15s
Excess sum	60s	0s	0s	45s
Positive excess sum	60s	0s	0s	45s
Effective High-Loss sum	120s	60s	60s	45s
Effective full sum	120s	60s	180s	105s
Effective whole sum	120s	120s	180s	105s
Missing sum	0s	60s	0s	0s
Pessimistic High-Loss sum	120s	120s	60s	45s
Optimistic exceed ratio	100%	50%	33.333%	42.857%
Pessimistic exceed ratio	100%	100%	33.333%	42.857%
Classification result	Upper Bound	Undecided	Lower Bound	Lower Bound

As designed for the "TST009" goal, one Full-Length High-Loss Trial can be tolerated. 120s worth of 1-second Trials is not useful, as this is allowed when Exceed Probability does not depend on Trial Duration. As the Goal Loss Ratio is zero, it is not possible for 60-second Trials to compensate for losses seen in 1-second Trial Results. But Load Classification Logic does not have that knowledge hardcoded, so the optimistic exceed ratio is still only 50%. But the 0.1% Trial Loss Ratio is lower than the "20% exceed" Goal Loss Ratio, so this unexpected Full-Length Low-Loss Trial changed the classification result of this Load to Lower Bound.

Point 6 This is the "first long good" point. The code for available Trial Results is: 60x1s0l+60x1s1l+1x60s.1l+1x60s0l.

Goal name	RFC2544	TST009	1s final	20% exceed
Goal code	60f60d0l0e	60f120d0l50e	1f120d.5l50e	60f60d0.5l20e
Full-Length High-Loss sum	60s	60s	60s	0s
Full-Length Low-Loss sum	60s	60s	180s	120s
Short High-Loss sum	60s	60s	0s	60s
Short Low-Loss sum	60s	60s	0s	60s
Balancing sum	0s	60s	0s	15s
Excess sum	60s	0s	0s	45s
Positive excess sum	60s	0s	0s	45s
Effective High-Loss sum	120s	60s	60s	45s
Effective full sum	180s	120s	240s	165s
Effective whole sum	180s	120s	240s	165s
Missing sum	0s	0s	0s	0s
Pessimistic High-Loss sum	120s	60s	60s	45s
Optimistic exceed ratio	66.667%	50%	25%	27.273%
Pessimistic exceed ratio	66.667%	50%	25%	27.273%
Classification result	Upper Bound	Lower Bound	Lower Bound	Lower Bound

This is the Low-Loss Trial the "TST009" goal was waiting for. This Load is now classified for all Search Goals; the Search may end. Or more realistically, it can focus on larger Loads only, as the three Search Goals will want an Upper Bound (unless this Load is Max Load).

Conditional Throughput Computations At the end of this hypothetical Search, the "RFC2544" goal labels the Load as an Upper Bound, making it ineligible for Conditional Throughput computation. By contrast, the other three Search Goals treat the same Load as a Lower Bound; if it is also accepted as their Relevant Lower Bound, Conditional Throughput values can be computed for each of them. (The Load under discussion is one million frames per second.)

Goal 2 The Conditional Throughput is computed from a sorted list of Full-Length Trial Results. As the "TST009" Goal Final Trial Duration is 60 seconds, only two of 122 Trials are considered Full-Length Trials. One has a Trial Loss Ratio of 0%, the other of 0.1%.

Full-Length High-Loss sum is 60 seconds.
Full-Length Low-Loss sum is 60 seconds.
Full-Length sum is 120 seconds.
Subceed ratio is 50%.
Remaining sum is initially 0.5x12s = 60 seconds.
Current loss ratio is initially 100%.
For first Trial Result (duration 60s, loss 0%):
- Remaining sum is larger than zero, not exiting the loop.
- Set current loss ratio to this Trial's Trial Loss Ratio, which is 0%.
- Decrease the remaining sum by this Trial's Trial Effective Duration.
- New remaining sum is 60s - 60s = 0s.
For second Trial Result (duration 60s, loss 0.1%):
- Remaining sum is not larger than zero, exiting the loop.
Current loss ratio was most recently set to 0%.
Current forwarding ratio is one minus the current loss ratio, so 100%.
Conditional Throughput is the current forwarding ratio multiplied by the Load value.
Conditional Throughput is one million frames per second.

Goal 3 The "1s final" has a Goal Final Trial Duration of 1 second, so all 122 Trial Results are considered Full-Length Trials. They are ordered like this:

60 1-second 0% loss Trials,
1 60-second 0% loss Trial,
1 60-second 0.1% loss Trial, and
60 1-second 1% loss Trials.

The Conditional Throughput value does not depend on the order of 0% loss Trials.

Full-Length High-Loss sum is 60 seconds.
Full-Length Low-Loss sum is 180 seconds.
Full-Length sum is 240 seconds.
Subceed ratio is 50%.
Remaining sum is initially 0.5x240s = 120 seconds.
Current loss ratio is initially 100%.
For first 61 Trial Results (duration varies, loss 0%):
- Remaining sum is larger than zero, not exiting the loop.
- Set current loss ratio to this Trial's Trial Loss Ratio, which is 0%.
- Decrease the remaining sum by this Trial's Trial Effective Duration.
- New remaining sum varies.
After 61 Trials, duration of 60x1s + 1x60s has been subtracted from 120s, leaving 0s.
For 62nd Trial Result (duration 60s, loss 0.1%):
- Remaining sum is not larger than zero, exiting the loop.
Current loss ratio was most recently set to 0%.
Current forwarding ratio is one minus the current loss ratio, so 100%.
Conditional Throughput is the current forwarding ratio multiplied by the Load value.
Conditional Throughput is one million frames per second.

Goal 4 The Conditional Throughput is computed from a sorted list of Full-Length Trial Results. As "20% exceed" Goal Final Trial Duration is 60 seconds, only two of 122 Trials are considered Full-Length Trials. One has a Trial Loss Ratio of 0%, the other of 0.1%.

Full-Length High-Loss sum is 60 seconds.
Full-Length Low-Loss sum is 60 seconds.
Full-Length sum is 120 seconds.
Subceed ratio is 80%.
Remaining sum is initially 0.8x120s = 96 seconds.
Current loss ratio is initially 100%.
For first Trial Result (duration 60s, loss 0%):
- Remaining sum is larger than zero, not exiting the loop.
- Set current loss ratio to this Trial's Trial Loss Ratio, which is 0%.
- Decrease the remaining sum by this Trial's Trial Effective Duration.
- New remaining sum is 96s - 60s = 36s.
For second Trial Result (duration 60s, loss 0.1%):
- Remaining sum is larger than zero, not exiting the loop.
- Set current loss ratio to this Trial's Trial Loss Ratio, which is 0.1%.
- Decrease the remaining sum by this Trial's Trial Effective Duration.
- New remaining sum is 36s - 60s = -24s.
No more Trials (and remaining sum is not larger than zero), exiting loop.
Current loss ratio was most recently set to 0.1%.
Current forwarding ratio is one minus the current loss ratio, so 99.9%.
Conditional Throughput is the current forwarding ratio multiplied by the Load value.
Conditional Throughput is 999 thousand frames per second.

Due to a stricter Goal Exceed Ratio, this Conditional Throughput is smaller than Conditional Throughput of the other two Search Goals.

Acknowledgements Special wholehearted gratitude and thanks to the late for his thorough reviews filled with very specific feedback and constructive guidelines. Thank you Al for the close collaboration over the years, your mentorship, and your continuous unwavering encouragement full of empathy and an energizing positive attitude. Al, you are dearly missed. Thanks to , , , and BMWG contributors for good discussions and thorough reviews, guiding and helping us to improve the clarity and formality of this document. Many thanks to the Linux Foundation FastData I/O (FD.io) project, specifically committers and contributors to the two core projects of FD.io: VPP and CSIT. It was there where the need for MLRsearch originally came up, and it was in FD.io CSIT labs where the first MLRsearch open-source code got prototyped and then over the years productized. Thanks also goes to of the OPNFV NFVbench project for a thorough review and numerous useful comments and suggestions in the earlier draft versions of this document. We are equally indebted to for a very thorough and detailed AD review, for providing many good comments and suggestions, for helping us make this document complete. Our appreciation is also extended to , , , , , , , and for their reviews and valuable comments.