A One-way Delay Metric for IPPM

1. Status of this Memo

This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited.

Copyright Notice

Copyright © The Internet Society (1999). All Rights Reserved.

2. Introduction

This memo defines a metric for one-way delay of packets across Internet paths. It builds on notions introduced and discussed in the IPPM Framework document, RFC 2330 [1]; the reader is assumed to be familiar with that document.

This memo is intended to be parallel in structure to a companion document for Packet Loss ("A One-way Packet Loss Metric for IPPM") [2].

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [6]. Although RFC 2119 was written with protocols in mind, the key words are used in this document for similar reasons. They are used to ensure the results of measurements from two different implementations are comparable, and to note instances when an implementation could perturb the network.

The structure of the memo is as follows:

   +  A 'singleton' analytic metric, called Type-P-One-way-Delay, will
   
      be introduced to measure a single observation of one-way delay.
   
   +  Using this singleton metric, a 'sample', called Type-P-One-way-
      Delay-Poisson-Stream, will be introduced to measure a sequence of
      singleton delays measured at times taken from a Poisson process.

• Using this sample, several 'statistics' of the sample will be defined and discussed.

This progression from singleton to sample to statistics, with clear separation among them, is important.

Whenever a technical term from the IPPM Framework document is first used in this memo, it will be tagged with a trailing asterisk. For example, "term*" indicates that "term" is defined in the Framework.

2.1. Motivation:

One-way delay of a Type-P* packet from a source host* to a destination host is useful for several reasons:

• Some applications do not perform well (or at all) if end-to-end delay between hosts is large relative to some threshold value.

• Erratic variation in delay makes it difficult (or impossible) to support many real-time applications.

• The larger the value of delay, the more difficult it is for transport-layer protocols to sustain high bandwidths.

• The minimum value of this metric provides an indication of the delay due only to propagation and transmission delay.

• The minimum value of this metric provides an indication of the delay that will likely be experienced when the path* traversed is lightly loaded.

• Values of this metric above the minimum provide an indication of the congestion present in the path.

The measurement of one-way delay instead of round-trip delay is motivated by the following factors:

• In today's Internet, the path from a source to a destination may be different than the path from the destination back to the source ("asymmetric paths"), such that different sequences of routers are used for the forward and reverse paths. Therefore round-trip measurements actually measure the performance of two distinct paths together. Measuring each path independently highlights the performance difference between the two paths which may traverse different Internet service providers, and even radically different types of networks (for example, research versus commodity networks, or ATM versus packet-over-SONET).

• Even when the two paths are symmetric, they may have radically different performance characteristics due to asymmetric queueing.

• Performance of an application may depend mostly on the performance in one direction. For example, a file transfer using TCP may depend more on the performance in the direction that data flows, rather than the direction in which acknowledgements travel.

   +  In quality-of-service (QoS) enabled networks, provisioning in one
      direction may be radically different than provisioning in the
      reverse direction, and thus the QoS guarantees differ.  Measuring
      the paths independently allows the verification of both
      guarantees.

It is outside the scope of this document to say precisely how delay metrics would be applied to specific problems.

2.2. General Issues Regarding Time

{Comment: the terminology below differs from that defined by ITU-T documents (e.g., G.810, "Definitions and terminology for synchronization networks" and I.356, "B-ISDN ATM layer cell transfer performance"), but is consistent with the IPPM Framework document. In general, these differences derive from the different backgrounds; the ITU-T documents historically have a telephony origin, while the authors of this document (and the Framework) have a computer systems background. Although the terms defined below have no direct equivalent in the ITU-T definitions, after our definitions we will provide a rough mapping. However, note one potential confusion: our definition of "clock" is the computer operating systems definition denoting a time-of-day clock, while the ITU-T definition of clock denotes a frequency reference.}

Whenever a time (i.e., a moment in history) is mentioned here, it is understood to be measured in seconds (and fractions) relative to UTC.

As described more fully in the Framework document, there are four distinct, but related notions of clock uncertainty:

   synchronization*

measures the extent to which two clocks agree on what time it is. For example, the clock on one host might be 5.4 msec ahead of the clock on a second host. {Comment: A rough ITU-T equivalent is "time error".}

   accuracy*

measures the extent to which a given clock agrees with UTC. For example, the clock on a host might be 27.1 msec behind UTC. {Comment: A rough ITU-T equivalent is "time error from UTC".}

   resolution*

measures the precision of a given clock. For example, the clock on an old Unix host might tick only once every 10 msec, and thus have a resolution of only 10 msec. {Comment: A very rough ITU-T equivalent is "sampling period".}

   skew*

measures the change of accuracy, or of synchronization, with time. For example, the clock on a given host might gain 1.3 msec per hour and thus be 27.1 msec behind UTC at one time and only 25.8 msec an hour later. In this case, we say that the clock of the given host has a skew of 1.3 msec per hour relative to UTC, which threatens accuracy. We might also speak of the skew of one clock relative to another clock, which threatens synchronization. {Comment: A rough ITU-T equivalent is "time drift".}

3. A Singleton Definition for One-way Delay

3.1. Metric Name:

   Type-P-One-way-Delay

3.2. Metric Parameters:

• Src, the IP address of a host

• Dst, the IP address of a host

• T, a time

3.3. Metric Units:

The value of a Type-P-One-way-Delay is either a real number, or an undefined (informally, infinite) number of seconds.

3.4. Definition:

For a real number dT, >>the *Type-P-One-way-Delay* from Src to Dst at T is dT<< means that Src sent the first bit of a Type-P packet to Dst at wire-time* T and that Dst received the last bit of that packet at wire-time T+dT.

>>The *Type-P-One-way-Delay* from Src to Dst at T is undefined (informally, infinite)<< means that Src sent the first bit of a Type-P packet to Dst at wire-time T and that Dst did not receive that packet.

Suggestions for what to report along with metric values appear in Section 3.8 after a discussion of the metric, methodologies for measuring the metric, and error analysis.

3.5. Discussion:

Type-P-One-way-Delay is a relatively simple analytic metric, and one that we believe will afford effective methods of measurement.

The following issues are likely to come up in practice:

• Real delay values will be positive. Therefore, it does not make sense to report a negative value as a real delay. However, an individual zero or negative delay value might be useful as part of a stream when trying to discover a distribution of a stream of delay values.

• Since delay values will often be as low as the 100 usec to 10 msec range, it will be important for Src and Dst to synchronize very closely. GPS systems afford one way to achieve synchronization to within several 10s of usec. Ordinary application of NTP may allow synchronization to within several msec, but this depends on the stability and symmetry of delay properties among those NTP agents used, and this delay is what we are trying to measure. A combination of some GPS-based NTP servers and a conservatively designed and deployed set of other NTP servers should yield good results, but this is yet to be tested.

• A given methodology will have to include a way to determine whether a delay value is infinite or whether it is merely very large (and the packet is yet to arrive at Dst). As noted by

Mahdavi and Paxson [4], simple upper bounds (such as the 255 seconds theoretical upper bound on the lifetimes of IP packets [5]) could be used, but good engineering, including an understanding of packet lifetimes, will be needed in practice. {Comment: Note that, for many applications of these metrics, the harm in treating a large delay as infinite might be zero or very small. A TCP data packet, for example, that arrives only after several multiples of the RTT may as well have been lost.}

• If the packet is duplicated along the path (or paths) so that multiple non-corrupt copies arrive at the destination, then the packet is counted as received, and the first copy to arrive determines the packet's one-way delay.

• If the packet is fragmented and if, for whatever reason, reassembly does not occur, then the packet will be deemed lost.

3.6. Methodologies:

   As with other Type-P-* metrics, the detailed methodology will depend
   on the Type-P (e.g., protocol number, UDP/TCP port number, size,
   precedence).

Generally, for a given Type-P, the methodology would proceed as follows:

• Arrange that Src and Dst are synchronized; that is, that they have clocks that are very closely synchronized with each other and each fairly close to the actual time.

• At the Src host, select Src and Dst IP addresses, and form a test packet of Type-P with these addresses. Any 'padding' portion of the packet needed only to make the test packet a given size should be filled with randomized bits to avoid a situation in which the measured delay is lower than it would otherwise be due to compression techniques along the path.

• At the Dst host, arrange to receive the packet.

• At the Src host, place a timestamp in the prepared Type-P packet, and send it towards Dst.

• If the packet arrives within a reasonable period of time, take a timestamp as soon as possible upon the receipt of the packet. By subtracting the two timestamps, an estimate of one-way delay can be computed. Error analysis of a given implementation of the method must take into account the closeness of synchronization between Src and Dst. If the delay between Src's timestamp and the actual sending of the packet is known, then the estimate could be adjusted by subtracting this amount; uncertainty in this value must be taken into account in error analysis. Similarly, if the delay between the actual receipt of the packet and Dst's timestamp is known, then the estimate could be adjusted by subtracting this amount; uncertainty in this value must be taken into account in error analysis. See the next section, "Errors and Uncertainties", for a more detailed discussion.

• If the packet fails to arrive within a reasonable period of time, the one-way delay is taken to be undefined (informally, infinite). Note that the threshold of 'reasonable' is a parameter of the methodology.

Issues such as the packet format, the means by which Dst knows when to expect the test packet, and the means by which Src and Dst are synchronized are outside the scope of this document. {Comment: We plan to document elsewhere our own work in describing such more detailed implementation techniques and we encourage others to as well.}

3.7. Errors and Uncertainties:

The description of any specific measurement method should include an accounting and analysis of various sources of error or uncertainty. The Framework document provides general guidance on this point, but we note here the following specifics related to delay metrics:

• Errors or uncertainties due to uncertainties in the clocks of the Src and Dst hosts.

• Errors or uncertainties due to the difference between 'wire time' and 'host time'.

In addition, the loss threshold may affect the results. Each of these are discussed in more detail below, along with a section ("Calibration") on accounting for these errors and uncertainties.

3.7.1. Errors or uncertainties related to Clocks

The uncertainty in a measurement of one-way delay is related, in part, to uncertainties in the clocks of the Src and Dst hosts. In the following, we refer to the clock used to measure when the packet was sent from Src as the source clock, we refer to the clock used to measure when the packet was received by Dst as the destination clock, we refer to the observed time when the packet was sent by the source clock as Tsource, and the observed time when the packet was received by the destination clock as Tdest. Alluding to the notions of synchronization, accuracy, resolution, and skew mentioned in the Introduction, we note the following:

• Any error in the synchronization between the source clock and the destination clock will contribute to error in the delay measurement. We say that the source clock and the destination clock have a synchronization error of Tsynch if the source clock is Tsynch ahead of the destination clock. Thus, if we know the value of Tsynch exactly, we could correct for clock synchronization by adding Tsynch to the uncorrected value of Tdest-Tsource.

• The accuracy of a clock is important only in identifying the time at which a given delay was measured. Accuracy, per se, has no importance to the accuracy of the measurement of delay. When computing delays, we are interested only in the differences between clock values, not the values themselves.

• The resolution of a clock adds to uncertainty about any time measured with it. Thus, if the source clock has a resolution of 10 msec, then this adds 10 msec of uncertainty to any time value measured with it. We will denote the resolution of the source clock and the destination clock as Rsource and Rdest, respectively.

• The skew of a clock is not so much an additional issue as it is a realization of the fact that Tsynch is itself a function of time. Thus, if we attempt to measure or to bound Tsynch, this needs to be done periodically. Over some periods of time, this function can be approximated as a linear function plus some higher order terms; in these cases, one option is to use knowledge of the linear component to correct the clock. Using this correction, the residual Tsynch is made smaller, but remains a source of uncertainty that must be accounted for. We use the function Esynch(t) to denote an upper bound on the uncertainty in synchronization. Thus, |Tsynch(t)| <= Esynch(t).

Taking these items together, we note that naive computation Tdest- Tsource will be off by Tsynch(t) +/- (Rsource + Rdest). Using the notion of Esynch(t), we note that these clock-related problems introduce a total uncertainty of Esynch(t)+ Rsource + Rdest. This estimate of total clock-related uncertainty should be included in the error/uncertainty analysis of any measurement implementation.

3.7.2. Errors or uncertainties related to Wire-time vs Host-time

   As we have defined one-way delay, we would like to measure the time
   between when the test packet leaves the network interface of Src and
   when it (completely) arrives at the network interface of Dst, and we
   refer to these as "wire times."  If the timings are themselves
   performed by software on Src and Dst, however, then this software can
   only directly measure the time between when Src grabs a timestamp
   just prior to sending the test packet and when Dst grabs a timestamp
   just after having received the test packet, and we refer to these two
   points as "host times".

To the extent that the difference between wire time and host time is accurately known, this knowledge can be used to correct for host time measurements and the corrected value more accurately estimates the desired (wire time) metric.

To the extent, however, that the difference between wire time and host time is uncertain, this uncertainty must be accounted for in an analysis of a given measurement method. We denote by Hsource an upper bound on the uncertainty in the difference between wire time and host time on the Src host, and similarly define Hdest for the Dst host. We then note that these problems introduce a total uncertainty of Hsource+Hdest. This estimate of total wire-vs-host uncertainty should be included in the error/uncertainty analysis of any measurement implementation.

3.7.3. Calibration

Generally, the measured values can be decomposed as follows:

measured value = true value + systematic error + random error

If the systematic error (the constant bias in measured values) can be determined, it can be compensated for in the reported results.

reported value = measured value - systematic error

   therefore

reported value = true value + random error

The goal of calibration is to determine the systematic and random error generated by the instruments themselves in as much detail as possible. At a minimum, a bound ("e") should be found such that the reported value is in the range (true value - e) to (true value + e) at least 95 percent of the time. We call "e" the calibration error for the measurements. It represents the degree to which the values produced by the measurement instrument are repeatable; that is, how closely an actual delay of 30 ms is reported as 30 ms. {Comment: 95 percent was chosen because (1) some confidence level is desirable to be able to remove outliers, which will be found in measuring any physical property; (2) a particular confidence level should be specified so that the results of independent implementations can be compared; and (3) even with a prototype user-level implementation, 95% was loose enough to exclude outliers.}

From the discussion in the previous two sections, the error in measurements could be bounded by determining all the individual uncertainties, and adding them together to form

Esynch(t) + Rsource + Rdest + Hsource + Hdest.

However, reasonable bounds on both the clock-related uncertainty captured by the first three terms and the host-related uncertainty captured by the last two terms should be possible by careful design techniques and calibrating the instruments using a known, isolated, network in a lab.

For example, the clock-related uncertainties are greatly reduced through the use of a GPS time source. The sum of Esynch(t) + Rsource + Rdest is small, and is also bounded for the duration of the measurement because of the global time source.

The host-related uncertainties, Hsource + Hdest, could be bounded by connecting two instruments back-to-back with a high-speed serial link or isolated LAN segment. In this case, repeated measurements are measuring the same one-way delay.

If the test packets are small, such a network connection has a minimal delay that may be approximated by zero. The measured delay therefore contains only systematic and random error in the instrumentation. The "average value" of repeated measurements is the systematic error, and the variation is the random error.

One way to compute the systematic error, and the random error to a 95% confidence is to repeat the experiment many times - at least hundreds of tests. The systematic error would then be the median. The random error could then be found by removing the systematic error from the measured values. The 95% confidence interval would be the range from the 2.5th percentile to the 97.5th percentile of these deviations from the true value. The calibration error "e" could then be taken to be the largest absolute value of these two numbers, plus the clock-related uncertainty. {Comment: as described, this bound is relatively loose since the uncertainties are added, and the absolute value of the largest deviation is used. As long as the resulting value is not a significant fraction of the measured values, it is a reasonable bound. If the resulting value is a significant fraction of the measured values, then more exact methods will be needed to compute the calibration error.}

Note that random error is a function of measurement load. For example, if many paths will be measured by one instrument, this might increase interrupts, process scheduling, and disk I/O (for example, recording the measurements), all of which may increase the random error in measured singletons. Therefore, in addition to minimal load measurements to find the systematic error, calibration measurements should be performed with the same measurement load that the instruments will see in the field.

We wish to reiterate that this statistical treatment refers to the calibration of the instrument; it is used to "calibrate the meter stick" and say how well the meter stick reflects reality.

In addition to calibrating the instruments for finite one-way delay, two checks should be made to ensure that packets reported as losses were really lost. First, the threshold for loss should be verified. In particular, ensure the "reasonable" threshold is reasonable: that it is very unlikely a packet will arrive after the threshold value, and therefore the number of packets lost over an interval is not sensitive to the error bound on measurements. Second, consider the possibility that a packet arrives at the network interface, but is lost due to congestion on that interface or to other resource exhaustion (e.g. buffers) in the instrument.

3.8. Reporting the metric:

The calibration and context in which the metric is measured MUST be carefully considered, and SHOULD always be reported along with metric results. We now present four items to consider: the Type-P of test packets, the threshold of infinite delay (if any), error calibration, and the path traversed by the test packets. This list is not exhaustive; any additional information that could be useful in interpreting applications of the metrics should also be reported.

3.8.1. Type-P

As noted in the Framework document [1], the value of the metric may depend on the type of IP packets used to make the measurement, or "type-P". The value of Type-P-One-way-Delay could change if the protocol (UDP or TCP), port number, size, or arrangement for special treatment (e.g., IP precedence or RSVP) changes. The exact Type-P used to make the measurements MUST be accurately reported.

3.8.2. Loss threshold

In addition, the threshold (or methodology to distinguish) between a large finite delay and loss MUST be reported.

3.8.3. Calibration results

• If the systematic error can be determined, it SHOULD be removed from the measured values.

• You SHOULD also report the calibration error, e, such that the true value is the reported value plus or minus e, with 95% confidence (see the last section.)

• If possible, the conditions under which a test packet with finite delay is reported as lost due to resource exhaustion on the measurement instrument SHOULD be reported.

3.8.4. Path

Finally, the path traversed by the packet SHOULD be reported, if possible. In general it is impractical to know the precise path a given packet takes through the network. The precise path may be known for certain Type-P on short or stable paths. If Type-P includes the record route (or loose-source route) option in the IP header, and the path is short enough, and all routers* on the path support record (or loose-source) route, then the path will be precisely recorded. This is impractical because the route must be short enough, many routers do not support (or are not configured for) record route, and use of this feature would often artificially worsen the performance observed by removing the packet from common-case processing. However, partial information is still valuable context. For example, if a host can choose between two links* (and hence two separate routes from Src to Dst), then the initial link used is valuable context. {Comment: For example, with Merit's NetNow setup, a Src on one NAP can reach a Dst on another NAP by either of several different backbone networks.}

4. A Definition for Samples of One-way Delay

Given the singleton metric Type-P-One-way-Delay, we now define one particular sample of such singletons. The idea of the sample is to select a particular binding of the parameters Src, Dst, and Type-P, then define a sample of values of parameter T. The means for defining the values of T is to select a beginning time T0, a final time Tf, and an average rate lambda, then define a pseudo-random

Poisson process of rate lambda, whose values fall between T0 and Tf. The time interval between successive values of T will then average 1/lambda.

{Comment: Note that Poisson sampling is only one way of defining a sample. Poisson has the advantage of limiting bias, but other methods of sampling might be appropriate for different situations. We encourage others who find such appropriate cases to use this general framework and submit their sampling method for standardization.}

4.1. Metric Name:

   Type-P-One-way-Delay-Poisson-Stream

4.2. Metric Parameters:

• Src, the IP address of a host

• Dst, the IP address of a host

• T0, a time

• Tf, a time

• lambda, a rate in reciprocal seconds

4.3. Metric Units:

A sequence of pairs; the elements of each pair are:

   +  T, a time, and

• dT, either a real number or an undefined number of seconds.

The values of T in the sequence are monotonic increasing. Note that T would be a valid parameter to Type-P-One-way-Delay, and that dT would be a valid value of Type-P-One-way-Delay.

4.4. Definition:

Given T0, Tf, and lambda, we compute a pseudo-random Poisson process beginning at or before T0, with average arrival rate lambda, and ending at or after Tf. Those time values greater than or equal to T0 and less than or equal to Tf are then selected. At each of the times in this process, we obtain the value of Type-P-One-way-Delay at this time. The value of the sample is the sequence made up of the resulting <time, delay> pairs. If there are no such pairs, the sequence is of length zero and the sample is said to be empty.

4.5. Discussion:

The reader should be familiar with the in-depth discussion of Poisson sampling in the Framework document [1], which includes methods to compute and verify the pseudo-random Poisson process.

We specifically do not constrain the value of lambda, except to note the extremes. If the rate is too large, then the measurement traffic will perturb the network, and itself cause congestion. If the rate is too small, then you might not capture interesting network behavior. {Comment: We expect to document our experiences with, and suggestions for, lambda elsewhere, culminating in a "best current practices" document.}

Since a pseudo-random number sequence is employed, the sequence of times, and hence the value of the sample, is not fully specified. Pseudo-random number generators of good quality will be needed to achieve the desired qualities.

   The sample is defined in terms of a Poisson process both to avoid the
   effects of self-synchronization and also capture a sample that is
   statistically as unbiased as possible.  {Comment: there is, of
   course, no claim that real Internet traffic arrives according to a
   Poisson arrival process.}  The Poisson process is used to schedule
   the delay measurements.  The test packets will generally not arrive
   at Dst according to a Poisson distribution, since they are influenced
   by the network.

All the singleton Type-P-One-way-Delay metrics in the sequence will have the same values of Src, Dst, and Type-P.

Note also that, given one sample that runs from T0 to Tf, and given new time values T0' and Tf' such that T0 <= T0' <= Tf' <= Tf, the subsequence of the given sample whose time values fall between T0' and Tf' are also a valid Type-P-One-way-Delay-Poisson-Stream sample.

4.6. Methodologies:

The methodologies follow directly from:

• the selection of specific times, using the specified Poisson arrival process, and

• the methodologies discussion already given for the singleton Type-P-One-way-Delay metric.

Care must, of course, be given to correctly handle out-of-order arrival of test packets; it is possible that the Src could send one test packet at TS[i], then send a second one (later) at TS[i+1], while the Dst could receive the second test packet at TR[i+1], and then receive the first one (later) at TR[i].

4.7. Errors and Uncertainties:

In addition to sources of errors and uncertainties associated with methods employed to measure the singleton values that make up the sample, care must be given to analyze the accuracy of the Poisson process with respect to the wire-times of the sending of the test packets. Problems with this process could be caused by several things, including problems with the pseudo-random number techniques used to generate the Poisson arrival process, or with jitter in the value of Hsource (mentioned above as uncertainty in the singleton delay metric). The Framework document shows how to use the Anderson-Darling test to verify the accuracy of a Poisson process over small time frames. {Comment: The goal is to ensure that test packets are sent "close enough" to a Poisson schedule, and avoid periodic behavior.}

4.8. Reporting the metric:

You MUST report the calibration and context for the underlying singletons along with the stream. (See "Reporting the metric" for Type-P-One-way-Delay.)

5. Some Statistics Definitions for One-way Delay

Given the sample metric Type-P-One-way-Delay-Poisson-Stream, we now offer several statistics of that sample. These statistics are offered mostly to be illustrative of what could be done.

5.1. Type-P-One-way-Delay-Percentile

Given a Type-P-One-way-Delay-Poisson-Stream and a percent X between 0% and 100%, the Xth percentile of all the dT values in the Stream. In computing this percentile, undefined values are treated as infinitely large. Note that this means that the percentile could thus be undefined (informally, infinite). In addition, the Type-P- One-way-Delay-Percentile is undefined if the sample is empty.

Example:

suppose we take a sample and the results are:

Stream1 = <
<T1, 100 msec>
<T2, 110 msec>
<T3, undefined>
<T4, 90 msec>
<T5, 500 msec>
>

Then the 50th percentile would be 110 msec, since 90 msec and 100 msec are smaller and 110 msec and 'undefined' are larger.

Note that if the possibility that a packet with finite delay is reported as lost is significant, then a high percentile (90th or 95th) might be reported as infinite instead of finite.

5.2. Type-P-One-way-Delay-Median

   Given a Type-P-One-way-Delay-Poisson-Stream, the median of all the dT
   values in the Stream.  In computing the median, undefined values are
   treated as infinitely large.  As with Type-P-One-way-Delay-
   Percentile, Type-P-One-way-Delay-Median is undefined if the sample is
   empty.

As noted in the Framework document, the median differs from the 50th percentile only when the sample contains an even number of values, in which case the mean of the two central values is used.

Example:

suppose we take a sample and the results are:

Stream2 = <

<T1, 100 msec>
<T2, 110 msec>
<T3, undefined>
<T4, 90 msec>
>

Then the median would be 105 msec, the mean of 100 msec and 110 msec, the two central values.

5.3. Type-P-One-way-Delay-Minimum

   Given a Type-P-One-way-Delay-Poisson-Stream, the minimum of all the
   dT values in the Stream.    In computing this, undefined values are
   treated as infinitely large.  Note that this means that the minimum
   could thus be undefined (informally, infinite) if all the dT values
   are undefined.  In addition, the Type-P-One-way-Delay-Minimum is

undefined if the sample is empty.

In the above example, the minimum would be 90 msec.

5.4. Type-P-One-way-Delay-Inverse-Percentile

Given a Type-P-One-way-Delay-Poisson-Stream and a time duration threshold, the fraction of all the dT values in the Stream less than or equal to the threshold. The result could be as low as 0% (if all the dT values exceed threshold) or as high as 100%. Type-P-One-way- Delay-Inverse-Percentile is undefined if the sample is empty.

In the above example, the Inverse-Percentile of 103 msec would be 50%.

6. Security Considerations

Conducting Internet measurements raises both security and privacy concerns. This memo does not specify an implementation of the metrics, so it does not directly affect the security of the Internet nor of applications which run on the Internet. However, implementations of these metrics must be mindful of security and privacy concerns.

There are two types of security concerns: potential harm caused by the measurements, and potential harm to the measurements. The measurements could cause harm because they are active, and inject packets into the network. The measurement parameters MUST be carefully selected so that the measurements inject trivial amounts of additional traffic into the networks they measure. If they inject "too much" traffic, they can skew the results of the measurement, and in extreme cases cause congestion and denial of service.

The measurements themselves could be harmed by routers giving measurement traffic a different priority than "normal" traffic, or by an attacker injecting artificial measurement traffic. If routers can recognize measurement traffic and treat it separately, the measurements will not reflect actual user traffic. If an attacker injects artificial traffic that is accepted as legitimate, the loss rate will be artificially lowered. Therefore, the measurement methodologies SHOULD include appropriate techniques to reduce the probability measurement traffic can be distinguished from "normal" traffic. Authentication techniques, such as digital signatures, may be used where appropriate to guard against injected traffic attacks.

The privacy concerns of network measurement are limited by the active measurements described in this memo. Unlike passive measurements, there can be no release of existing user data.

7. Acknowledgements

Special thanks are due to Vern Paxson of Lawrence Berkeley Labs for his helpful comments on issues of clock uncertainty and statistics. Thanks also to Garry Couch, Will Leland, Andy Scherrer, Sean Shapira, and Roland Wittig for several useful suggestions.

8. References

   [1]  Paxson, V., Almes, G., Mahdavi, J. and M. Mathis, "Framework for
        IP Performance Metrics", RFC 2330, May 1998.
   
   [2]  Almes, G., Kalidindi, S. and M. Zekauskas, "A One-way Packet
        Loss Metric for IPPM", RFC 2680, September 1999.
   
   [3]  Mills, D., "Network Time Protocol (v3)", RFC 1305, April 1992.
   
   [4]  Mahdavi J. and V. Paxson, "IPPM Metrics for Measuring
        Connectivity", RFC 2678, September 1999.
   
   [5]  Postel, J., "Internet Protocol", STD 5, RFC 791, September 1981.
   
   [6]  Bradner, S., "Key words for use in RFCs to Indicate Requirement
        Levels", BCP 14, RFC 2119, March 1997.
   
   [7]  Bradner, S., "The Internet Standards Process -- Revision 3", BCP
        9, RFC 2026, October 1996.

9. Authors' Addresses

   Guy Almes
   Advanced Network & Services, Inc.
   200 Business Park Drive
   Armonk, NY  10504
   USA
   
   Phone: +1 914 765 1120
   EMail: almes@advanced.org
   
   Sunil Kalidindi
   Advanced Network & Services, Inc.
   200 Business Park Drive
   Armonk, NY  10504
   USA
   
   Phone: +1 914 765 1128
   EMail: kalidindi@advanced.org

Matthew J. Zekauskas
Advanced Network & Services, Inc.
200 Business Park Drive
Armonk, NY 10504
USA

   Phone: +1 914 765 1112
   EMail: matt@advanced.org

10. Full Copyright Statement

Copyright © The Internet Society (1999). All Rights Reserved.

This document and translations of it may be copied and furnished to others, and derivative works that comment on or otherwise explain it or assist in its implementation may be prepared, copied, published and distributed, in whole or in part, without restriction of any kind, provided that the above copyright notice and this paragraph are included on all such copies and derivative works. However, this document itself may not be modified in any way, such as by removing the copyright notice or references to the Internet Society or other Internet organizations, except as needed for the purpose of developing Internet standards in which case the procedures for copyrights defined in the Internet Standards process must be followed, or as required to translate it into languages other than English.

The limited permissions granted above are perpetual and will not be revoked by the Internet Society or its successors or assigns.

This document and the information contained herein is provided on an "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.

Acknowledgement

Funding for the RFC Editor function is currently provided by the Internet Society.