Network Working Group G. Almes, Advanced Network & Services
Internet Draft W. Cerveny, Advanced Network & Services
P. Krishnaswamy, BellCore
J. Mahdavi, Pittsburgh Supercomputer Center
M. Mathis, Pittsburgh Supercomputer Center
V. Paxson, Lawrence Berkeley Labs
Expiration Date: May 1997 November 1996
Framework for IP Provider Metrics
1. Status of this Memo
This document is an Internet Draft. Internet Drafts are working doc-
uments of the Internet Engineering Task Force (IETF), its areas, and
its working groups. Note that other groups may also distribute work-
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Internet Drafts are draft documents valid for a maximum of six
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ftp.isi.edu (US West Coast).
This memo provides information for the Internet community. This memo
does not specify an Internet standard of any kind. Distribution of
this memo is unlimited.
2. Introduction
The purpose of this memo is to define a general framework for partic-
ular metrics to be developed by the IP Provider Metrics (IPPM) effort
within the Benchmarking Methodology Working Group (BMWG) of the Oper-
ational Requirements Area (OR) of the IETF.
We begin by laying out several criteria for the metrics that we
adopt. These criteria are designed to promote an IPPM effort that
will maximize an accurate common understanding by Internet users and
Internet providers of the performance and reliability both of end-to-
end paths through the Internet and of specific 'IP clouds' that
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comprise portions of those paths.
We next define some Internet vocabulary that will allow us to speak
clearly about Internet components such as routers, paths, and clouds.
We next define three fundamental concepts, metrics, measurement
methodology, and uncertainties/errors, that will allow us to speak
clearly about specific metrics. Given these concepts, we proceed to
discuss how they relate to the analytical framework shared by many
aspects of the Internet engineering discipline. We then introduce
the notion of empirically defined metrics, and continue to discuss
two forms of composition.
Based on experience in applying the (original Jul-96) framework to
specific metrics for delay, we have introduced (in the Nov-96 revi-
sion) some additional material on measurement technology. This con-
sists of guidelines related to clock issues, the notion of 'wire
time' as distinct from 'host time', and some ideas for sampling of
singleton metrics.
In some sections of the memo, we will surround some commentary text
with the brackets {Comment: ... }. We stress that this commentary is
only commentary, and is not itself part of the framework document or
a proposal of particular metrics. In some cases this commentary will
discuss some of the properties of metrics that might be envisioned,
but the reader should assume that any such discussion is intended
only to shed light on points made in the framework document, and not
to suggest any specific metrics.
3. Criteria for IP Provider Metrics
The overarching goal of the IP Provider Metrics effort is to achieve
a situation in which users and providers of Internet transport ser-
vice have an accurate common understanding of the performance and
reliability of the Internet component 'clouds' that they use/provide.
To achieve this, performance and reliability metrics for paths
through the Internet must be developed. In several meetings of the
BMWG criteria for these metrics have been specified:
+ The metrics must be concrete and well-defined,
+ A methodology for a metric should have the property that it is
repeatable: if the methodology is used multiple times under iden-
tical conditions, the same measurements should result in the same
measurements.
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+ The metrics must exhibit no bias for IP clouds implemented with
identical technology,
+ The metrics must exhibit understood and fair bias for IP clouds
implemented with non-identical technology,
+ The metrics must be useful to users and providers in understanding
the performance they experience or provide,
+ The metrics must avoid inducing artificial performance goals.
4. Terminology for Paths and Clouds
The following list defines terms that need to be precise in the
development of path metrics. We proceed from low-level notions of
host, router, and link, then proceed to define the notions of path
and notions of IP cloud and exchange that allow us to segment a path
into relevant pieces.
host A computer capable of communicating using the Internet protocols;
includes "routers".
link A single link-level connection between two (or more) hosts;
includes leased lines, ethernets, frame relay clouds, etc.
router
A host which facilitates network-level communication between hosts
by forwarding IP packets.
path A sequence of the form < h0, l1, h1, ..., ln, hn >, where n >= 0,
each hi is a host, each li is a link between hi-1 and hi, each
h1...hn-1 is a router. In an appropriate operational configura-
tion, the links and routers in the path facilitate network-layer
communication of packets from h0 to hn. Note that path is a unidi-
rectional concept.
subpath
Given a path, a subpath is any subsequence of the given path which
is itself a path. (Thus, the first and last element of a subpath
is a host.)
cloud
An undirected (possibly cyclic) graph whose vertices are routers
and whose edges are links that connect pairs of routers. Formally,
ethernets, frame relay clouds, and other links that connect more
than two routers are modelled as fully-connected meshes of graph
edges. Note that to connect to a cloud means to connect to a
router of the cloud over a link; this link is not itself part of
the cloud.
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exchange
A special case of a link, an exchange directly connects either a
host to a cloud and/or one cloud to another cloud.
cloud subpath
A subpath of a given path, all of whose hosts are routers of a
given cloud.
path digest
A sequence of the form < h0, e1, C1, ..., en, hn >, where n >= 0,
h0 and hn are hosts, each e1 ... en is an exchange, and each C1 ...
Cn-1 is a cloud subpath.
5. Three Fundamental Concepts
5.1. Metrics
In the operational Internet, there are several quantities related to
the performance and reliability of the Internet that we'd like to
know the value of. When such a quantity is carefully specified, we
term the quantity a metric. We anticipate that there will be sepa-
rate RFCs for each metric (or for each closely related group of met-
rics).
In some cases, there might be no obvious means to effectively measure
the metric; this is allowed, and even understood to be very useful in
some cases. It is required, however, that the specification of the
metric be as clear as possible about what quantity is being speci-
fied. Thus, difficulty in practical measurement is sometimes
allowed, but ambiguity in meaning is not.
Each metric will be defined in terms of standard units of measure-
ment. The international metric system will be used, with the follow-
ing points specifically noted:
+ When a unit is expressed in simple meters (for distance/length) or
seconds (for duration), appropriate related units based on thou-
sands or thousandths of acceptable units are acceptable. Thus,
distances expressed in kilometers (Km), durations expressed in
milliseconds (msec), or microseconds (usec) are allowed, but not
centimeters (because the prefix is not in terms of thousands or
thousandths).
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+ When a unit is expressed in a combination of units, appropriate
related units based on thousands or thousandths of acceptable
units are acceptable, but all such thousands/thousandths must be
grouped at the beginning. Thus, kilo-meters per second (Km/sec)
is allowed, but meters per millisecond is not.
+ The unit of information is the bit.
+ When metric prefixes are used with bits or with combinations
including bits, those prefixes will have their metric meaning
(related to decimal 1000), and not the meaning conventional with
computer storage (related to decimal 1024). In any RFC that
defines a metric whose units include bits, this convention will be
followed and will be repeated to ensure clarity for the reader.
+ When a time is given, it will be taken in UTC.
Note that these points apply to the specifications for metrics and
not, for example, to packet formats where octets will likely be used
in preference/addition to bits.
Finally, we note that some metrics may be defined purely in terms of
other metrics; such metrics are call 'derived metrics'.
5.2. Measurement Methodology
For a given set of well-defined metrics, a number of distinct mea-
surement methodologies may exist. A partial list includes:
+ Direct measurement of a performance metric using injected test
traffic. Example: measurement of the round-trip delay of an IP
packet of a given size over a given route at a given time.
+ Projection of a metric from lower-level measurements. Example:
given accurate measurements of propagation delay and bandwidth for
each step along a path, projection of the complete delay for the
path for an IP packet of a given size.
+ Estimation of a consituent metric from a set of more aggregated
measurements. Example: given accurate measurements of delay for a
given one-hop path for IP packets of different sizes, estimation
of propagation delay for the link of that one-hop path.
+ Estimation of a given metric at one time from a set of related
metrics at other times. Example: given an accurate measurement of
flow capacity at a past time, together with a set of accurate
delay measurements for that past time and the current time, and
given a model of flow dynamics, estimate the flow capacity that
would be observed at the current time.
This list is by no means exhaustive. The purpose is to point out the
variety of measurement techniques.
When a given metric is specified, a given measurement approach might
be noted and discussed. That approach, however, is not formally part
of the specification.
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A methodology for a metric should have the property that it is
repeatable: if the methodology is used multiple times under identical
conditions, it should result in consistent measurements.
Backing off a little from the word 'identical' in the previous para-
graph, we could more accurately use the word 'continuity' to describe
a property of a given methodology: a methodology for a given metric
exhibits continuity if, for small variations in conditions, it
results in small variations in the resulting measurements. Slightly
more precisely, for every positive epsilon, there exists a positive
delta, such that if two sets of conditions are within delta of each
other, then the resulting measurements will be within epsilon of each
other. At this point, this should be taken as a heuristic driving
our intuition about one kind of robustness property rather than as a
precise notion.
A metric that has at least one methodology that exhibits continuity
is said itself to exhibit continuity.
Note that some metrics, such as hop-count along a path, are integer-
valued and therefore cannot exhibit continuity in quite the sense
given above.
Note further that, in practice, it may not be practical to know (or
be able to quantify) the conditions relevant to a measurement at a
given time. For example, since the instantaneous load (in packets to
be served) at a given router in a high-speed wide-area network can
vary widely over relatively brief periods and will be very hard for
an external observer to quantify, various statistics of a given met-
ric may be more repeatable, or may better exhibit continuity. In
that case those particular statistics should be specified when the
metric is specified.
Finally, some measurement methodologies may be 'conservative' in the
sense that a measurement that may themselves modify the value of the
performance metric they attempt to measure. {Comment: for example,
in a wide-are high-speed network under modest load, a test using sev-
eral small 'ping' packets to measure delay would likely not interfere
(much) with the delay properties of that network as observed by oth-
ers. The corresponding statement about tests using a large flow to
measure flow capacity would likely fail.}
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5.3. Measurements, Uncertainties, and Errors
Even the very best measurement methodologies for the very most well
behaved metrics will exhibit errors. Those who develop such measure-
ment methodologies, however, should strive to:
+ minimize their uncertainties/errors,
+ understand and document the sources of uncertainty/error, and
+ quantify the amounts of uncertainty/error.
by doing so, the measurement community will work together to improve
our ability to understand the performance and reliability of the
Internet.
For example, when developing a method for measuring delay, understand
how any errors in your clocks introduce errors into your delay mea-
surement, and quantify this effect as well as you can. In some
cases, this will result in a requirement that a clock be at least up
to a certain quality if it is to be used to make a certain measure-
ment.
As a second example, consider the timing error due to measurement
overheads within the computer making the measurement, as opposed to
delays due to the Internet component being measured. The former is a
measurement error, while the latter reflects the metric of interest.
Note that one technique that can help avoid this overhead is the use
of a packet filter/sniffer, running on a separate computer that
records network packets and timestamps them accurately. The result-
ing trace can then be analysed to assess the test traffic, minimising
the effect of measurement host delays, or at least allowing those
delays to be accounted for.
Finally, we note that derived metrics (defined above) or metrics that
exhibit spatial or temporal composition (defined below) offer occa-
sion for the analysis of measurement uncertainty of related measure-
ments to be themselves related.
6. Metrics and the Analytical Framework
As the Internet has evolved from the early packet-switching studies
of the 1960s, the Internet engineering community has evolved a common
analytical framework of concepts. This analytical framework, or A-
frame, used by designers and implementers of protocols, by those
involved in measurement, and by those who study computer network per-
formance using the tools of simulation and analysis, has great advan-
tage to our work. A major objective here is to generate network
characterizations that are consistent in both analytical and practi-
cal settings, since this will maximize the chances that non-empirical
network study can be better correlated with, and used to further our
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understanding of, real network behavior.
Whenever possible, therefore, we would like to develop and leverage
the A-frame. Thus, whenever a metric to be specified is understood
to be closely related to concepts (such as the Internet components
defined above) within the A-frame, we will attempt to specify the
metric in the A-frame's terms. In such a specification we will
develop the A-frame by precisely defining the concepts needed for the
metric, then leverage the A-frame by defining the metric in terms of
those concepts.
Such a metric will be called an 'analytically specified metric' or,
more simply an analytical metric.
{Comment: Examples of such analytical metrics might include:
propagation time of a link
The time, in seconds, required by a single bit to travel from the
output port on one Internet host across a single link to another
Internet host.
bandwidth of a link for packets of size k
The capacity, in bits/second, where only those bits of the IP
packet are counted, for a packet of size k bytes.
route
The path, as defined in Section 4, from A to B at a given time.
hop count of a route
The value 'n' of the route path.
}
Note that we make no a priori list of just what A-frame concepts
will emerge in these specifications, but we do encourage their use
and urge that they be carefully specified so that, as our set of
metrics develops, so will a specified set of A-frame concepts tech-
nically consistent with each other and consonent with the common
understanding of those concepts within the general Internet commu-
nity.
These A-frame concepts will be intended to abstract from actual
Internet components in such a way that:
+ the essential function of the component is retained,
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+ properties of the component relevant to the metrics we aim to cre-
ate are retained,
+ a subset of these component properties are defined as analytical
metrics, and
+ those properties of actual Internet components not relevant to
defining the metrics we aim to create are dropped.
{Comment: for example, when considering a router in the context of
packet forwarding, we might model the router as a component that
receives packets on an input link, queues them on a FIFO packet queue
of finite size, employs tail-drop when the packet queue is full, and
forwards them on an output link. The transmission speed (in
bits/second) of the input and output links, the latency in the router
(in seconds), and the maximum size of the packet queue (in bits) are
relevant analytical metrics.}
In some cases, such analytical metrics used in relation to a router
will be very closely related to specific metrics of the performance
of Internet paths. For example, an obvious formula (L + P/B) involv-
ing the latency in the router (L), the packet size (in bits) (P), and
the transmission speed of the output link (B) might closely approxi-
mate the increase in packet delay due to the insertion of a given
router along a path.
We stress, however, that well-chosen and well-specified A-frame con-
cepts and their analytical metrics will support more general metric
creation efforts in less obvious ways.
{Comment: for example, when considering the flow capacity of a path,
it may be of real value to be able to model each of the routers along
the path as packet forwarders as above. Techniques for estimating
the flow capacity of a path might use the maximum packet queue size
as a parameter in decidedly non-obvious ways. For example, as the
maximum queue size increases, so will the ability of the router to
continuously move traffic along an output link despite fluctuations
in traffic from an input link. Estimating this increase, however,
remains a research topic.}
The key role of these concepts is to abstract the properties of the
Internet components relevant to given metrics. Judgement is required
to avoid making assumptions that bias the modeling and metric effort
toward one kind of design.
{Comment: for example, routers might not use tail-drop, even though
tail-drop might be easier to model analytically.}
Note that, when we specify A-frame concepts and analytical metrics,
we will inevitably make simplifying assumptions. Further, as noted
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above, judgement is required in making these assumptions in order to
make them best suit our purposes.
Finally, note that different elements of the A-frame might well make
different simplifying assumptions. For example, the abstraction of a
router used to further the definition of delay might treat the
router's packet queue as a single FIFO queue, but the abstraction of
a router used to further the definition of the handling of an RSVP-
enabled packet might treat the router's packet queue to support
bounded delay -- a contradictory assumption. This is not to say that
we make contradictory assumptions at the same time, but that two dif-
ferent parts of our work might refine the simpler base concept in two
divergent ways for different purposes.
7. Empirically Specified Metrics
There are useful performance and reliability metrics that do not fit
so neatly into the A-frame, usually because the A-frame lacks the
complexity or power for dealing with them. For example, "the best
flow capacity achievable along a path using an RFC-1122-compliant
TCP" would be good to be able to measure, but we have no analytical
framework of sufficient complexity to allow us to cast that flow
capacity as an analytical metric.
These notions can still be well specified by instead describing a
reference methodology for measuring them.
Such a metric will be called an 'empirically specified metric', or
more simply, an empirical metric.
Such empirical metrics should have three properties:
+ we should have a clear definition for each in terms of real-world
Internet components,
+ we should have at least one effective means to measure them, and
+ to the extent possible, we should have an (necessarily incomplete)
understanding of the metric in terms of the A-frame so that we can
use our measurements to reason about the performance and reliabil-
ity of A-frame components and of aggregations of A-frame compo-
nents.
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8. Two Forms of Composition
8.1. Spatial Composition of Metrics
In some cases, it may be realistic and useful to define metrics in
such a fashion that they exhibit spatial composition.
By spatial composition, we mean a characteristic of some path met-
rics, in which the metric as applied to a (complete) path can also be
defined for various subpaths (cf. definition above), and in which the
appropriate A-frame concepts for the metric suggest useful relation-
ships between the metric applied to these various subpaths (including
the complete path, the various cloud subpaths of a given path digest,
and even single routers along the path). The effectiveness of spa-
tial composition depends:
+ on the usefulness in analysis of these relationships as applied to
the relevant A-frame components, and
+ on the practical use of the corresponding relationships as applied
to metrics and to measurement methodologies.
{Comment: for example, consider some metric for delay of a 100-byte
packet across a path P, and consider further a path digest of P. The definition of such a metric might include
a conjecture that the delay across P is very nearly the sum of the
corresponding metric across the exhanges (ei) and clouds (Ci) of the
given path digest. The definition would further include a note on
how a corresponding relation applies to relevant A-frame components,
both for the path P and for the exchanges and clouds of the path
digest.}
When the definition of a metric includes a conjecture that the metric
across the path is related to the metric across the subpaths of the
path, that conjecture constitutes a claim that the metric exhibits
spatial composition. The definition should then include:
+ the specific conjecture applied to the metric,
+ a justification of the practical utility of the composition in
terms of making accurate measurements of the metric on the path,
and
+ a justification of the usefulness of the composition in terms of
making analysis of the path using A-frame concepts more effective.
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8.2. Temporal Composition of Formal Models and Empirical Metrics
In some cases, it may be realistic and useful to define metrics in
such a fashion that they exhibit temporal composition.
By temporal composition, we mean a characteristic of some path met-
rics, in which the metric as applied to a path at a given time T is
also defined for various times t0 < t1 < ... < tn < T, and in which
the appropriate A-frame concepts for the metric suggests useful rela-
tionships between the metric applied at times t0, ..., tn and the
metric applied at time T. The effectiveness of temporal composition
depends:
+ on the usefulness in analysis of these relationships as applied to
the relevant A-frame components, and
+ on the practical use of the corresponding relationships as applied
to metrics and to measurement methodologies.
{Comment: for example, consider some metric for the expected flow
capacity across a path P during the five-minute period surrounding
the time T, and suppose further that we have the corresponding values
for each of the four previous five-minute periods t0, t1, t2, and t3.
The definition of such a metric might include a conjecture that the
flow capacity at time T can be estimated from a certain kind of
extrapolation from the values of t0, ..., t3. The definition would
further include a note on how a corresponding relation applies to
relevant A-frame components.
Note: any (spatial or temporal) compositions involving flow capacity
are likely to be subtle, and temporal compositions are generally more
subtle than spatial compositions, so the reader should understand
that the foregoing example is intentionally naive.}
When the definition of a metric includes a conjecture that the metric
across the path at a given time T is related to the metric across the
path for a set of other times, that conjecture constitutes a claim
that the metric exhibits temporal composition. The definition should
then include:
+ the specific conjecture applied to the metric,
+ a justification of the practical utility of the composition in
terms of making accurate measurements of the metric on the path,
and
+ a justification of the usefulness of the composition in terms of
making analysis of the path using A-frame concepts more effective.
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9. Two Sets of Issues related to Time
9.1. Clock Issues
Measurements of time lie at the heart of many Internet metrics.
Because of this, it will often be crucial when designing a methodol-
ogy for measuring a metric to understand the different types of
errors and uncertainties introduced by imperfect clocks. In this
section we define terminology for discussing the characteristics of
clocks and touch upon related measurement issues which need to be
addressed by any sound methodology.
The Network Time Protocol (NTP; RFC 1305) defines a nomenclature for
discussing clock characteristics, which we will also use when appro-
priate [Mi92]. The main goal of NTP is to provide accurate timekeep-
ing over fairly long time scales, such as minutes to days, while for
measurement purposes often what is more important is short-term accu-
racy, between the beginning of the measurement and the end, or over
the course of gathering a body of measurements (a sample). This dif-
ference in goals sometimes leads to different definitions of termi-
nology as well, as discussed below.
To begin, we define a clock's "offset" at a particular moment as the
difference between the time reported by the clock and the "true" time
as defined by international standards. If the clock reports a time
Tc and the true time is Tt, then the clock's offset is Tc - Tt.
We will refer to a clock as "accurate" at a particular moment if the
clock's offset is zero, and more generally a clock's "accuracy" is
how close the absolute value of the offset is to zero. For NTP,
accuracy also includes a notion of the frequency of the clock; for
our purposes, we split out this notion into that of "skew", because
we define accuracy in terms of a single moment in time rather than
over an interval of time.
A clock's "skew" at a particular moment is the frequency difference
(first derivative of its offset with respect to true time) between
the clock and true time.
As noted in RFC 1305, real clocks exhibit some variation in skew.
That is, the second derivative of the clock's offset with respect to
true time is generally non-zero. In keeping with RFC 1305, we define
this quantity as the clock's "drift".
A clock's "resolution" is the smallest unit by which the clock's time
is updated. It gives a lower bound on the clock's uncertainty.
(Note that clocks can have very fine resolutions and yet be wildly
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inaccurate.) Resolution is defined in terms of seconds. However,
resolution is relative to the clock's reported time and not to true
time, so for example a resolution of 10 msec only means that the
clock updates its notion of time in 0.01 second increments, not that
this is the true amount of time between updates.
{Comment: Systems differ on how an application interface to the clock
reports the time on subsequent calls during which the clock has not
advanced. Some systems simply return the same unchanged time as
given for previous calls. Others may add a small increment to the
reported time to maintain monotonic increasing timestamps. For sys-
tems that do the latter, we do *not* consider these small increments
when defining the clock's resolution. They are instead an impediment
to assessing the clock's resolution, since a natural method for doing
so is to repeatedly query the clock to determine the smallest non-
zero difference in reported times.}
It is expected that a clock's resolution changes only rarely (for
example, due to a hardware upgrade).
There are a number of interesting metrics for which some natural mea-
surement methodologies involve comparing times reported by two dif-
ferent clocks. An example is one-way packet delay (currently an
Internet Draft [Al96]). Here, the time required for a packet to
travel through the network is measured by comparing the time reported
by a clock at one end of the the packet's path, corresponding to when
the packet first entered the network, with the time reported by a
clock at the other end of the path, corresponding to when the packet
finished traversing the network.
We are thus also interested in terminology for describing how two
clocks C1 and C2 compare. To do so, we introduce terms related to
those above in which the notion of "true time" is replaced by the
time as reported by clock C1. For example, clock C2's offset rela-
tive to C1 at a particular moment is Tc2 - Tc1, the instantaneous
difference in time reported by C2 and C1. To disambiguate between
the use of the terms to compare two clocks versus the use of the
terms to compare to true time, we will in the former case use the
phrases "relative". So the offset defined earlier in this paragraph
is the "relative offset" between C2 and C1. {Comment: Note that the
notion of "resolution" does not have an analog when comparing
clocks.}
If two clocks are "accurate" with respect to one another (their rela-
tive offset is zero), we will refer to the pair of clocks as "syn-
chronized". Note that clocks can be highly synchronized yet arbi-
trarily inaccurate in terms of how well they tell true time. This
point is important because for many Internet measurements,
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synchronization between two clocks is more important than the accu-
racy of the clocks. The same is *not* true of skew: it is generally
(much) more important that the clocks have minimal absolute skew than
that they have minimal relative skew. These distinctions arise
because for Internet measurement what is often most important are
differences in time as computed by comparing the output of two
clocks. The process of computing the difference removes any error
due to clock inaccuracies with respect to true time; but it is cru-
cial that the differences themselves accurately reflect differences
in true time.
Measurement methodologies will often begin with the step of assuring
that two clocks are synchronized and have minimal skew and drift.
{Comment: An effective way to assure these conditions (and also clock
accuracy) is by using clocks that derive their notion of time from an
external source, rather than only the host computer's clock. (These
latter are often subject to large errors.) It is further preferable
that the clocks directly derive their time, for example by having
immediate access to a GPS (Global Positioning System) unit.}
Two important concerns arise if the clocks indirectly derive their
time using a network time synchronization protocol such as NTP:
+ First, NTP's accuracy depends in part on the properties (particu-
larly delay) of the Internet paths used by the NTP peers, and
these might be exactly the properties that we wish to measure, so
it would be unsound to use NTP to calibrate such measurements.
+ Second, NTP focuses on clock accuracy, which can come at the
expense of short-term clock skew and drift. For example, when a
host's clock is indirectly synchronized to a time source, if the
synchronization intervals occur infrequently, then the host will
sometimes be faced with the problem of how to adjust its current,
incorrect time, Ti, with a considerably different, more accurate
time it has just learned, Ta. Two general ways in which this is
done are to either immediately set the current time to Ta, or to
adjust the local clock's update frequency (hence, its skew) so
that at some point in the future the local time Ti' will agree
with the more accurate time Ta'. The first mechanism introduces
discontinuities and can also violate common assumptions that
timestamps are monotone increasing. If the host's clock is set
backward in time, sometimes this can be easily detected. If the
clock is set forward in time, this can be harder to detect. The
skew induced by the second mechanism can lead to considerable
inaccuracies when computing differences in time, as discussed
above.
To illustrate why skew is a crucial concern, consider samples of one-
way delays between two Internet hosts made at one minute intervals.
The true transmission delay between the hosts might plausibly be on
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the order of 50 msec for a transcontinental path. If the skew
between the two clocks is 0.01%, that is, 1 part in 10,000, then
after 10 minutes of observation the error introduced into the mea-
surement is 60 msec. Unless corrected, this error is enough to com-
pletely wipe out any accuracy in the transmission delay measurement.
Finally, we note that assessing skew errors between unsynchronized
network clocks is an open research area, so we are not aware of any
further guidance presently available for how to compensate for these
errors. This shortcoming makes use of a solid, independent clock
source such as GPS especially desirable.
9.2. The Notion of "Wire Time"
Internet measurement is often complicated by the use of Internet
hosts themselves to perform the measurement. These hosts can intro-
duce delays, bottlenecks, and the like that are due to hardware or
operating system effects and have nothing to do with the network
behavior we would like to measure.
In order to provide a general way of talking about these effects, we
introduce two notions of "wire time". These notions are only defined
in terms of a particular Internet link L.
+ For a given packet P, the wire arrival time of P on L is the first
time T at which all the bits of P have begun transmission across
L.
+ For a given packet P, the wire exit time of P on L is the first
time T at which all the bits of P have completed transmission
across L.
Note that it may well be that some of P's bits have finished trans-
mission across L prior to other bits beginning transmission -- in
general, there may never be a time when all of P is simultaneously
being transmitted, which is why we need to pick a (somewhat arbi-
trary) notion like "all the bits" in order to designate a precise
time. Also note that the link L may be comprised of multiple physi-
cal channels. For defining wire time, we consider these channels to
together comprise a single logical link, and P's wire time is the
first time during which all of its bits have been sent over any of
the channels.
It is possible, though one hopes uncommon, that a packet P might make
multiple trips over a particular link L, due to a forwarding loop.
These trips might even overlap, depending on the link technology.
Whenever this occurs, we define a separate wire time associated with
each instance of P seen on the link. This definition is worth making
because it serves as a reminder that notions like *the* unique time a
packet passes a point in the Internet are inherently slippery.
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The term wire time has historically been used to loosely denote the
time at which a packet appeared on a link, without exactly specifying
whether this refers to the first bit, the last bit, or some other
consideration. This informal definition is generally already very
useful, as it is usually used to make a distinction between when the
packet's propagation delays begin and cease to be due to the network
rather than the endpoint hosts.
When appropriate, metrics should be defined in terms of wire times
rather than host endpoint times, so that the metric's definition
highlights the issue of separating delays due to the host from those
due to the network.
We note that these notions are delicate, and hope to improve our
understanding of them with experience.
{Comment: It can sometimes be difficult to measure wire times. One
technique is to use a packet filter to monitor traffic on a link.
The architecture of these filters often attempts to associate with
each packet a timestamp as close to the wire time as possible. We
note however that one common source of error is to run the packet
filter on one of the endpoint hosts. In this case, it has been
observed that some packet filters receive for some packets timestamps
corresponding to when the packet was *scheduled* to be injected into
the network, rather than when it actually was *sent* out onto the
network (wire time). There can be a substantial difference between
these two times. A technique for dealing with this problem is to run
the packet filter on a separate host that passively monitors the
given link. This can be problematic however for some link technolo-
gies.}
10. Singletons, Samples, and Statistics
In the process of applying early versions of the Framework to spe-
cific metrics, it became clear that a separation was needed between
three distinct -- yet related -- notions:
+ By a 'singleton' metric, we refer to metrics that are, in a sense,
atomic. For example, a single instance of one-way delay from one
host to another might be defined as a singleton metric.
+ By a 'sample' metric, we refer to metrics derived from a given
singleton metric by taking a number of distinct instances
together. For example, a sample of one-way delays from one host
to another taken at one-second intervals over a given one-hour
period might be defined as a sample metric based.
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+ By a 'statistical' metric, we refer to metrics derived from a
given sample metric by taking some statistic of the values defined
by the singleton metric on the sample. For example, the mean of
all the one-way delay values on the sample given above might be
defined as a statistical metric.
By applying these notions of singleton, sample, and statistic in a
consistent way, we will be able to reuse lessons learned about how to
define samples and statistics on various metrics. The orthogonality
among these three notions will thus make all our work more effective
and more intelligible by the community.
In the remainder of this section, we will cover some topics in sam-
pling and statistics that we believe will be important to a variety
of metric definitions and measurement efforts.
10.1. Methods of Collecting Samples
The main reason for collecting samples is to see what sort of varia-
tions and consistencies are present in the metric being measured.
These variations might be with respect to different points in the
Internet, or different measurement times. When assessing variations
based on a sample, one generally makes an assumption that the sample
is "unbiased", meaning that the process of collecting the measure-
ments in the sample did not skew the sample so that it no longer
accurately reflects the metric's variations and consistencies.
One common way of collecting samples is to make measurements sepa-
rated by fixed amounts of time: periodic sampling. Periodic sampling
is particularly attractive because of its simplicity, but it suffers
from two potential problems:
+ If the metric being measured itself exhibits periodic behavior,
then there is a possibility that the sampling will observe only
part of the periodic behavior if the periods happen to agree
(either directly, or if one is a multiple of the other). Related
to this problem is the notion that periodic sampling is highly
predictable. Predictable sampling is susceptible to manipulation
if there are mechanisms by which a network component's behavior
can be temporarily changed such that the sampling only sees the
modified behavior.
+ The act of measurement can perturb what is being measured (for
example, injecting measurement traffic into a network alters the
congestion level of the network), and repeated periodic perturba-
tions can drive a network into a state of synchronization (cf.
[FJ94]), greatly magnifying what might individually be minor
effects.
A more sound approach is based on "random additive sampling".
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Samples are separated by independent, randomly generated intervals
that have a common statistical distribution G(t). The quality of
this sampling depends on the distribution G(t). For example, if G(t)
generates a constant value g with probability one, then the sampling
reduces to periodic sampling with a period of g.
10.1.1. Poisson Sampling
It can be proved that if G(t) is an exponential distribution with
rate lambda, that is
G(t) = 1 - exp(-lambda * t)
then the arrival of new samples *cannot* be predicted, and the sam-
pling is unbiased. Furthermore, the sampling is asymptotically unbi-
ased even if the act of sampling affects the network's state. Such
sampling is referred to as "Poisson sampling". It is not prone to
inducing synchronization, it can be used to accurately collect mea-
surements of periodic behavior, and it is not prone to manipulation
by anticipating when new samples will occur.
Because of these valuable properties, samples of Internet measure-
ments should be gathered using Poisson sampling unless there is a
compelling reason to use a different approach.
In its purest form, Poisson sampling is done by generating indepen-
dent, exponentially distributed intervals and gathering a single mea-
surement after each interval has elapsed. It can be shown that if
starting at time T one performs Poisson sampling over an interval dT,
during which a total of N measurements happen to be made, then those
measurements will be uniformly distributed over the interval [T,
T+dT]. So another way of conducting Poisson sampling is to pick dT
and N and generate N random sampling times uniformly over the inter-
val [T, T+dT]. The two approaches are equivalent, except if N and dT
are externally known. In that case, the property of not being able
to predict measurement times is weakened (the other properties still
hold). The N/dT approach has an advantage that dealing with fixed
values of N and dT can be simpler than dealing with a fixed lambda
but variable numbers of measurements over variably-sized intervals.
10.1.2. Geometric Sampling
Closely related to Poisson sampling is "geometric sampling", in which
external events are measured with a fixed probability p. For exam-
ple, one might capture all the packets over a link but only record
the packet to a trace file if a randomly generated number uniformly
distributed between 0 and 1 is less than a given p. Geometric sam-
pling has the same properties of being unbiased and not predictable
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in advance as Poisson sampling, so if it fits a particular Internet
measurement task, it too is sound. See [CPB93] for more discussion.
10.1.3. Generating Poisson Sampling Intervals
To generate Poisson sampling intervals, one first determines the rate
lambda at which the samples will on average be made (e.g., for an
average sampling interval of 30 seconds, we have lambda = 1/30, if
the units of time are seconds). One then generates a series of expo-
nentially-distributed (pseudo-)random numbers E1, E2, ..., En. The
first measurement is made at time E1, the next at time E1+E2, and so
on.
One technique for generating exponentially-distributed
(pseudo-)random numbers is based on the ability to generate U1, U2,
..., Un, (pseudo-)random numbers that are uniformly distributed
between 0 and 1. Many computers provide libraries that can do this.
Given such Ui, to generate Ei one uses:
Ei = -log(Ui) / lambda
where log(Ui) is the natural logarithm of Ui.
Implementation details:
There are at least three different methods for approximating Poisson
sampling, which we describe here as Methods 1 through 3. Method 1 is
the easiest to implement and has the most error, and method 3 is the
most difficult to implement and has the least error (potentially
none).
Method 1 is to proceed as follows:
1. Generate E1 and wait that long.
2. Perform a measurement.
3. Generate E2 and wait that long.
4. Perform a measurement.
5. Generate E3 and wait that long.
6. Perform a measurement ...
The problem with this approach is that the "Perform a measurement"
steps themselves take time, so the sampling is not done at times E1,
E1+E2, etc., but rather at E1, E1+M1+E2, etc., where Mi is the amount
of time required for the i'th measurement. If Mi is very small com-
pared to 1/lambda then the potential error introduced by this tech-
nique is likewise small. As Mi becomes a non-negligible fraction of
1/lambda, the potential error increases.
Method 2 attempts to correct this error by taking into account the
amount of time required by the measurements (i.e., the Mi's) and
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adjusting the waiting intervals accordingly:
1. Generate E1 and wait that long.
2. Perform a measurement and measure M1, the time it took to do so.
3. Generate E2 and wait for a time E2-M1.
4. Perform a measurement and measure M2 ..
This approach works fine as long as E{i+1} >= Mi. But if E{i+1} < Mi
then it is impossible to wait the proper amount of time. (Note that
this case corresponds to needing to perform two measurements simulta-
neously.)
Method 3 is generating a schedule of measurement times E1, E1+E2,
etc., and then sticking to it:
1. Generate E1, E2, ..., En.
2. Compute measurement times T1, T2, ..., Tn, as Ti = E1 + ... + Ei.
3. Arrange that at times T1, T2, ..., Tn, a measurement is made.
By allowing simultaneous measurements, Method 3 avoids the shortcom-
ings of Methods 1 and 2. If, however, simultaneous measurements
interfere with one another, then Method 3 does not gain any benefit
and may actually prove worse than Methods 1 or 2.
For Internet phenomena, it is not known to what degree the inaccura-
cies of these methods are significant. If the Mi's are much less
than 1/lambda, then any of the three should suffice. If the Mi's are
less than 1/lambda but perhaps not greatly less, then Method 2 is
preferred to Method 1. If simultaneous measurements do not interfere
with one another, then Method 3 is preferred, though it can be con-
siderably harder to implement.
10.2. Self-Consistency
A fundamental requirement for a sound measurement methodology is that
measurement be made using as few unconfirmed assumptions as possible.
Experience has painfully shown how easy it is to make an (often
implicit) assumption that turns out to be incorrect. An example is
incorporating into a measurement the reading of a clock synchronized
to a highly accurate source. It is easy to assume that the clock is
therefore accurate; but due to software bugs, a loss of power in the
source, or a loss of communication between the source and the clock,
the clock could actually be quite inaccurate.
This is not to argue that one must not make any assumptions when mea-
suring, but rather that, to the extent which is practical, assump-
tions should be tested. One powerful way for doing so involves
checking for self-consistency. Such checking applies both to the
observed value(s) of the measurement *and the values used by the
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measurement process itself*. A simple example of the former is that
when computing a round trip time, one should check to see if it is
negative. Since negative time intervals are non-physical, if it ever
is negative that finding immediately flags an error. *These sorts of
errors should then be investigated!* It is crucial to determine
where the error lies, because only by doing so diligently can we
build up faith in a methodology's fundamental soundness. For exam-
ple, it could easily be that the round trip time is negative because
during the measurement the clock was set backward in the process of
synchronizing it with another source. But it could also be that the
measurement program accesses uninitialized memory in one of its com-
putations and, only very rarely, that leads to a bogus computation.
This second error is more serious, if the same program is used by
others to perform the same measurement. Furthermore, once uncovered
it can be completely fixed.
A more subtle example of testing for self-consistency comes from
gathering samples of one-way Internet delays. If one has a large
sample of such delays, it may well be highly telling to, for example,
fit a line to the pairs of (time of measurement, measured delay), to
see if the resulting line has a clearly non-zero slope. If so, a
possible interpretation is that one of the clocks used in the mea-
surements is skewed compared to the other. Another interpretation is
that the slope is actually due to genuine network effects. Determin-
ing which is indeed the case will often be highly illuminating. Fur-
thermore, if making this check is part of the methodology, then a
finding that the long-term slope is very near zero is positive evi-
dence that the measurements are probably not biased by a difference
in skew.
A final example illustrates checking the measurement process itself
for self-consistency. Above we outline Poisson sampling techniques,
based on generating exponentially-distributed intervals. A sound
measurement methodology would include testing the generated intervals
to see whether they are indeed exponentially distributed (and also to
see if they suffer from correlation). In appendix [To Be Written] we
discuss and give C code for one such technique, a general-purpose,
well-regarded goodness-of-fit test called the Anderson-Darling test.
Finally, we note that what is truly relevant for Poisson sampling of
Internet metrics is often not when the measurements began but the
wire times corresponding to the measurement process. These could
well be different, due to complications on the hosts used to perform
the measurement. Thus, even those with complete faith in their
pseudo-random generators and subsequent algorithms are encouraged to
consider how they might test the assumptions of each measurement pro-
cedure as much as possible.
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10.3. Defining Statistical Distributions
One way of describing a collection of measurements (a sample) is as a
statistical distribution -- informally, as percentiles. There are
several slightly different ways of doing so. In this section we
define a standard definition to give uniformity to these descrip-
tions.
The "empirical distribution function" (EDF) of a set of scalar mea-
surements is a function F(x) which for any x gives the fractional
proportion of the total measurements that were <= x. If x is less
than the minimum value observed, then F(x) is 0. If it is greater or
equal to the maximum value observed, then F(x) is 1.
For example, given the 6 measurements:
-2, 7, 7, 4, 18, -5
Then F(-8) = 0, F(-5) = 1/6, F(-5.0001) = 0, F(-4.999) = 1/6, F(7) =
5/6, F(18) = 1, F(239) = 1.
Note that we can recover the different measured values and how many
times each occurred from F(x) -- no information regarding the range
in values is lost. Summarizing measurements using histograms, on the
other hand, in general loses information about the different values
observed, so the EDF is preferred.
Using either the EDF or a histogram, however, we do lose information
regarding the order in which the values were observed. Whether this
loss is potentially significant will depend on the metric being mea-
sured.
We will use the term "percentile" to refer to the smallest value of x
for which F(x) >= a given percentage. So the 50th percentile of the
example above is 4, since F(4) = 3/6 = 50%; the 25th percentile is
-2, since F(-5) = 1/6 < 25%, and F(-2) = 2/6 >= 25%; the 100th per-
centile is 18; and the 0th percentile is -infinity, as is the 15th
percentile.
Care must be taken when using percentiles to summarize a sample,
because they can lend an unwarranted appearance of more precision
than is really available. Any such summary MUST include the sample
size N, because any percentile difference finer than 1/N is below the
resolution of the sample.
See [DS86] for more details regarding EDF's.
We close with a note on the common (and important!) notion of median.
In statistics, the median of a distribution is defined to be the
point X for which the probability of observing a value <= X is equal
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to the probability of observing a value > X. When estimating the
median of a set of observations, the estimate depends on whether the
number of observations, N, is odd or even:
+ If N is odd, then the 50th percentile as defined above is used as
the estimated median.
+ If N is even, then the estimated median is the average of the cen-
tral two observations; that is, if the observations are sorted in
ascending order and numbered from 1 to N, where N = 2*K, then the
estimated median is the average of the (K)'th and (K+1)'th obser-
vations.
Usually the term "estimated" is dropped from the phrase "estimated
median" and this value is simply referred to as the "median".
10.4. Testing For Goodness-of-Fit
For some forms of measurement calibration we need to test whether a
set of numbers is consistent with those numbers having been drawn
from a particular distribution. An example is that to apply a self-
consistency check to measurements made using a Poisson process, one
test is to see whether the sampling times do indeed reflect an expo-
nential distribution; or if the dT/N approach discussed above was
used, whether the times are uniformly distributed across [T, dT].
There are a large number of statistical goodness-of-fit techniques
for performing such tests. See [DS86] for a thorough discussion.
That reference recommends the Anderson-Darling EDF test as being a
good all-purpose test, as well as one that is especially good at
detecting deviations from a given distribution in the lower and upper
tails of the EDF.
It is important to understand that the nature of goodness-of-fit
tests is that one first selects a "significance level", which is the
probability that the test will erroneously declare that the EDF of a
given set of measurements fails to match a particular distribution
when in fact the measurements do indeed reflect that distribution.
Unless otherwise stated, IPPM goodness-of-fit tests are done using 5%
significance. This means that if the test is applied to 100 samples
and 5 of those samples are deemed to have failed the test, then the
samples are all consistent with the distribution being tested. If
significantly more of the samples fail the test, then the assumption
that the samples are consistent with the distribution being tested
must be rejected. If significantly fewer of the samples fail the
test, then the samples have potentially been doctored too well to fit
the distribution. Similarly, some goodness-of-fit tests (including
Anderson-Darling) can detect whether it is likely that a given sample
was doctored. We also use a significance of 5% for this case; that
is, the test will report that a given honest sample is "too good to
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ID Framework for IP Provider Metrics November 1996
be true" 5% of the time, so if the test reports this finding signifi-
cantly more often than one time out of twenty, it is an indication
that something unusual is occurring.
Appendix [To Be Written] gives sample C code for implementing the
Anderson-Darling test, as well as further discussing its use.
See [Pa94] for a discussion of goodness-of-fit and closeness-of-fit
tests in the context of network measurement.
11. Avoiding Stochastic Metrics
When defining metrics applying to a path, subpath, cloud, or other
network element, we in general do not define them in stochastic terms
(probabilities). We instead prefer a deterministic definition. So,
for example, rather than defining a metric about a "packet loss prob-
ability between A and B", we would define a metric about a "packet
loss rate between A and B". (A measurement given by the first defi-
nition might be "0.73", and by the second "73 packets out of 100".)
The reason for this distinction is as follows. When definitions are
made in terms of probabilities, there are often hidden assumptions in
the definition about a stochastic model of the behavior being mea-
sured. The fundamental goal with avoiding probabilities in our met-
ric definitions is to avoid biasing our definitions by these hidden
assumptions.
For example, an easy hidden assumption to make is that packet loss in
a network component due to queueing overflows can be described as
something that happens to any given packet with a particular proba-
bility. Usually, however, queueing drops are actually *determinis-
tic*, and assuming that they should be described probabilistically
can obscure crucial correlations between queueing drops among a set
of packets. So it's better to explicitly note stochastic assump-
tions, rather than have them sneak into our definitions implicitly.
This does *not* mean that we abandon stochastic models for under-
standing network performance!, only that when defining IP metrics we
avoid terms such as "probability" for terms like "proportion" or
"rate". We will still use, for example, random sampling in order to
estimate probabilities used by stochastic models related to the IP
metrics. We also do not rule out the possibility of stochastic met-
rics when they are truly appropriate (for example, perhaps to model
transmission errors caused by certain types of line noise).
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12. Packets of Type P
A fundamental property of many Internet metrics is that the value of
the metric depends on the type of IP packet(s) used to make the mea-
surement. Consider an IP-connectivity metric: one obtains different
results depending on whether one is interested in connectivity for
packets destined for well-known TCP ports or unreserved UDP ports, or
those with invalid IP checksums, or those with TTL's of 16, for exam-
ple. In some circumstances these distinctions will be highly inter-
esting (for example, in the presence of firewalls, or RSVP reserva-
tions).
Because of this distinction, we introduce the generic notion of a
"packet of type P", where in some contexts P will be explicitly
defined (i.e., exactly what type of packet we mean), partially
defined (e.g., "with a payload of B octets"), or left generic. Thus
we may talk about generic IP-type-P-connectivity or more specific IP-
port-HTTP-connectivity. Some metrics and methodologies may be fruit-
fully defined using generic type P definitions which are then made
specific when performing actual measurements.
Whenever a metric's value depends on the type of the packets involved
in the metric, the metric's name will include either a specific type
or a phrase such as "type-P". Thus we will not define an "IP-
connectivity" metric but instead an "IP-type-P-connectivity" metric
and/or perhaps an "IP-port-HTTP-connectivity" metric. This serves as
an important reminder that one must be conscious of the exact type of
traffic being measured.
A closely related note: it would be very useful to know if a given
Internet component treats equally a class C of different types of
packets. If so, then any one of those types of packets can be used
for subsequent measurement of the component. This suggests we devise
a metric or suite of metrics that attempt to determine C.
13. Internet Addresses vs. Hosts
When considering a metric for some path through the Internet, it is
often natural to think about it as being for the path from Internet
host H1 to host H2. A definition in these terms, though, can be
ambiguous, because Internet hosts can be attached to more than one
network. In this case, the result of the metric will depend on which
of these networks is actually used.
Because of this ambiguitiy, usually such definitions should instead
be defined in terms of Internet IP addresses. For the common case of
a unidirectional path through the Internet, we will use the term
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ID Framework for IP Provider Metrics November 1996
"Src" to denote the IP address of the beginning of the path, and
"Dst" to denote the IP address of the end.
14. Well-Formed Packets
Unless otherwise stated, all metric definitions that concern IP pack-
ets include an implicit assumption that the packet is *well formed*.
A packet is well formed if it meets all of the following criteria:
+ Its length as given in the IP header corresponds to the size of
the IP header plus the size of the payload.
+ It includes a valid IP header: the version field is 4 (later, we
will expand this to include 6); the header length is >= 5; the
checksum is correct.
+ It is not an IP fragment.
+ The source and destination addresses correspond to the hosts in
question.
+ Either the packet possesses sufficient TTL to travel from the
source to the destination if the TTL is decremented by one at each
hop, or it possesses the maximum TTL of 255.
+ It does not contain IP options unless explicitly noted.
+ If a transport header is present, it too contains a valid checksum
and other valid fields.
We further require that if a packet is described as having a "length
of B octets", then 0 <= B <= 65535; and if B is the payload length in
octets, then B <= (65535-IP header size in octets).
So, for example, one might imagine defining an IP connectivity metric
as "IP-type-T-connectivity for well-formed packets with the IP TOS
field set to 0", or, more succinctly, "IP-type-T-connectivity with
the IP TOS field set to 0", since well-formed is already implied.
A particular type of well-formed packet often useful to consider is
the "minimal IP packet from A to B" - this is an IP packet with the
following properties:
- It is well-formed.
- Its data payload is 0 octets.
- It contains no options.
- Its protocol field is 4 (IP) ??? 0 (reserved) ???
When defining IP metrics we keep in mind that no packet smaller or
simpler than this can be transmitted over a correctly operating IP
network.
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ID Framework for IP Provider Metrics November 1996
15. Acknowledgements
The comments of Brian Carpenter and Jeff Sedayao are appreciated.
16. Security Considerations
This memo raises no security issues.
17. References
[Al96] G. Almes and S. Kalidindi, "A One-way Delay Metric for IPPM",
Internet Draft , November 1996.
[DS86] R. D'Agostino and M. Stephens, editors, Goodness-of-Fit Tech-
niques, Marcel Dekker, Inc., 1986.
[CPB93] K. Claffy, G. Polyzos, and H-W. Braun, ``Application of Sam-
pling Methodologies to Network Traffic Characterization,'' Proc. SIG-
COMM '93, pp. 194-203, San Francisco, September 1993.
[FJ94] S. Floyd and V. Jacobson, ``The Synchronization of Periodic
Routing Messages,'' IEEE/ACM Transactions on Networking, 2(2), pp.
122-136, April 1994.
[Mi92] D. Mills, "Network Time Protocol (v3)", April 1992
[Pa94] V. Paxson, ``Empirically-Derived Analytic Models of Wide-Area
TCP Connections,'' IEEE/ACM Transactions on Networking, 2(4), pp.
316-336, August 1994.
[Pa96] V. Paxson, ftp://ftp.ee.lbl.gov/papers/metrics-framework-
INET96.ps.Z
18. Authors' Addresses
Guy Almes
Advanced Network & Services, Inc.
200 Business Park Drive
Armonk, NY 10504
USA
Phone: +1 914/273-7863
Bill Cerveny
Advanced Network & Services, Inc.
200 Business Park Drive
Almes et al. [Page 28]
ID Framework for IP Provider Metrics November 1996
Armonk, NY 10504
USA
Padma Krishnaswamy
Bell Communications Research
445 South Street
Morristown, NJ 07960
USA
Jamshid Mahdavi
Pittsburgh Supercomputing Center
4400 5th Avenue
Pittsburgh, PA 15213
USA
Matt Mathis
Pittsburgh Supercomputing Center
4400 5th Avenue
Pittsburgh, PA 15213
USA
Vern Paxson
MS 50B/2239
Lawrence Berkeley National Laboratory
University of California
Berkeley, CA 94720
USA
Phone: +1 510/486-7504
Almes et al. [Page 29]