In certain real-time applications (such as packet voice and video),
the loss pattern or loss distribution is a key parameter that
determines the performance observed by the users. For the same loss
rate, two different loss distributions could potentially produce
widely different perceptions of performance. The impact of loss
pattern is also extremely important for non-real-time applications
that use an adaptive protocol such as TCP. Refer to [4], [5], [6],
[11] for evidence as to the importance and existence of loss
burstiness and its effect on packet voice and video applications.
Previously, the focus of the IPPM had been on specifying base metrics
such as delay, loss and connectivity under the framework described in
RFC 2330. However, specific Internet behaviors can also be captured
under the umbrella of the IPPM framework, specifying new concepts
while reusing existing guidelines as much as possible. In this
document, we propose two derived metrics, called "loss distance" and
"loss period", with associated statistics, to capture packet loss
patterns. The loss period metric captures the frequency and length
(burstiness) of loss once it starts, and the loss distance metric
captures the spacing between the loss periods. It is important to
note that these metrics are derived based on the base metric Type-P-
One-Way-packet-Loss.
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", "OPTIONAL", and
"silently ignore" in this document are to be interpreted as described
in BCP 14, RFC 2119 [2].
This document closely follows the guidelines specified in [3].
Specifically, the concepts of singleton, sample, statistic,
measurement principles, Type-P packets, as well as standard-formed
packets all apply. However, since the document proposes to capture
specific Internet behaviors, modifications to the sampling process
MAY be needed. Indeed, this is mentioned in [1], where it is noted
that alternate sampling procedures may be useful depending on
specific circumstances. This document proposes that the specific
behaviors be captured as "derived" metrics from the base metrics the
behaviors are related to. The reasons for adopting this position are
the following:
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- it provides consistent usage of singleton metric definition for
different behaviors (e.g., a single definition of packet loss is
needed for capturing burst of losses, 'm out of n' losses etc.)
- it allows re-use of the methodologies specified for the singleton
metric with modifications whenever necessary
- it clearly separates few base metrics from many Internet behaviors
Following the guidelines in [3], this translates to deriving sample
metrics from the respective singletons. The process of deriving
sample metrics from the singletons is specified in [3], [1], and
others.
In the following sections, we apply this approach to a particular
Internet behavior, namely the packet loss process.
Sequence number: Consecutive packets in a time series sample are
given sequence numbers that are consecutive
integers. This document does not specify exactly
how to associate sequence numbers with packets. The
sequence numbers could be contained within test
packets themselves, or they could be derived through
post-processing of the sample.
Bursty loss: The loss involving consecutive packets of a stream.
Loss Distance: The difference in sequence numbers of two successively
lost packets which may or may not be separated by
successfully received packets.
Example: In a packet stream, the packet with sequence number 20 is
considered lost, followed by the packet with sequence number
50. The loss distance is 30.
Loss period: Let P_i be the i'th packet. Define f(P_i) = 1 if P_i is
lost, 0 otherwise. Then, a loss period begins if
f(P_i) = 1 and f(P_(i-1)) = 0
Example: Consider the following sequence of lost (denoted by x) and
received (denoted by r) packets.
r r r x r r x x x r x r r x x x
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Then, with `i' assigned as follows,
1 1 1 1 1 1
i: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
f(P_i) is,
f(P_i): 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1
and there are four loss periods in the above sequence beginning at
P_3, P_6, P_10, and P_13.
Src, the IP address of a host
Dst, the IP address of a host
T0, a time
Tf, a time
lambda, a rate of any sampling method chosen in reciprocal of
seconds
A sequence of pairs of the form <loss distance, loss>, where loss is
derived from the sequence of <time, loss> in [1], and loss distance
is either zero or a positive integer.
A sequence of pairs of the form <loss period, loss>, where loss is
derived from the sequence of <time, loss> in [1], and loss period is
an integer.
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When a packet is considered lost (using the definition in [1]), we
look at its sequence number and compare it with that of the
previously lost packet. The difference is the loss distance between
the lost packet and the previously lost packet. The sample would
consist of <loss distance, loss> pairs. This definition assumes that
sequence numbers of successive test packets increase monotonically by
one. The loss distance associated with the very first packet loss is
considered to be zero.
The sequence number of a test packet can be derived from the
timeseries sample collected by performing the loss measurement
according to the methodology in [1]. For example, if a loss sample
consists of <T0,0>, <T1,0>, <T2,1>, <T3,0>, <T4,0>, the sequence
numbers of the five test packets sent at T0, T1, T2, T3, and T4 can
be 0, 1, 2, 3 and 4 respectively, or 100, 101, 102, 103 and 104
respectively, etc.
We start a counter 'n' at an initial value of zero. This counter is
incremented by one each time a lost packet satisfies the definition
outlined in 4. The metric is defined as <loss period, loss> where
"loss" is derived from the sequence of <time, loss> in Type-P-One-
Way-Loss-Stream [1], and loss period is set to zero when "loss" is
zero in Type-P-One-Way-Loss-Stream, and loss period is set to 'n'
(above) when "loss" is one in Type-P-One-Way-Loss-Stream.
Essentially, when a packet is lost, the current value of "n"
indicates the loss period to which this packet belongs. For a packet
that is received successfully, the loss period is defined to be zero.
Let the following set of pairs represent a Type-P-One-Way-Loss-
Stream.
{<T1,0>,<T2,1>,<T3,0>,<T4,0>,<T5,1>,<T6,0>,<T7,1>,<T8,0>,
<T9,1>,<T10,1>}
where T1, T2,..,T10 are in increasing order.
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Packets sent at T2, T5, T7, T9, T10 are lost. The two derived
metrics can be obtained from this sample as follows.
(i) Type-P-One-Way-Loss-Distance-Stream:
Since packet 2 is the first lost packet, the associated loss distance
is zero. For the next lost packet (packet 5), loss distance is 5-2
or 3. Similarly, for the remaining lost packets (packets 7, 9, and
10) their loss distances are 2, 2, and 1 respectively. Therefore,
the Type-P-One-Way-Loss-Distance-Stream is:
{<0,0>,<0,1>,<0,0>,<0,0>,<3,1>,<0,0>,<2,1>,<0,0>,<2,1>,<1,1>}
(ii) The Type-P-One-Way-Loss-Period-Stream:
The packet 2 sets the counter 'n' to 1, which is incremented by one
for packets 5, 7 and 9 according to the definition in 4. However,
for packet 10, the counter remains at 4, again satisfying the
definition in 4. Thus, the Type-P-One-Way-Loss-Period-Stream is:
{<0,0>,<1,1>,<0,0>,<0,0>,<2,1>,<0,0>,<3,1>,<0,0>,<4,1>,<4,1>}
The same methodology outlined in [1] can be used to conduct the
sample experiments. A synopsis is listed below.
Generally, for a given Type-P, one possible methodology would proceed
as follows:
- Assume that Src and Dst have clocks that are synchronized with
each other. The degree of synchronization is a parameter of the
methodology, and depends on the threshold used to determine loss
(see below).
- At the Src host, select Src and Dst IP addresses, and form a test
packet of Type-P with these addresses.
- At the Dst host, arrange to receive the packet.
- At the Src host, place a timestamp in the prepared Type-P packet,
and send it towards Dst.
- If the packet arrives within a reasonable period of time, the
one-way packet-loss is taken to be zero.
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- If the packet fails to arrive within a reasonable period of time,
the one-way packet-loss is taken to be one. Note that the
threshold of "reasonable" here is a parameter of the methodology.
The Loss-Distance-Stream metric allows one to study the separation
between packet losses. This could be useful in determining a "spread
factor" associated with the packet loss rate. In conjunction, the
Loss-Period-Stream metric allows the study of loss burstiness for
each occurrence of loss. A single loss period of length 'n' can
account for a significant portion of the overall loss rate. Note
that it is possible to measure distance between loss bursts separated
by one or more successfully received packets. (Refer to Sections 6.4
and 6.5).
The proposed metrics can be used independent of the particular
sampling method used. We note that Poisson sampling may not yield
appropriate values for these metrics for certain real-time
applications such as voice over IP, as well as to TCP-based
applications. For real-time applications, it may be more appropriate
to use the ON-OFF [10] model, in which an ON period starts with a
certain probability 'p', during which a certain number of packets are
transmitted with mean 'lambda-on' according to geometric distribution
and an OFF period starts with probability '1-p' and lasts for a
period of time based on exponential distribution with rate 'lambda-
off'.
For TCP-based applications, one may use the model proposed in [8].
See [9] for an application of the model.
The measurement aspects, including the packet size, loss threshold,
type of the test machine chosen etc, invariably influence the packet
loss metric itself and hence the derived metrics described in this
document. Thus, when making an assessment of the results pertaining
to the metrics outlined in this document, attention must be paid to
these matters. See [1] for a detailed consideration of errors and
uncertainties regarding the measurement of base packet loss metric.
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Define loss of a packet to be "noticeable" [7] if the distance
between the lost packet and the previously lost packet is no greater
than delta, a positive integer, where delta is the "loss constraint".
Example: Let delta = 99. Let us assume that packet 50 is lost
followed by a bursty loss of length 3 starting from packet 125. All
the three losses starting from packet 125 are noticeable.
Given a Type-P-One-Way-Loss-Distance-Stream, this statistic can be
computed simply as the number of losses that violate some constraint
delta, divided by the number of losses. (Alternatively, it can also
be defined as the number of "noticeable losses" to the number of
successfully received packets). This statistic is useful when the
actual distance between successive losses is important. For example,
many multimedia codecs can sustain losses by "concealing" the effect
of loss by making use of past history information. Their ability to
do so degrades with poor history resulting from losses separated by
close distances. By choosing delta based on this sensitivity, one
can measure how "noticeable" a loss might be for quality purposes.
The noticeable loss requires a certain "spread factor" for losses in
the timeseries. In the above example where loss constraint is equal
to 99, a loss rate of one percent with a spread of 100 between losses
(e.g., 100, 200, 300, 400, 500 out of 500 packets) may be more
desirable for some applications compared to the same loss rate with a
spread that violates the loss constraint (e.g., 100, 175, 275, 290,
400: losses occurring at 175 and 290 violate delta = 99).
This represents the total number of loss periods, and can be derived
from the loss period metric Type-P-One-Way-Loss-Period-Stream as
follows:
Type-P-One-Way-Loss-Period-Total = maximum value of the first entry
of the set of pairs, <loss period, loss>, representing the loss
metric Type-P-One-Way-Loss-Period-Stream.
Note that this statistic does not describe the duration of each loss
period itself. If this statistic is large, it does not mean that the
losses are more spread out than they are otherwise; one or more loss
periods may include bursty losses. This statistic is generally
useful in gathering first order approximation of loss spread.
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This statistic is a sequence of pairs <loss period, length>, with the
"loss period" entry ranging from 1 - Type-P-One-Way-Loss-Period-
Total. Thus the total number of pairs in this statistic equals
Type-P-One-Way-Loss-Period-Total. In each pair, the "length" is
obtained by counting the number of pairs, <loss period, loss>, in the
metric Type-P-One-Way-Loss-Period-Stream which have their first entry
equal to "loss period."
Since this statistic represents the number of packets lost in each
loss period, it is an indicator of burstiness of each loss period.
In conjunction with loss-period-total statistic, this statistic is
generally useful in observing which loss periods are potentially more
influential than others from a quality perspective.
This statistic measures distance between successive loss periods. It
takes the form of a set of pairs <loss period, inter-loss-period-
length>, with the "loss period" entry ranging from 1 - Type-P-One-
Way-Loss-Period-Total, and "inter-loss-period-length" is the loss
distance between the last packet considered lost in "loss period"
'i-1', and the first packet considered lost in "loss period" 'i',
where 'i' ranges from 2 to Type-P-One-Way-Loss-Period-Total. The
"inter-loss-period-length" associated with the first "loss period" is
defined to be zero.
This statistic allows one to consider, for example, two loss periods
each of length greater than one (implying loss burst), but separated
by a distance of 2 to belong to the same loss burst if such a
consideration is deemed useful. When the Inter-Loss-Period-Length
between two bursty loss periods is smaller, it could affect the loss
concealing ability of multimedia codecs since there is relatively
smaller history. When it is larger, an application may be able to
rebuild its history which could dampen the effect of an impending
loss (period).
We continue with the same example as in Section 5.4.3. The three
statistics defined above will have the following values.
- Let delta = 2. In Type-P-One-Way-Loss-Distance-Stream
{<0,0>,<0,1>,<0,0>,<0,0>,<3,1>,<0,0>,<2,1>,<0,0>,<2,1>,<1,1>},
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there are 3 loss distances that violate the delta of 2. Thus,
Type-P-One-Way-Loss-Noticeable-Rate = 3/5 ((number of noticeable
losses)/(number of total losses))
- In Type-P-One-Way-Loss-Period-Stream
{<0,0>,<1,1>,<0,0>,<0,0>,<2,1>,<0,0>,<3,1>,<0,0>,<4,1>,<4,1>},
the largest of the first entry in the sequence of <loss
period,loss> pairs is 4. Thus,
Type-P-One-Way-Loss-Period-Total = 4
- In Type-P-One-Way-Loss-Period-Stream
{<0,0>,<1,1>,<0,0>,<0,0>,<2,1>,<0,0>,<3,1>,<0,0>,<4,1>,<4,1>},
the lengths of individual loss periods are 1, 1, 1 and 2
respectively. Thus,
Type-P-One-Way-Loss-Period-Lengths =
{<1,1>,<2,1>,<3,1>,<4,2>}
- In Type-P-One-Way-Loss-Period-Stream
{<0,0>,<1,1>,<0,0>,<0,0>,<2,1>,<0,0>,<3,1>,<0,0>,<4,1>,<4,1>},
the loss periods 1 and 2 are separated by 3 (5-2), loss periods 2
and 3 are separated by 2 (7-5), and 3 and 4 are separated by 2
(9-7). Thus, Type-P-One-Way-Inter-Loss-Period-Lengths =
{<1,0>,<2,3>,<3,2>,<4,2>}
Conducting Internet measurements raises both security and privacy
concerns. This document does not specify a particular implementation
of metrics, so it does not directly affect the security of the
Internet nor of applications which run on the Internet. However,
implementations of these metrics must be mindful of security and
privacy concerns.
The derived sample metrics in this document are based on the loss
metric defined in RFC 2680 [1], and thus they inherit the security
considerations of that document. The reader should consult [1] for a
more detailed treatment of security considerations. Nevertheless,
there are a few things to highlight.
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The lambda specified in the Type-P-Loss-Distance-Stream and Type-P-
Loss-Period-Stream controls the rate at which test packets are sent,
and therefore if it is set inappropriately large, it could perturb
the network under test, cause congestion, or at worst be a denial-
of-service attack to the network under test. Legitimate measurements
must have their parameters selected carefully in order to avoid
interfering with normal traffic in the network.
Privacy of user data is not a concern, since the underlying metric is
intended to be implemented using test packets that contain no user
information. Even if packets contained user information, the derived
metrics do not release data sent by the user.
Results could be perturbed by attempting to corrupt or disrupt the
underlying stream, for example adding extra packets that look just
like test packets. To ensure that test packets are valid and have
not been altered during transit, packet authentication and integrity
checks, such as a signed cryptographic hash, MAY be used.
Matt Zekauskas provided insightful feedback and the text for the
Security Considerations section. Merike Kao helped revising the
Security Considerations and the Abstract to conform with RFC
guidelines. We thank both of them. Thanks to Guy Almes for
encouraging the work, and Vern Paxson for the comments during the
IETF meetings. Thanks to Steve Glass for making the presentation at
the Oslo meeting.
[1] Almes, G., Kalindindi, S. and M. Zekauskas, "A One-way Packet
Loss Metric for IPPM", RFC 2680, September 1999.
[2] Bradner, S., "Key words for use in RFCs to Indicate Requirement
Levels", BCP 14, RFC 2119, March 1997.
Koodli & Ravikanth Informational [Page 12]
RFC 3357 One-way Loss Pattern Sample Metrics August 2002
[3] Paxson, V., Almes, G., Mahdavi, J. and M. Mathis, "Framework for
IP Performance Metrics", RFC 2330, May 1998.
[4] J.-C. Bolot and A. vega Garcia, "The case for FEC-based error
control for Packet Audio in the Internet", ACM Multimedia
Systems, 1997.
[5] M. S. Borella, D. Swider, S. Uludag, and G. B. Brewster,
"Internet Packet Loss: Measurement and Implications for End-
to-End QoS," Proceedings, International Conference on Parallel
Processing, August 1998.
[6] M. Handley, "An examination of MBONE performance", Technical
Report, USC/ISI, ISI/RR-97-450, July 1997
[7] R. Koodli, "Scheduling Support for Multi-tier Quality of Service
in Continuous Media Applications", PhD dissertation, Electrical
and Computer Engineering Department, University of
Massachusetts, Amherst, MA 01003, September 1997.
[8] J. Padhye, V. Firoiu, J. Kurose and D. Towsley, "Modeling TCP
throughput: a simple model and its empirical validation", in
Proceedings of SIGCOMM'98, 1998.
[9] J. Padhye, J. Kurose, D. Towsley and R. Koodli, "A TCP-friendly
rate adjustment protocol for continuous media flows over best-
effort networks", short paper presentation in ACM SIGMETRICS'99.
Available as Umass Computer Science tech report from
ftp://gaia.cs.umass.edu/pub/Padhye98-tcp-friendly-TR.ps.gz
[10] K. Sriram and W. Whitt, "Characterizing superposition arrival
processes in packet multiplexers for voice and data", IEEE
Journal on Selected Areas of Communication, pages 833-846,
September 1986,
[11] M. Yajnik, J. Kurose and D. Towsley, "Packet loss correlation in
the MBONE multicast network", Proceedings of IEEE Global
Internet, London, UK, November 1996.
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Authors' Addresses
Rajeev Koodli
Communications Systems Lab
Nokia Research Center
313 Fairchild Drive
Mountain View, CA 94043
USA
Phone: +1-650 625-2359
Fax: +1 650 625-2502
EMail: rajeev.koodli@nokia.com
Rayadurgam Ravikanth
Axiowave Networks Inc.
200 Nickerson Road
Marlborough, MA 01752
USA
EMail: rravikanth@axiowave.com
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