IP Performance Working Group M. Mathis
Internet-Draft Google, Inc
Intended status: Experimental Oct 15, 2012
Expires: April 18, 2013
Model Based Internet Performance Metrics
draft-mathis-ippm-model-based-metrics-00.txt
Abstract
We introduce a new class of model based Internet metrics designed to
determine if a long path can be expected to meet a predefined end-to-
end application performance target by applying a suite of single
property tests to successive sections of the long path. In many
cases these single property tests are based on existing IPPM metrics,
with the addition of success and validity criteria. The sub-path at
a time tests are designed to eliminate all known conditions that
might prevent the full path from meeting the target performance.
Status of this Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Background . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Common Models and Parameters . . . . . . . . . . . . . . . . . 5
3.1. End-to-end parameters . . . . . . . . . . . . . . . . . . 5
3.2. Per sub-path parameters . . . . . . . . . . . . . . . . . 7
3.3. Common Calculations for Single Property Tests . . . . . . 7
3.4. Parameter Derating . . . . . . . . . . . . . . . . . . . . 8
3.5. Single Property Tests Results . . . . . . . . . . . . . . 9
4. Single Property Tests . . . . . . . . . . . . . . . . . . . . 9
4.1. Verify the absence of cross traffic . . . . . . . . . . . 9
4.1.1. Parameter Calculation . . . . . . . . . . . . . . . . 10
4.1.2. Cross traffic Measurement . . . . . . . . . . . . . . 10
4.2. Full Data Rate Loss Rate Tests . . . . . . . . . . . . . . 10
4.2.1. Loss Rate Measurement . . . . . . . . . . . . . . . . 11
4.3. Background Loss Rate Tests . . . . . . . . . . . . . . . . 11
4.3.1. Background Loss Rate Measurement . . . . . . . . . . . 11
4.4. Queue Capacity Test . . . . . . . . . . . . . . . . . . . 12
4.4.1. Model Calculation . . . . . . . . . . . . . . . . . . 12
4.4.2. Queue Capacity Measurement . . . . . . . . . . . . . . 12
4.5. AQM Test . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.5.1. Model Calculation . . . . . . . . . . . . . . . . . . 12
4.5.2. AQM Measurement . . . . . . . . . . . . . . . . . . . 12
4.6. Reordering Test . . . . . . . . . . . . . . . . . . . . . 12
4.6.1. Model Calculation . . . . . . . . . . . . . . . . . . 12
4.6.2. Reordering Measurement . . . . . . . . . . . . . . . . 12
5. Calibration . . . . . . . . . . . . . . . . . . . . . . . . . 12
6. References . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.1. Normative References . . . . . . . . . . . . . . . . . . . 13
6.2. Informative References . . . . . . . . . . . . . . . . . . 13
Appendix A. Model Derivations . . . . . . . . . . . . . . . . . . 13
Appendix B. Old text from an earlier document . . . . . . . . . . 13
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 15
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1. Introduction
We introduce a new class of model based metrics designed to determine
if a long path can be expected to meet a predefined application end-
to-end performance target by applying a suite of single property
tests to successive sections of the long path. In many cases these
single property tests are based on existing IPPM metrics, with the
addition of success and validity criteria. The sub-path at a time
tests are designed to eliminate all known conditions that might
prevent the full path from meeting the target performance. The end-
to-end target performance must be specified in advance, in order to
be able to open-loop the control systems (such as congestion control)
that are present in all Internet transport protocols and
applications. Since a singleton (see [RFC2330]) is only a pass/fail
measurement of a sub-path, these metrics are most useful in
composition over large pools of samples, such as across a collection
of paths or a time interval [RFC5835].
For Bulk Transport Capacity (BTC) the target performance to be
measured is a data rate. TCP's ability to compensate for less than
ideal network conditions is fundamentally affected by the RTT and MTU
of the end-to-end Internet path that it traverses. Since the minimum
RTT and maximum MTU are both fixed properties of the path, they are
also taken as parameters. The target values for these three
parameters, Data Rate, RTT and MTU, are determined by the
application, its intended use and the physical infrastructure over
which it traverses. They are described in more detail in Section 3
together with the models used to infer the required performance of
the underlying Internet fabric.
Traditional end-to-end BTC metrics have proven to be difficult or
unsatisfactory for the reasons described in Section 2. Rather than
testing the end-to-end path with TCP or other some other BTC, each
sub-path is evaluated using suite of far simpler and more predictable
single property tests described in Section 4. For BTC the following
tests are sufficient: raw data rate, background loss rate, queue
burst capacity, reordering extent, onset of congestion/AQM and return
path quality. If every sub-path passes all of these tests, then an
end-to-end application using any reasonably modern TCP or similar
protocol should be able to attain the specified target data rate,
over the full end-to-end path at the specified RTT and MTU.
There exists the potential that model based metric might fail, in the
sense that every sub-path of an end-to-end path passes every single
property test and yet a application might still fall to attain its
performance target. If so, then a traditional BTC needs to be used
to validate the tests for each sub-path, as described in Section 5.
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Future text (or a more likely a future document) will describe model
based metrics for real time traffic. The salient point will be that
concurrently meeting the goals of both RT and throughput maximizing
traffic implicitly requires some form of traffic segregation, such
that the two traffic classes are not placed in the same queue. Some
technique as simple as SFQ[SFQ] might be a sufficient alternative to
full QoS.
TODO:
Add discussion of protocol overhead: MSS vs IP MTU vs link MTU
2. Background
(Fragments of earlier text)
The holy grail of IPPM has been BTC measurement, but it has proven to
be a very hard problem for a number of reasons:
TCP is a control systems - everything affects performance,
including components that are explicitly not part of the the test.
Congestion control is an equilibrium process, transport protocols
change the network (raise loss probability and/or RTT) to conform
to their behavior.
TCP's ability to compensate for network flaws is directly
proportional to the number of round trips per second (e.g.
inversely proportional to the RTT). As a consequence a flawed
link that passes a local test is likely to completely fail when
the path is extended by a perfect network to some larger RTT.
TCP has a meta Heisenberg problem - Measurement and cross traffic
interact in unknown and ill defined ways. The situation is
actually worse than the traditional physics problem where you can
at least estimate the relative masses of the measurement and
measured particles. For network measurement you can not in
general determine the relative "masses" of the measurement traffic
and cross traffic, so you can not even gage the relative magnitude
of their effects on each other.
The new approach is to "open loop" congestion control. Defeat CC,
typically by throttling TCP to a lower rate, such that it does not
respond to network conditions. In this mode the measurement software
explicitly controls TCP's state variables (e.g. cwnd) to create
controlled traffic patterns, which are manipulated to measure the
network.
Models are used to determine the actual test parameters (loss rate,
etc) from the target parameters. The basic method is to use models
to estimate simple network properties required to sustain a given
transport flow (or set of flows), and using a suite of simpler
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metrics to confirm that the network meets the required properties.
For example a network can sustain a Bulk TCP flow of a given data
rate, MTU and RTT when 4 (and probably more) conditions are met:
The raw link rate is higher than the target data rate.
The raw packet loss rate is lower than required by a suitable TCP
performance model
There is sufficient buffering at any bottleneck smooth bursts.
When the link is overfilled (congested), the onset of packet loss
is progressive.
These condition can all be verified with simple tests, using model
parameters and acceptance thresholds derived from the target data
rate, MTU and RTT. Note that this procedure is not invertible: a
singleton measurement is a pass/fail evaluation of a given path or
subpath at a given performance. Measurements to confirm that a link
passes at one particular performance may not be generally be useful
to predict if the link will pass at a different performance.
Although they are not invertible, they do have several other valuable
properties, such as natural ways to define several different
composition metrics.
3. Common Models and Parameters
Transport performance models are used to derive the test parameters
for each single property test from the end-to-end target parameters
and additional ancillary parameters.
It is envisioned that the modeling phase (to compute the test
parameters) and testing phases will be decoupled. This section
covers common derived parameters, used by multiple single property
tests. For some tests, additional modeling is described with the
tests.
Since some aspects of the models are very conservative, the modeling
framework permits some latitude in derating test parameters, as
described in Section 3.4.
For certain sub-paths (e.g. common types of access links) it would be
appropriate for the single property test parameters to be documented
as a "measurement profile" together with the modeling assumptions and
derating factors described in Section 3.3 and Section 3.4.
3.1. End-to-end parameters
These parameters are determined by the needs of the application or
the ultimate end user and the end-to-end Internet path.
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Target Data Rate: The application or ultimate user's performance
goal (in aggregate across all connections).
Permitted Number of Connections: The target rate can be more easily
obtained by dividing the traffic across more than one connection.
In general the number of concurrent connections is determined by
the application, however see the comments below on multiple
connections.
Target RTT (Round Trip Time): For fundamental reasons a long path
makes it more difficult for TCP or other transport protocol to
meet the target rate. The target RTT must be representative for
the actual applications expected to use the network. This
parameter may be subject to a future convention (e.g. continental
scale paths should be assumed to be some fixed RTT, such as 100
ms) or alternatively be an property of an ISP's topology (e.g. a
ISP with richer and better placed peering may actually have lower
RTTs for typical users.)
Target MTU (Maximum Transmission Unit): Assume 1500 Bytes unless
otherwise specified. If some sub-path forces a smaller MTU, then
all sub-paths must be tested with the same smaller MTU.
The use of multiple connections has been very controversial since the
beginning of the World-Wide-Web[first complaint]. Modern browsers
open many connections [BScope]. Experts in the IETF transport area
have frequently spoken against this practice [long list]. It is not
inappropriate to assume some small number of concurrent connections
(e.g. 4 or 6), to compensate for limitation in TCP. However,
choosing too large a number is at risk of being taken as a signal by
the web browser community that this practice has been embraced by the
Internet community. It may not be desirable to send such a signal.
The following optional parameters apply for testing generalized end-
to-end paths that include subpaths with known specific types of
behaviors that are not well represented by simple queueing models:
Bottleneck link clock rate: This applies to links that are using
virtual queues or other techniques to police or shape users
traffic at lower rates full link rate. The bottleneck link clock
rate should be representative of queue drain times for short
bursts of packets on an otherwise unloaded link.
Channel hold time: For channels that have relatively expensive
channel arbitration algorithms, this is the typical (maximum?)
time that data and or ACKs are held pending acquiring the channel.
WHile under heavy load, the RTT may be inflated by this parameter,
unless it is built into the target RTT
Preload traffic volume: If the user's traffic is shaped on the basis
of average traffic volume, this is volume necessary to invoke
"heavy hitter" policies.
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Unloaded traffic volume: If the user's traffic is shaped on the
basis of average traffic volume, this is the maximum traffic
volume that a test can use and stay within a "light user"
policies.
Note on a ConEx enabled network [ConEx], the word "traffic" in the
last two items should be replaced by "congestion" i.e. "preload
congestion volume" and "unloaded congestion volume".
3.2. Per sub-path parameters
Some single parameter tests also need parameter of the sub-path.
sub-path RTT: RTT of the sub-path under test.
sub-path link clock rate: If different than the Bottleneck link
clock rate
3.3. Common Calculations for Single Property Tests
The most important derived parameter is target_pipe_size (in
packets), which is the number of packets needed exactly meet the
target rate, with no cross traffic for the specified RTT and MTU. It
is given by:
target_pipe_size = target_rate * target_RTT / target_MTU
If the transport protocol (e.g. TCP) average window size is smaller
than this, the link will be under filled.
If target_data_rate is equal to bottleneck link_data_rate, then
target_pipe_size also predicts the onset of queueing. If the
transport protocol (e.g. TCP) average window size is larger than the
target_pipe_size, the excess packets will be in a standing queue at
the bottleneck.
If the transport protocol is using Reno congestion control [RFC5681],
then there must be target_pipe_size roundtrips between losses.
Otherwise the multiplicative window reduction triggered by a loss
would cause the network to be underfilled. Following [MSMO97], we
derive the losses must be no more frequent than every 1 in
(3/2)(target_pipe_size^2) packets. This provides the reference value
for target_run_length which is typically the number of packets that
must be delivered between loss episodes in hte tests below:
reference_target_run_length = (3/2)(target_pipe_size^2)
Note that this calculation is based on a number of assumptions that
may not apply. Appendix A discusses these assumptions and provides
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some alternative models. The actual method for computing
target_run_length MUST be published along with the rationale for the
underlying assumptions and the ratio of chosen target_run_length to
reference_target_run_length.
Although this document gives a lot of latitude for calculating
target_run_length people specifying profiles for suites of single
property tests need to consider the effect of their choices on the
ongoing conversation and tussle about the relevance of "TCP
friendliness" as an appropriate model for capacity allocation.
Choosing a target_run_length that is substantially smaller than
reference_target_run_length is equivalent to saying that it is
appropriate for the research community to abandon "TCP friendliness"
as a fairness model and to develop more aggressive Internet transport
protocols, and for applications to continue (or even increase) the
number of connections that they open.
The calculations for individual parameters are presented with the
each single property test. In general these calculations are
permitted some as described in Section 3.4
3.4. Parameter Derating
Since some aspects of the models are very conservative, the modeling
framework permits some latitude in derating some specific test
parameters, as indicated in Section 4. For example classical
performance models suggest that in order to be sure that a single TCP
stream can fill a link, it needs to have a full bandwidth-delay-
product worth of buffering at the bottleneck[QueueSize]. In real
networks with real applications this is sometimes overly
conservative. Rather than trying to formalize more complicated
models we permit some test parameters to be relaxed as long as they
meet some additional procedural constraints:
The method used compute and justify the derated metrics is
published in such a way that it becomes a matter of public record.
The calibration procedures described in Section 5 are used to
demonstrate the feasibility of meeting the performance targets
with the derated test parameters.
The calibration process itself is documented is such a way that
other researchers can duplicate the experiments and validate the
results.
Note that some single property test parameters are not permitted to
be derated.
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3.5. Single Property Tests Results
TBD Define: Pass, Fail and inconclusive test results.
The inconclusive outcome is needed to address the case where a test
failed to attain the specified test conditions. This is important to
the extent that the tests themselves have built in control systems
which might interfere with some aspepect of the test. It is required
for example to use TCP for testing.
4. Single Property Tests
The single property tests confirm that each sub-path can sustain the
normal traffic patterns caused by TCP running at the specified target
performance. Specifically they confirm that each sub-path has:
sufficient raw capacity (e.g. sufficient data rate); low enough
background loss rate where mandatory congestion control stays out of
the way; large enough queue space to absorb TCP's normal bursts; does
not cause unreasonable packet reordering; progressive AQM to
appropriately invoke congestion control. Appropriately invoking
congestion control requires that packet losses or ECN marks start
progressively before TCP creates an excessive sustained
queues[BufferBloat] or excessively bursty losses. The return path
must also subject to a similar suite of tests, although potentially
with different test parameters.
Note that many of the sub-path tests resemble metrics that have
already been defined in the IPPM context, with the addition of
criteria for passing or failing the test. The models used to derive
the test parameters make specific assumptions about network
conditions, a test is deemed "inconclusive" (as opposed to failing)
if tester does not meet the underlying assumption. For example a
loss rate test at a specified data rate is inconclusive if the tester
fails to send data at the specified rate for some reason. This
concept of an inconclusive test is necessary to build tests out of
protocols or technologies that they themselves have built in or
implicit control systems.
Some single property test can be combined, since their parameters are
not mutually exclusive.
4.1. Verify the absence of cross traffic
Use a passive packet or SNMP monitoring to verify that the traffic
volume on the sub-path agrees with the traffic generated by each
test. Ideally this should be performed before during and after each
test.
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The goal is provide quality assurance on the overall measurement
process, and specifically to detect the following measurement
failure: a user observes unexpectedly poor application performance,
the ISP observes that the access link is running at the rated
capacity. Both fail to observe that the user's computer has been
infected by a virus which is spewing traffic as fast as it can.
Parameters:
Maximum Cross Traffic Data Rate The amount of excess traffic
permitted. Note that this might be different for different tests.
Maximum Data Rate underage The permitted amount that the traffic can
be less than predicted for the current test. Normally this would
just be a statement of the maximum permitted measurement error,
however it might also detect cases where the passive and active
tests are misaligned: testing different subscriber lines. This is
important because the vantage points are so different: in-band
active measurement vs out-of-band passive measurement.
4.1.1. Parameter Calculation
TBA
4.1.2. Cross traffic Measurement
One possible method is an adaptation of: www-didc.lbl.gov/papers/
SCNM-PAM03.pdf D Agarwal etal. "An Infrastructure for Passive
Network Monitoring of Application Data Streams". Use the same
technique as that paper to trigger the capture of SNMP statistics for
the link.
4.2. Full Data Rate Loss Rate Tests
We propose two versions of the loss rate test. One, performed at
data full rate, is intrusive and recommend for infrequent testing,
such as when a service is first turned up or as part of an auditing
process. Note that this test also implicitly confirms that sub_path
has sufficient capacity to carry the target_data_rate.
The second background loss rate, described below, is designed for
ongoing monitoring for change is sub-path quality.
Parameters:
Run Length Same as target_run_lenght
Data Rate Same as target_data_rate
Note that these parameters MUST NOT be derated. If the default
parameters are too stringent use an alternate model for
arget_data_rate as described in Appendix A.
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4.2.1. Loss Rate Measurement
Data is sent at the specified data_rate. The receiver accumulates
the total data delivered and packets lost [and ECN marks, which are
nominally treated as losses by conforming transport protocols]. The
observed average_run_lenght is computed from total_data_delivered
divided by the total_loss_rate. A [TBD] statistical test is applied
to determine when or if the average_run_lenght is larger than
target_run_lenght.
TODO: add language about monitoring cross traffic.
The test is deemed to have passed only if the observed data rate
matches the target_data_rate and it is statistically significant that
the average_run_lenght is larger than target_run_lenght. It is
deemed inconclusive if: the statistical test is inconclusive; there
is too much background load; or the target_data_rate could not be
attained.
4.3. Background Loss Rate Tests
The background loss rate is designed for ongoing monitoring for
change is sub-path quality. It should be used in conjunction with
the above full rate test.
Parameters:
Run Length Same as target_run_lenght
Data Rate Some small fraction of target_data_rate, such as 1%.
4.3.1. Background Loss Rate Measurement
The receiver accumulates the total data delivered and packets losses
[and ECN marks, which are nominally treated as losses by conforming
transport protocols]. The observed average_run_lenght is computed
from total_data_delivered divided by the total_loss_rate. A [TBD]
statistical test is applied to determine when or if the
average_run_lenght is larger than target_run_lenght.
TODO: add language about monitoring cross traffic.
The test is deemed to have passed if it is statistically significant
that the average_run_lenght is larger than target_run_lenght. It is
deemed inconclusive if there is too much background traffic or the
statistical test is inconclusive.
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4.4. Queue Capacity Test
Parameters:
TBA TBA
4.4.1. Model Calculation
TBA
4.4.2. Queue Capacity Measurement
TBA
4.5. AQM Test
Parameters:
TBA TBA
4.5.1. Model Calculation
TBA
4.5.2. AQM Measurement
TBA
4.6. Reordering Test
Parameters:
TBA TBA
4.6.1. Model Calculation
TBA
4.6.2. Reordering Measurement
TBA
5. Calibration
If using derated metrics, or when something goes wrong, the results
must be calibrated against a traditional BTC......
6. References
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6.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2026] Bradner, S., "The Internet Standards Process -- Revision
3", BCP 9, RFC 2026, October 1996.
6.2. Informative References
[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
"Framework for IP Performance Metrics", RFC 2330,
May 1998.
[RFC5681] Allman, M., Paxson, V., and E. Blanton, "TCP Congestion
Control", RFC 5681, September 2009.
[RFC5835] Morton, A. and S. Van den Berghe, "Framework for Metric
Composition", RFC 5835, April 2010.
[MSMO97] Mathis, M., Semke, J., Mahdavi, J., and T. Ott, "The
Macroscopic Behavior of the TCP Congestion Avoidance
Algorithm", Computer Communications Review volume 27,
number3, July 1997.
[BScope] Broswerscope, "Browserscope Network tests", Sept 2012,
<http://www.browserscope.org/?category=network>.
See Max Connections column
Appendix A. Model Derivations
This appendix describes several different ways to calculate
target_run_length and the implication of the chosen calculation.
Rederive MSMO97 under two different assumptions: target_rate =
link_rate and target_rate < 2 * link_rate.
Show equivalent derivation for CUBIC.
Commentary on the consequence of the choice.
Appendix B. Old text from an earlier document
To be moved, removed or absorbed
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Step 0: select target end-to-end parameters: a target rate and target
RTT. The primary test will be to confirm that the link quality is
sufficient to meet the specified target rate for the link under test,
when extended to the target RTT by an ideal network. The target rate
must be below the actual link rate and nominally the target RTT would
be longer than the link RTT. There should probably be a convention
for the relationship between link and target rates (e.g. 85%).
For example on a 10 Mb/s link, the target rate might be 1 MBytes/s,
at an RTT of 100 mS (a typical continental scale path).
Step 1: On the basis of the target rate and RTT and your favorite TCP
performance model, compute the "required run length", which is the
required number of consecutive non-losses between loss episodes. The
run length resembles one over the loss probability, if clustered
losses only count as a single event. Also select "test duration" and
"test rate". The latter would nominally the same as the target rate,
but might be different in some situations. There must be
documentation connecting the test rate, duration and required run
length, to the target rate and RTT selected in step 0.
Continuing the above example: Assuming a 1500 Byte MTU. The
calculated model loss rate for a single TCP stream is about 0.01% (1
loss in 1E4 packets).
Step 2, the actual measurement proceeds as follows: Start an
unconstrained bulk data flow using any modern TCP (with large buffers
and/or autotuning). During the first interval (no rate limits)
observe the slowstart (e.g. tcpdump) and measure: Peak burst size;
link clock rate (delivery rate for each round); peak data rate for
the fastest single RTT interval; fraction of segments lost at the end
of slow start. After the flow has fully recovered from the slowstart
(details not important) throttle the flow down to the test rate (by
clamping cwnd or application pacing at the sender or receiver).
While clamped to the test rate, observe the losses (run length) for
the chosen test duration. The link passes the test if the slowstart
ends with less than approximately 50% losses and no timeouts, the
peak rate is at least the target rate, and the measured run length is
better than the required run length. There will also need to be some
ancillary metrics, for example to discard tests where the receiver
closes the window, invalidating the slowstart test. [This needs to
be separated into multiple subtests]
Optional step 3: In some cases it might make sense to compute an
"extrapolated rate", which is the minimum of the observed peak rate,
and the rate computed from the specified target RTT and the observed
run length by using a suitable TCP performance model. The
extrapolated rate should be annotated to indicate if it was run
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length or peak rate limited, since these have different predictive
values.
Other issues:
If the link RTT is not substantially smaller than the target RTT and
the actual run length is close to the target rate, a standards
compliant TCP implementation might not be effective at accurately
controlling the data rate. To be independent of the details of the
TCP implementation, failing to control the rate has to be treated as
a spoiled measurement, not a infrastructure failure. This can be
overcome by "stiffening" TCP by using a non-standard congestion
control algorithm. For example if the rate controlling by clamping
cwnd then use "relentless TCP" style reductions on loss, and lock
ssthresh to the cwnd clamp. Alternatively, implement an explicit
rate controller for TCP. In either case the test must be abandoned
(aborted) if the measured run length is substantially below the
target run length.
If the test is run "in situ" in a production environment, there also
needs to be baseline tests using alternate paths to confirm that
there are no bottlenecks or congested links between the test end
points and the link under test.
It might make sense to run multiple tests with different parameters,
for example infrequent tests with test rate equal to the target rate,
and more frequent, less disruptive tests with the same target rate
but the test rate equal to 1% of the target rate. To observe the
required run length, the low rate test would take 100 times longer to
run.
Returning to the example: a full rate test would entail sending 690
pps (1 MByte/s) for several tens of seconds (e.g. 50k packets), and
observing that the total loss rate is below 1:1e4. A less disruptive
test might be to send at 6.9 pps for 100 times longer, and observing
Formatted: Mon Oct 15 16:00:51 PDT 2012
Mathis Expires April 18, 2013 [Page 15]
Internet-Draft Model Based Metrics Oct 2012
Author's Address
Matt Mathis
Google, Inc
1600 Amphitheater Parkway
Mountain View, California 93117
USA
Email: mattmathis@google.com
Mathis Expires April 18, 2013 [Page 16]