Request for Comments: 6534
Category: Standards Track
ISSN: 20701721
AT&T LabsResearch
A. Morton
AT&T Labs
J. Sommers
Colgate University
May 2012
Loss Episode Metrics for IP Performance Metrics (IPPM)
Abstract

The IETF has developed a oneway packet loss metric that measures the loss rate on a Poisson and Periodic probe streams between two hosts. However, the impact of packet loss on applications is, in general, sensitive not just to the average loss rate but also to the way in which packet losses are distributed in loss episodes (i.e., maximal sets of consecutively lost probe packets). This document defines oneway packet loss episode metrics, specifically, the frequency and average duration of loss episodes and a probing methodology under which the loss episode metrics are to be measured.
Status of This Memo

This is an Internet Standards Track document.
This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Further information on Internet Standards is available in Section 2 of RFC 5741.
Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at http://www.rfceditor.org/info/rfc6534.
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Table of Contents

1. Introduction ....................................................4 1.1. Background and Motivation ..................................4 1.1.1. Requirements Language ...............................5 1.2. Loss Episode Metrics and BiPacket Probes ..................5 1.3. Outline and Contents .......................................6 2. Singleton Definition for TypePOneway BiPacket Loss ..........7 2.1. Metric Name ................................................7 2.2. Metric Parameters ..........................................7 2.3. Metric Units ...............................................7 2.4. Metric Definition ..........................................7 2.5. Discussion .................................................8 2.6. Methodologies ..............................................8 2.7. Errors and Uncertainties ...................................8 2.8. Reporting the Metric .......................................8 3. General Definition of Samples for TypePOnewayBiPacketLoss ...................................8 3.1. Metric Name ................................................9 3.2. Metric Parameters ..........................................9 3.3. Metric Units ...............................................9 3.4. Metric Definition ..........................................9 3.5. Discussion .................................................9 3.6. Methodologies .............................................10 3.7. Errors and Uncertainties ..................................10 3.8. Reporting the Metric ......................................10 4. An Active Probing Methodology for BiPacket Loss ...............10 4.1. Metric Name ...............................................10 4.2. Metric Parameters .........................................10 4.3. Metric Units ..............................................11 4.4. Metric Definition .........................................11 4.5. Discussion ................................................11 4.6. Methodologies .............................................11 4.7. Errors and Uncertainties ..................................12 4.8. Reporting the Metric ......................................12 5. Loss Episode ProtoMetrics .....................................12 5.1. LossPairCounts ..........................................13 5.2. BiPacketLossRatio ......................................13 5.3. BiPacketLossEpisodeDurationNumber ....................13 5.4. BiPacketLossEpisodeFrequencyNumber ...................13 6. Loss Episode Metrics Derived from BiPacket Loss Probing .......14 6.1. Geometric Stream: Loss Ratio ..............................14 6.1.1. Metric Name ........................................14 6.1.2. Metric Parameters ..................................14 6.1.3. Metric Units .......................................15 6.1.4. Metric Definition ..................................15 6.1.5. Discussion .........................................15 6.1.6. Methodologies ......................................15 6.1.7. Errors and Uncertainties ...........................15 6.1.8. Reporting the Metric ...............................15 6.2. Geometric Stream: Loss Episode Duration ...................16 6.2.1. Metric Name ........................................16 6.2.2. Metric Parameters ..................................16 6.2.3. Metric Units .......................................16 6.2.4. Metric Definition ..................................16 6.2.5. Discussion .........................................16 6.2.6. Methodologies ......................................16 6.2.7. Errors and Uncertainties ...........................17 6.2.8. Reporting the Metric ...............................17 6.3. Geometric Stream: Loss Episode Frequency ..................17 6.3.1. Metric Name ........................................17 6.3.2. Metric Parameters ..................................17 6.3.3. Metric Units .......................................17 6.3.4. Metric Definition ..................................18 6.3.5. Discussion .........................................18 6.3.6. Methodologies ......................................18 6.3.7. Errors and Uncertainties ...........................18 6.3.8. Reporting the Metric ...............................18 7. Applicability of Loss Episode Metrics ..........................18 7.1. Relation to Gilbert Model .................................18 8. Security Considerations ........................................19 9. References .....................................................20 9.1. Normative References ......................................20 9.2. Informative References ....................................20
1. Introduction
1.1. Background and Motivation

Packet loss in the Internet is a complex phenomenon due to the bursty nature of traffic and congestion processes, influenced by both end users and applications and the operation of transport protocols such as TCP. For these reasons, the simplest model of packet loss  the single parameter Bernoulli (independent) loss model  does not represent the complexity of packet loss over periods of time. Correspondingly, a single loss metric  the average packet loss ratio over some period of time  arising, e.g., from a stream of Poisson probes as in [RFC2680] is not sufficient to determine the effect of packet loss on traffic in general.
Moving beyond single parameter loss models, Markovian and Markov modulated loss models involving transitions between a good and bad state, each with an associated loss rate, have been proposed by Gilbert [Gilbert] and more generally by Elliot [Elliot]. In principle, Markovian models can be formulated over state spaces involving patterns of loss of any desired number of packets. However, further increase in the size of the state space makes such models cumbersome both for parameter estimation (accuracy decreases) and prediction in practice (due to computational complexity and sensitivity to parameter inaccuracy). In general, the relevance and importance of particular models can change in time, e.g., in response to the advent of new applications and services. For this reason, we are drawn to empirical metrics that do not depend on a particular model for their interpretation.
An empirical measure of packet loss complexity, the index of dispersion of counts (IDC), comprise, for each t >0, the ratio v(t) / a(t) of the variance v(t) and average a(t) of the number of losses over successive measurement windows of a duration t. However, a full characterization of packet loss over time requires specification of the IDC for each window size t>0.
In the standards arena, loss pattern sample metrics are defined in [RFC3357]. Following the GilbertElliot model, burst metrics specific for Voice over IP (VoIP) that characterize complete episodes of lost, transmitted, and discarded packets are defined in [RFC3611].
The above considerations motivate the formulation of empirical metrics of oneway packet loss that provide the simplest generalization of [RFC2680] (which is widely adopted but only defines a single losstototal ratio metric). The metrics defined here capture deviations from independent packet loss in a robust model independent manner. The document also defines efficient measurement methodologies for these metrics.
1.1.1. Requirements Language

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 [RFC2119].
1.2. Loss Episode Metrics and BiPacket Probes

The losses experienced by the packet stream can be viewed as occurring in loss episodes, i.e., a maximal set of consecutively lost packets. This memo describes oneway loss episode metrics: their frequency and average duration. Although the average loss ratio can be expressed in terms of these quantities, they go further in characterizing the statistics of the patterns of packet loss within the stream of probes. This is useful information in understanding the effect of packet losses on application performance, since different applications can have different sensitivities to patterns of loss, being sensitive not only to the longterm average loss rate, but how losses are distributed in time. As an example, MPEG video traffic may be sensitive to loss involving the Iframe in a group of pictures, but further losses within an episode of sufficiently short duration have no further impact; the damage is already done.
The loss episode metrics presented here have the following useful properties:
 the metrics are empirical and do not depend on an underlying model; e.g., the loss process is not assumed to be Markovian. On the other hand, it turns out that the metrics of this memo can be related to the special case of the Gilbert Model parameters; see Section 7.
 the metric units can be directly compared with applications or user requirements or tolerance for network loss performance, in the frequency and duration of loss episodes, as well as the usual packet loss ratio, which can be recovered from the loss episode metrics upon dividing the average loss episode duration by the loss episode frequency.
 the metrics provide the smallest possible increment in complexity beyond, but in the spirit of, the IP Performance Metrics (IPPM) average packet loss ratio metrics [RFC2680], i.e., moving from a single metric (average packet loss ratio) to a pair of metrics (loss episode frequency and average loss episode duration).
The document also describes a probing methodology under which loss episode metrics are to be measured. The methodology comprises sending probe packets in pairs, where packets within each probe pair have a fixed separation, and the time between pairs takes the form of a geometric distributed number multiplied by the same separation. This can be regarded a generalization of Poisson probing where the probes are pairs rather than single packets as in [RFC2680], and also of geometric probing described in [RFC2330]. However, it should be distinguished from backtoback packet pairs whose change in separation on traversing a link is used to probe bandwidth. In this document, the separation between the packets in a pair is the temporal resolution at which different loss episodes are to be distinguished. The methodology does not measure episodes of loss of consecutive background packets on the measured path. One key feature of this methodology is its efficiency: it estimates the average length of loss episodes without directly measuring the complete episodes themselves. Instead, this information is encoded in the observed relative frequencies of the four possible outcomes arising from the loss or successful transmission of each of the two packets of the probe pairs. This is distinct from the approach of [RFC3611], which reports on directly measured episodes.
The metrics defined in this memo are "derived metrics", according to Section 6.1 of [RFC2330] (the IPPM framework). They are based on the singleton loss metric defined in Section 2 of [RFC2680] .
1.3. Outline and Contents

 Section 2 defines the fundamental singleton metric for the possible outcomes of a probe pair: TypePOnewayBiPacketLoss.
 Section 3 defines sample sets of this metric derived from a general probe stream: TypePOnewayBiPacketLossStream.
 Section 4 defines the prime example of the BiPacketLossStream metrics, specifically TypePOnewayBiPacketLossGeometric Stream arising from the geometric stream of packetpair probes that was described informally in Section 1.
 Section 5 defines loss episode protometrics that summarize the outcomes from a stream metrics as an intermediate step to forming the loss episode metrics; they need not be reported in general.
 Section 6 defines the final loss episode metrics that are the focus of this memo, the new metrics:
* TypePOnewayBiPacketLossGeometricStreamEpisode Duration, the average duration, in seconds, of a loss episode. * TypePOnewayBiPacketLossGeometricStreamEpisode Frequency, the average frequency, per second, at which loss episodes start. * TypePOnewayBiPacketLossGeometricStreamRatio, which is the average packet loss ratio metric arising from the geometric stream probing methodology
 Section 7 details applications and relations to existing loss models.
2. Singleton Definition for TypePOneway BiPacket Loss
2.1. Metric Name

TypePOnewayBiPacketLoss
2.2. Metric Parameters

 Src, the IP address of a source host
 Dst, the IP address of a destination host
 T1, a sending time of the first packet
 T2, a sending time of the second packet, with T2>T1
 F, a selection function defining unambiguously the two packets from the stream selected for the metric
 P, the specification of the packet type, over and above the source and destination addresses
2.3. Metric Units

A Loss Pair is pair (l1, l2) where each of l1 and l2 is a binary value 0 or 1, where 0 signifies successful transmission of a packet and 1 signifies loss.
The metric unit of TypePOnewayBiPacketLoss is a Loss Pair.
2.4. Metric Definition

 "The TypePOnewayBiPacketLoss with parameters (Src, Dst, T1, T2, F, P) is (1,1)" means that Src sent the first bit of a TypeP packet to Dst at wiretime T1 and the first bit of a TypeP packet to Dst at wiretime T2>T1 and that neither packet was received at Dst.
 "The TypePOnewayBiPacketLoss with parameters (Src, Dst, T1, T2, F, P) is (1,0)" means that Src sent the first bit of a TypeP packet to Dst at wiretime T1 and the first bit of a TypeP packet to Dst at wiretime T2>T1 and that the first packet was not received at Dst, and the second packet was received at Dst
 "The TypePOnewayBiPacketLoss with parameters (Src, Dst, T1, T2, F, P) is (0,1)" means that Src sent the first bit of a TypeP packet to Dst at wiretime T1 and the first bit of a TypeP packet to Dst at wiretime T2>T1 and that the first packet was received at Dst, and the second packet was not received at Dst
 "The TypePOnewayBiPacketLoss with parameters (Src, Dst, T1, T2, F, P) is (0,0)" means that Src sent the first bit of a TypeP packet to Dst at wiretime T1 and the first bit of a TypeP packet to Dst at wiretime T2>T1 and that both packets were received at Dst.
2.5. Discussion

The purpose of the selection function is to specify exactly which packets are to be used for measurement. The notion is taken from Section 2.5 of [RFC3393], where examples are discussed.
2.6. Methodologies

The methodologies related to the TypePOnewayPacketLoss metric in Section 2.6 of [RFC2680] are similar for the TypePOnewayBi PacketLoss metric described above. In particular, the methodologies described in RFC 2680 apply to both packets of the pair.
2.7. Errors and Uncertainties

Sources of error for the TypePOnewayPacketLoss metric in Section 2.7 of [RFC2680] apply to each packet of the pair for the TypePOne wayBiPacketLoss metric.
2.8. Reporting the Metric

Refer to Section 2.8 of [RFC2680].
3. General Definition of Samples for TypePOnewayBiPacketLoss

Given the singleton metric for TypePOnewayBiPacketLoss, we now define examples of samples of singletons. The basic idea is as follows. We first specify a set of times T1 < T2 <...<Tn, each of which acts as the first time of a packet pair for a single TypeP OnewayBiPacketLoss measurement. This results is a set of n metric values of TypePOnewayBiPacketLoss.
3.1. Metric Name

TypePOnewayBiPacketLossStream
3.2. Metric Parameters

 Src, the IP address of a source host
 Dst, the IP address of a destination host
o (T11,T12), (T21,T22)....,(Tn1,Tn2) a set of n times of sending times for packet pairs, with T11 < T12 <= T21 < T22 <=...<= Tn1 < Tn2
 F, a selection function defining unambiguously the two packets from the stream selected for the metric
 P, the specification of the packet type, over and above the source and destination address
3.3. Metric Units

A set L1,L2,...,Ln of Loss Pairs
3.4. Metric Definition

Each Loss Pair Li for i = 1,....n is the TypePOnewayBiPacket Loss with parameters (Src, Dst, Ti1, Ti2, Fi, P) where Fi is the restriction of the selection function F to the packet pair at time Ti1, Ti2.
3.5. Discussion

The metric definition of TypePOnewayBiPacketLossStream is sufficiently general to describe the case where packets are sampled from a preexisting stream. This is useful in the case in which there is a general purpose measurement stream set up between two hosts, and we wish to select a substream from it for the purposes of loss episode measurement. Packet pairs selected as bipacket loss probes need not be consecutive within such a stream. In the next section, we specialize this somewhat to more concretely describe a purpose built packet stream for loss episode measurement.
3.6. Methodologies

The methodologies related to the TypePOnewayPacketLoss metric in Section 2.6 of [RFC2680] are similar for the TypePOnewayBi PacketLossStream metric described above. In particular, the methodologies described in RFC 2680 apply to both packets of each pair.
3.7. Errors and Uncertainties

Sources of error for the TypePOnewayPacketLoss metric in Section 2.7 of [RFC2680] apply to each packet of each pair for the TypeP OnewayBiPacketLossStream metric.
3.8. Reporting the Metric

Refer to Section 2.8 of [RFC2680].
4. An Active Probing Methodology for BiPacket Loss

This section specializes the preceding section for an active probing methodology. The basic idea is a follows. We set up a sequence of evenly spaced times T1 < T2 < ... < Tn. Each time Ti is potentially the first packet time for a packet pair measurement. We make an independent random decision at each time, whether to initiate such a measurement. Hence, the interval count between successive times at which a pair is initiated follows a geometric distribution. We also specify that the spacing between successive times Ti is the same as the spacing between packets in a given pair. Thus, if pairs happen to be launched at the successive times Ti and T(i+1), the second packet of the first pair is actually used as the first packet of the second pair.
4.1. Metric Name

TypePOnewayBiPacketLossGeometricStream
4.2. Metric Parameters

 Src, the IP address of a source host
 Dst, the IP address of a destination host
 T0, the randomly selected starting time [RFC3432] for periodic launch opportunities
 d, the time spacing between potential launch times, Ti and T(i+1)
 n, a count of potential measurement instants
 q, a launch probability
 F, a selection function defining unambiguously the two packets from the stream selected for the metric
 P, the specification of the packet type, over and above the source and destination address
4.3. Metric Units

A set of Loss Pairs L1, L2, ..., Lm for some m <= n
4.4. Metric Definition

For each i = 0, 1, ..., n1 we form the potential measurement time Ti = T0 + i*d. With probability q, a packet pair measurement is launched at Ti, resulting in a TypePOnewayBiPacketLoss with parameters (Src, Dst, Ti, T(i+1), Fi, P) where Fi is the restriction of the selection function F to the packet pair at times Ti, T(i+1). L1, L2,...Lm are the resulting Loss Pairs; m can be less than n since not all times Ti have an associated measurement.
4.5. Discussion

The above definition of TypePOnewayBiPacketLossGeometric Stream is equivalent to using TypePOnewayBiPacketLossStream with an appropriate statistical definition of the selection function F.
The number m of Loss Pairs in the metric can be less than the number of potential measurement instants because not all instants may generate a probe when the launch probability q is strictly less than 1.
4.6. Methodologies

The methodologies follow from:
 the specific time T0, from which all successive Ti follow, and
 the specific time spacing, and
 the methodologies discussion given above for the singleton TypeP OnewayBiPacketLoss metric.
The issue of choosing an appropriate time spacing (e.g., one that is matched to expected characteristics of loss episodes) is outside the scope of this document.
Note that as with any active measurement methodology, consideration must be made to handle outoforder arrival of packets; see also Section 3.6. of [RFC2680].
4.7. Errors and Uncertainties

In addition to sources of errors and uncertainties related to methodologies for measuring the singleton TypePOnewayBiPacket Loss metric, a key source of error when emitting packets for Bi Packet Loss relates to resource limits on the host used to send the packets. In particular, the choice of T0, the choice of the time spacing, and the choice of the launch probability results in a schedule for sending packets. Insufficient CPU resources on the sending host may result in an inability to send packets according to schedule. Note that the choice of time spacing directly affects the ability of the host CPU to meet the required schedule (e.g., consider a 100 microsecond spacing versus a 100 millisecond spacing).
For other considerations, refer to Section 3.7 of [RFC2680].
4.8. Reporting the Metric

Refer to Section 3.8. of [RFC2680].
5. Loss Episode ProtoMetrics

This section describes four generic protometric quantities associated with an arbitrary set of Loss Pairs. These are the Loss PairCounts, BiPacketLossRatio, BiPacketLossEpisodeDuration Number, BiPacketLossEpisodeFrequencyNumber. Specific loss episode metrics can then be constructed when these protometrics take, as their input, sets of Loss Pairs samples generated by the TypePOnewayBiPacketLossStream and TypePOnewayBiPacket LossGeometricStream. The second of these is described in Section 4. It is not expected that these protometrics would be reported themselves. Rather, they are intermediate quantities in the production of the final metrics of Section 6 below, and could be rolled up into metrics in implementations. The metrics report loss episode durations and frequencies in terms of packet counts, since they do not depend on the actual time between probe packets. The final metrics of Section 6 incorporate timescales and yield durations in seconds and frequencies as per second.
5.1. LossPairCounts

LossPairCounts are the absolute frequencies of the four types of Loss Pair outcome in a sample. More precisely, the LossPairCounts associated with a set of Loss Pairs L1,,,,Ln are the numbers N(i,j) of such Loss Pairs that take each possible value (i,j) in the set ( (0,0), (0,1), (1,0), (1,1)).
5.2. BiPacketLossRatio

The BiPacketLossRatio associated with a set of n Loss Pairs L1,,,,Ln is defined in terms of their LossPairCounts by the quantity (N(1,0) + N(1,1))/n.
Note this is formally equivalent to the loss metric TypePOneway PacketLossAverage from [RFC2680], since it averages single packet losses.
5.3. BiPacketLossEpisodeDurationNumber

The BiPacketLossEpisodeDurationNumber associated with a set of n Loss Pairs L1,,,,Ln is defined in terms of their LossPairCounts in the following cases:
o (2*N(1,1) + N(0,1) + N(1,0)) / (N(0,1) + N(1,0)) if N(0,1) + N(1,0) > 0
 0 if N(0,1) + N(1,0) + N(1,1) = 0 (no probe packets lost)
 Undefined if N(0,1) + N(1,0) + N(0,0) = 0 (all probe packets lost)
Note N(0,1) + N(1,0) is zero if there are no transitions between loss and noloss outcomes.
5.4. BiPacketLossEpisodeFrequencyNumber

The BiPacketLossEpisodeFrequencyNumber associated with a set of n Loss Pairs L1,,,,Ln is defined in terms of their LossPairCounts as BiPacketLossRatio / BiPacketLossEpisodeDurationNumber, when this can be defined, specifically, it is as follows: o (N(1,0) + N(1,1)) * (N(0,1) + N(1,0)) / (2*N(1,1) + N(0,1) + N(1,0) ) / n if N(0,1) + N(1,0) > 0
 0 if N(0,1) + N(1,0) + N(1,1) = 0 (no probe packets lost)
 1 if N(0,1) + N(1,0) + N(0,0) = 0 (all probe packets lost)
6. Loss Episode Metrics Derived from BiPacket Loss Probing

Metrics for the time frequency and time duration of loss episodes are now defined as functions of the set of n Loss Pairs L1,....,Ln. Although a loss episode is defined as a maximal set of successive lost packets, the loss episode metrics are not defined directly in terms of the sequential patterns of packet loss exhibited by Loss Pairs. This is because samples, including TypePOnewayBiPacket LossGeometricStream, generally do not report all lost packets in each episode. Instead, the metrics are defined as functions of the LossPairCounts of the sample, for reasons that are now described.
Consider an idealized TypePOnewayBiPacketLossGeometricStream sample in which the launch probability q =1. It is shown in [SBDR08] that the average number of packets in a loss episode of this ideal sample is exactly the BiPacketLossEpisodeDuration derived from its set of Loss Pairs. Note this computation makes no reference to the position of lost packet in the sequence of probes.
A general TypePOnewayBiPacketLossGeometricStream sample with launch probability q < 1, independently samples, with probability q, each Loss Pair of an idealized sample. On average, the LossPair Counts (if normalized by the total number of pairs) will be the same as in the idealized sample. The loss episode metrics in the general case are thus estimators of those for the idealized case; the statistical properties of this estimation, including a derivation of the estimation variance, is provided in [SBDR08].
6.1. Geometric Stream: Loss Ratio
6.1.1. Metric Name

TypePOnewayBiPacketLossGeometricStreamRatio
6.1.2. Metric Parameters

 Src, the IP address of a source host
 Dst, the IP address of a destination host
 T0, the randomly selected starting time [RFC3432] for periodic launch opportunities
 d, the time spacing between potential launch times, Ti and T(i+1)
 n, a count of potential measurement instants
 q, a launch probability
 F, a selection function defining unambiguously the two packets from the stream selected for the metric
 P, the specification of the packet type, over and above the source and destination address
6.1.3. Metric Units

A decimal number in the interval [0,1]
6.1.4. Metric Definition

The result obtained by computing the BiPacketLossRatio over a TypePOnewayBiPacketLossGeometricStream sample with the metric parameters.
6.1.5. Discussion

TypePOnewayBiPacketLossGeometricStreamRatio estimates the fraction of packets lost from the geometric stream of BiPacket probes.
6.1.6. Methodologies

Refer to Section 4.6.
6.1.7. Errors and Uncertainties

Because TypePOnewayBiPacketLossGeometricStream is sampled in general (when the launch probability q <1), the metrics described in this section can be regarded as statistical estimators of the corresponding idealized version corresponding to q = 1. Estimation variance as it applies to TypePOnewayBiPacketLossGeometric StreamLossRatio is described in [SBDR08].
For other issues, refer to Section 4.7
6.1.8. Reporting the Metric

Refer to Section 4.8.
6.2. Geometric Stream: Loss Episode Duration
6.2.1. Metric Name

TypePOnewayBiPacketLossGeometricStreamEpisodeDuration
6.2.2. Metric Parameters

 Src, the IP address of a source host
 Dst, the IP address of a destination host
 T0, the randomly selected starting time [RFC3432] for periodic launch opportunities
 d, the time spacing between potential launch times, Ti and T(i+1)
 n, a count of potential measurement instants
 q, a launch probability
 F, a selection function defining unambiguously the two packets from the stream selected for the metric
 P, the specification of the packet type, over and above the source and destination address
6.2.3. Metric Units

A nonnegative number of seconds
6.2.4. Metric Definition

The result obtained by computing the BiPacketLossEpisodeDuration Number over a TypePOnewayBiPacketLossGeometricStream sample with the metric parameters, then multiplying the result by the launch spacing parameter d.
6.2.5. Discussion

TypePOnewayBiPacketLossGeometricStreamEpisodeDuration estimates the average duration of a loss episode, measured in seconds. The duration measured in packets is obtained by dividing the metric value by the packet launch spacing parameter d.
6.2.6. Methodologies

Refer to Section 4.6.
6.2.7. Errors and Uncertainties

Because TypePOnewayBiPacketLossGeometricStream is sampled in general (when the launch probability q <1), the metrics described in this section can be regarded as statistical estimators of the corresponding idealized version corresponding to q = 1. Estimation variance as it applies to TypePOnewayBiPacketLossGeometric StreamEpisodeDuration is described in [SBDR08].
For other issues, refer to Section 4.7
6.2.8. Reporting the Metric

Refer to Section 4.8.
6.3. Geometric Stream: Loss Episode Frequency
6.3.1. Metric Name

TypePOnewayBiPacketLossGeometricStreamEpisodeFrequency
6.3.2. Metric Parameters

 Src, the IP address of a source host
 Dst, the IP address of a destination host
 T0, the randomly selected starting time [RFC3432] for periodic launch opportunities
 d, the time spacing between potential launch times, Ti and T(i+1)
 n, a count of potential measurement instants
 q, a launch probability
 F, a selection function defining unambiguously the two packets from the stream selected for the metric
 P, the specification of the packet type, over and above the source and destination address
6.3.3. Metric Units

A positive number
6.3.4. Metric Definition

The result obtained by computing the BiPacketLossEpisode FrequencyNumber over a TypePOnewayBiPacketLossGeometric Stream sample with the metric parameters, then dividing the result by the launch spacing parameter d.
6.3.5. Discussion

TypePOnewayBiPacketLossGeometricStreamEpisodeFrequency estimates the average frequency per unit time with which loss episodes start (or finish). The frequency relative to the count of potential probe launches is obtained by multiplying the metric value by the packet launch spacing parameter d.
6.3.6. Methodologies

Refer to Section 4.6.
6.3.7. Errors and Uncertainties

Because TypePOnewayBiPacketLossGeometricStream is sampled in general (when the launch probability q <1), the metrics described in this section can be regarded as statistical estimators of the corresponding idealized version corresponding to q = 1. Estimation variance as it applies to TypePOnewayBiPacketLossGeometric StreamEpisodeFrequency is described in [SBDR08].
For other issues, refer to Section 4.7
6.3.8. Reporting the Metric

Refer to Section 4.8.
7. Applicability of Loss Episode Metrics
7.1. Relation to Gilbert Model

The general GilbertElliot model is a discrete time Markov chain over two states, Good (g) and Bad (b), each with its own independent packet loss ratio. In the simplest case, the Good loss ratio is 0, while the Bad loss ratio is 1. Correspondingly, there are two independent parameters, the Markov transition probabilities P(gb) = 1 P(bb) and P(bg) = 1 P(gg), where P(ij) is the probability to transition from state j and step n to state i at step n+1. With these parameters, the fraction of steps spent in the bad state is P(bg)/(P(bg) + P(gb)), while the average duration of a sojourn in the bad state is 1/P(gb) steps.
Now identify the steps of the Markov chain with the possible sending times of packets for a TypePOnewayBiPacketLossGeometricStream with launch spacing d. Suppose the loss episode metrics TypePOne wayBiPacketLossGeometricStreamRatio and TypePOnewayBi PacketLossGeometricStreamEpisodeDuration take the values r and m, respectively. Then, from the discussion in Section 6.1.5, the following can be equated:
r = P(bg)/(P(bg) + P(gb)) and m/d = 1/P(gb).
These relationships can be inverted in order to recover the Gilbert model parameters:
P(gb) = d/m and P(bg)=d/m/(1/r  1)
8. 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 or of applications that 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 may 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 that 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: they involve no release of user data.
9. References
9.1. Normative References

[RFC2680] Almes, G., Kalidindi, S., and M. Zekauskas, "A Oneway Packet Loss Metric for IPPM", RFC 2680, September 1999. [RFC3393] Demichelis, C. and P. Chimento, "IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)", RFC 3393, November 2002. [RFC3611] Friedman, T., Caceres, R., and A. Clark, "RTP Control Protocol Extended Reports (RTCP XR)", RFC 3611, November 2003. [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. [RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network performance measurement with periodic streams", RFC 3432, November 2002.
9.2. Informative References

[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis, "Framework for IP Performance Metrics", RFC 2330, May 1998. [RFC3357] Koodli, R. and R. Ravikanth, "Oneway Loss Pattern Sample Metrics", RFC 3357, August 2002. [SBDR08] IEEE/ACM Transactions on Networking, 16(2): 307320, "A Geometric Approach to Improving Active Packet Loss Measurement", 2008. [Gilbert] Gilbert, E.N., "Capacity of a BurstNoise Channel. Bell System Technical Journal 39 pp 12531265", 1960. [Elliot] Elliott, E.O., "Estimates of Error Rates for Codes on BurstNoise Channels. Bell System Technical Journal 42 pp 19771997", 1963.
Authors' Addresses

Nick Duffield AT&T LabsResearch 180 Park Avenue Florham Park, NJ 07932 USA Phone: +1 973 360 8726 Fax: +1 973 360 8871 EMail: duffield@research.att.com URI: http://www.research.att.com/people/Duffield_Nicholas_G Al Morton AT&T Labs 200 Laurel Avenue South Middletown,, NJ 07748 USA Phone: +1 732 420 1571 Fax: +1 732 368 1192 EMail: acmorton@att.com URI: http://home.comcast.net/~acmacm/ Joel Sommers Colgate University 304 McGregory Hall Hamilton, NY 13346 USA Phone: +1 315 228 7587 Fax: EMail: jsommers@colgate.edu URI: http://cs.colgate.edu/faculty/jsommers