Network Working Group D. Newman
Internet-Draft Network Test
Expires: August 13, 2006 T. Player
Spirent Communications
February 9, 2006
Hash and Stuffing: Overlooked Factors in Network Device Benchmarking
draft-ietf-bmwg-hash-stuffing-05.txt
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Copyright Notice
Copyright (C) The Internet Society (2006).
Abstract
Test engineers take pains to declare all factors that affect a given
measurement, including intended load, packet length, test duration,
and traffic orientation. However, current benchmarking practice
overlooks two factors that have a profound impact on test results.
First, existing methodologies do not require the reporting of
addresses or other test traffic contents, even though these fields
can affect test results. Second, "stuff" bits and bytes inserted in
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test traffic by some link-layer technologies add significant and
variable overhead, which in turn affects test results. This document
describes the effects of these factors; recommends guidelines for
test traffic contents; and offers formulas for determining the
probability of bit- and byte-stuffing in test traffic.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. General considerations . . . . . . . . . . . . . . . . . . . . 5
3.1. Repeatability . . . . . . . . . . . . . . . . . . . . . . 5
3.2. Randomness . . . . . . . . . . . . . . . . . . . . . . . . 5
4. Packet Content Variations . . . . . . . . . . . . . . . . . . 6
4.1. Problem Statement . . . . . . . . . . . . . . . . . . . . 6
4.2. Ethernet MAC Addresses . . . . . . . . . . . . . . . . . . 7
4.2.1. Randomized Sets of MAC Addresses . . . . . . . . . . . 8
4.3. MPLS Addressing . . . . . . . . . . . . . . . . . . . . . 10
4.4. Network-layer Addressing . . . . . . . . . . . . . . . . . 10
4.5. Transport-layer Addressing . . . . . . . . . . . . . . . . 11
4.6. Application-layer Patterns . . . . . . . . . . . . . . . . 11
5. Control Character Stuffing . . . . . . . . . . . . . . . . . . 12
5.1. Problem Statement . . . . . . . . . . . . . . . . . . . . 12
5.2. PPP Bit Stuffing . . . . . . . . . . . . . . . . . . . . . 12
5.2.1. Calculating Bit-Stuffing Probability . . . . . . . . . 15
5.2.2. Bit Stuffing for Finite Strings . . . . . . . . . . . 16
5.2.3. Applied Bit Stuffing . . . . . . . . . . . . . . . . . 17
5.3. POS Byte Stuffing . . . . . . . . . . . . . . . . . . . . 17
5.3.1. Nullifying ACCM . . . . . . . . . . . . . . . . . . . 18
5.3.2. Other Stuffed Characters . . . . . . . . . . . . . . . 18
5.3.3. Applied Byte Stuffing . . . . . . . . . . . . . . . . 18
6. Security Considerations . . . . . . . . . . . . . . . . . . . 20
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 21
8. References . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.1. Normative References . . . . . . . . . . . . . . . . . . . 22
8.2. Informative References . . . . . . . . . . . . . . . . . . 22
Appendix A. Acknowledgements . . . . . . . . . . . . . . . . . . 23
Appendix B. Proof of Formula for Finite Bit Stuffing . . . . . . 24
Appendix C. Explicit Calculation of Bit Stuffing Overhead . . . . 25
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 27
Intellectual Property and Copyright Statements . . . . . . . . . . 28
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1. Introduction
Experience in benchmarking networking devices suggests that the
contents of test traffic can have a profound impact on test results.
For example, some devices may forward randomly addressed traffic
without loss, but drop significant numbers of packets when offered
packets containing nonrandom addresses.
Methodologies such as [RFC2544] and [RFC2889] do not require any
declaration of packet contents. These methodologies do require the
declaration of test parameters such as traffic distribution and
traffic orientation, and yet packet contents can have at least as
great an impact on test results as the other factors. Variations in
packet contents also can lead to non-repeatability of test results:
Two individuals may follow methodology procedures to the letter, and
still obtain very different results.
A related issue is the insertion of stuff bits or bytes by link-layer
technologies using PPP with HDLC-like framing. This stuffing is done
to ensure sequences in test traffic will not be confused with flag or
control characters.
Stuffing adds significant and variable overhead. Currently there is
no standard method for determining the probability that stuffing will
occur for a given pattern, and thus no way to determine what impact
stuffing will have on test results.
This document covers two areas. First, we discuss strategies for
dealing with randomness and nonrandomness in test traffic. Second,
we present formulas to determine the probability of bit- and byte-
stuffing on PPP and POS circuits. In both areas, we provide
recommendations for obtaining more repeatability in test results.
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2. Requirements
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
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3. General considerations
3.1. Repeatability
Repeatability is a desirable trait in benchmarking, but it can be an
elusive goal. It is a common but mistaken belief that test results
can always be reproduced provided the device under test and test
instrument are configured identically for each test iteration. In
fact, even identical configurations may introduce some variations in
test traffic, such as changes in timestamps, TCP sequence numbers, or
other naturally occurring phenomena.
While this variability does not necessarily invalidate test results,
it is important to recognize such variation exists. Exact bit-for-
bit reproduction of test traffic in all cases is a hard problem. A
simpler approach is to acknowledge that some variation exists,
characterize that variation, and describe it when analyzing test
results.
3.2. Randomness
This document recommends the use of pseudorandom patterns in test
traffic under controlled lab conditions. The rand() functions
available in many programming languages produce output that is
pseudorandom rather than truly random. Pseudorandom patterns are
sufficient for the recommendations given in this document, provided
they produce output that is uniformly distributed across the pattern
space.
Specifically, for any random bit pattern of length L, the probability
of generating that specific pattern SHOULD equal 1 over 2 to the Lth
power.
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4. Packet Content Variations
4.1. Problem Statement
The contents of test traffic can have a significant impact on metrics
such as throughput, jitter, latency, and loss. For example, many
network devices feed addresses into a hashing algorithm to determine
which path upon which to forward a given packet.
Consider the simple case of an Ethernet switch with eight network
processors (NPs) in its switching fabric:
ingress
||
\/
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ___ ___ ___ ___ ___ ___ ___ ___ |
|| | | | | | | | | | | | | | | | |
||NP0| |NP1| |NP2| |NP3| |NP4| |NP5| |NP6| |NP7| |
||___| |___| |___| |___| |___| |___| |___| |___| |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
||
\/
egress
To assign incoming traffic to the various NPs, suppose a hashing
algorithm performs an exclusive-or (XOR) operation on the least
significant 3 bits of the source and destination MAC addresses in
each frame. (This is an actual example the authors have observed in
multiple devices from multiple manufacturers.)
In theory, a random distribution of source and destination MAC
addresses should result in traffic being uniformly distributed across
all eight NPs. (Instances of the term "random" in this document
refer to a random uniform distribution across a given address space.
Section 3.2 describes random uniform distributions in more detail.)
In practice, the actual outcome of the hash (and thus any test
results) will be very different depending on the degree of randomness
in test traffic.
Suppose the traffic is nonrandom so that every interface of the test
instrument uses this pattern in its source MAC addresses:
00:00:PP:00:00:01
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where PP is the source interface number of the test instrument.
In this case, the least significant 3 bits of every source and
destination MAC address are 001, regardless of interface number.
Thus, the outcome of the XOR operation will always be 0, given the
same three least significant bits:
001 ^ 001 = 000
Thus, the switch will assign all traffic to NP0, leaving the other
seven NPs idle. Given a heavy enough load, NP0 and the switch will
become congested, even though seven other NPs are available. At
most, this device will be able to utilize approximately 12.5 percent
of its total capacity, with the remaining 87.5 percent of capacity
unused.
Now consider the same example with randomly distributed addresses.
In this case, the test instrument offers traffic using MAC addresses
with this pattern:
00:00:PP:00:00:RR
where PP is the source interface number of the test instrument and RR
is a pseudorandom number. In this case, there should be an equal
probability of the least significant 3 bits of the MAC address having
any value from 000 to 111 inclusive. Thus, the outcome of XOR
operations should be equally distributed from 0 to 7, and
distribution across NPs should also be equal (at least for this
particular 3-bit hashing algorithm). Absent other impediments, the
device should be able to utilize 100 percent of available bandwidth.
This simple example presumes knowledge on the tester's part of the
hashing algorithm used by the device under test. Knowledge of such
algorithms is not always possible beforehand, and in any event
violates the "black box" spirit of many documents produced by the
IETF BMWG.
Therefore, this memo adds a new consideration for benchmarking
methodologies, to select traffic patterns that overcome the effects
of non-randomness regardless of the hashing algorithms in use. The
balance of this section offers recommendations for test traffic
patterns to avoid these effects, starting at the link layer and
working up to the application layer.
4.2. Ethernet MAC Addresses
Test traffic SHOULD use pseudorandom patterns in Ethernet addresses.
The following source and destination Ethernet address pattern is
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RECOMMENDED for use when benchmarking Ethernet devices:
(RR & 0xFE):PP:PP:RR:RR:RR
where (RR & 0xFE) is a pseudorandom number bitwise ANDed with 0xFE,
PP:PP is the 1-indexed interface number of the test instrument and
RR:RR:RR is a pseudorandom number.
The bitwise ANDing of the high-order byte in the MAC address with
0xFE guarantees a non multicast address.
Test traffic SHOULD use PP:PP to identify the source interface number
of the test instrument. Such identification can be useful in
troubleshooting. Allocating 2 bytes of the MAC address for interface
identification allows for tests of up to 65,536 interfaces. A 2-byte
space allows for tests much larger than those currently used in
device benchmarking; however, tests involving more than 256
interfaces (fully utilizing a 1-byte space) are fairly common.
Note that the "PP:PP" designation refers to the source interface of
the test instrument, not the DUT/SUT. There are situations where the
DUT/SUT interface number may change during the test; one example
would be a test of wireless LAN roaming. By referring to the
(presumably static) source interface number of the test instrument,
test engineers can keep track of test traffic regardless of any
possible DUT/SUT changes.
Further, source interface numbers SHOULD be 1-indexed and SHOULD NOT
be 0-indexed. This avoids the low but nonzero probability of an
all-0s Ethernet address. Some devices will drop frames with all-0s
Ethernet addresses.
It is RECOMMENDED to use pseudorandom patterns in the least
significant 3 bytes of the MAC address. Using pseudorandom values
for the low-order 3 bytes means choosing one of 16.7 million unique
addresses. While this address space is vastly larger than is
currently required in lab benchmarking, it does assure more realistic
test traffic.
Note also that since only 31 of 48 bits in the MAC address have
pseudorandom values, there is no possibility of randomly generating a
broadcast or multicast value by accident.
4.2.1. Randomized Sets of MAC Addresses
It is common benchmarking practice for a test instrument to emulate
multiple hosts, even on a single interface. This is desirable in
assessing DUT/SUT scalability.
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However, test instruments may emulate multiple MAC addresses by
incrementing and/or decrementing addresses from a fixed starting
point. This leads to situations as described above in "Address
Pattern Variations" where hashing algorithms produce nonoptimal
outcomes.
The outcome can be nonoptimal even if the set of addresses begins
with a pseudorandom number. For example, the following source/
destination pairs will not be equally distributed by the 3-bit
hashing algorithm discussed above:
Source Destination
00:00:01:FC:B3:45 00:00:19:38:8C:80
00:00:01:FC:B3:46 00:00:19:38:8C:81
00:00:01:FC:B3:47 00:00:19:38:8C:82
00:00:01:FC:B3:48 00:00:19:38:8C:83
00:00:01:FC:B3:49 00:00:19:38:8C:84
00:00:01:FC:B3:4A 00:00:19:38:8C:85
00:00:01:FC:B3:4B 00:00:19:38:8C:86
00:00:01:FC:B3:4C 00:00:19:38:8C:87
Again working with our 3-bit XOR hashing algorithm, we get the
following outcomes:
101 ^ 000 = 101
110 ^ 001 = 111
111 ^ 010 = 101
000 ^ 011 = 011
001 ^ 100 = 101
010 ^ 101 = 111
011 ^ 110 = 101
100 ^ 111 = 011
Note that only three of eight possible outcomes are achieved when
incrementing addresses. This is actually the best case.
Incrementing from other combinations of pseudorandom address pairs
produces only one or two out of eight possible outcomes.
Every MAC address SHOULD be pseudorandom, not just the starting one.
When generating traffic with multiple addresses, it is RECOMMENDED
that all addresses use pseudorandom values. There are multiple ways
to use sets of pseudorandom numbers. One strategy would be for the
test instrument to iterate over an array of pseudorandom values
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rather than incrementing/decrementing from a starting address. The
actual method is an implementation detail; in the end, any method
that uses multiple addresses and avoids the undesired effects of
address processing in the DUT/SUT will be sufficient
4.3. MPLS Addressing
Similiar to L2 switches, MPLS routers make forwarding decisions based
on a 20 bit MPLS label. Unless specific labels are required, it is
RECOMMENDED that uniformly random values between 0 and 1,048,575 be
used for all labels assigned by test equipment.
4.4. Network-layer Addressing
When routers make forwarding decisions based solely on destination
network address, there may be no potential for hashing collision of
source and destination addresses, as in the case of Ethernet
switching discussed earlier. However, the potential still exists for
hashing collisions to exist at the network layer, and testers SHOULD
take this potential into consideration when crafting the network-
layer contents of test traffic.
For example, the equal cost multipath (ECMP) feature performs load-
sharing across multiple links. Routers implementing ECMP may perform
a hash of source and destination IP addresses in assigning flows.
Since multiple ECMP routes by definition have the same metric,
routers use some other "tiebreaker" mechanism to assign traffic to
each link. As far as the authors are aware, there is no standard
algorithm for ECMP link assignment. Some implementations perform a
hash of all bits of the source and destination IP addresses for this
purpose. Others may perform a hash on one or more bytes in the
source and destination IP addresses.
Just as in the case of MAC addresses, nonrandom IP addresses can have
an adverse effect on the outcome of ECMP link assignment decisions.
When benchmarking devices that implement ECMP or any other form of
Layer 3 aggregation, it is RECOMMENDED to use a randomly distributed
range of IP addresses. In particular, testers SHOULD NOT use
addresses that produce the undesired effects of address processing.
If, for example, a DUT can be observed to exhibit high packet loss
when offered IP network addresses that take the form x.x.1.x/24, and
relatively low packet loss when the source and destination network
addresses take the form of x.x.R.x/24 (where R is some random value
between 0 and 9), test engineers SHOULD use the random pattern.
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4.5. Transport-layer Addressing
Some devices with transport- or application-layer awareness use TCP
or UDP port numbers in making forwarding decisions. Examples of such
devices include load balancers and application-layer firewalls.
Test instruments have the capability of generating packets with
random TCP and UDP source and destination port numbers. Known
destination port numbers are often required for testing application-
layer devices. However, unless known port numbers are specifically
required for a test, it is RECOMMENDED to use randomly distributed
values for both source and destination port numbers.
In addition, it may be desirable to pick pseudorandom values from a
selected pool of numbers. Many services identify themselves through
use of reserved destination port numbers between 1 and 1023
inclusive. Unless specific port numbers are required, it is
RECOMMENDED to pick randomly distributed destination port numbers
between these lower and upper boundaries.
Similarly, clients typically choose source port numbers in the space
between 1024 and 65535 inclusive. Unless specific port numbers are
required, it is RECOMMENDED to pick randomly distributed source port
numbers between these lower and upper boundaries.
4.6. Application-layer Patterns
Many measurements require the insertion of application-layer
header(s) and payload into test traffic. Application-layer packet
contents offer additional opportunities for stuffing to occur, and
may also present nonrandom outcomes when fed through application
layer-aware hashing algorithms. Given the vast number of
application-layer protocols in use, we make no recommendation for
specific test traffic patterns to be used; however, test engineers
SHOULD be aware that application-layer traffic contents MAY produce
nonrandom outcomes with some hashing algorithms. The same issues
that apply with lower-layer traffic patterns also apply at the
application layer. As discussed in section 5, the potential for
stuffing exists with any part of a test packet, including
application-layer contents. For example, some traffic generators
insert fields into packet payloads to distinguish test traffic.
These fields may contain a transmission timestamp; sequence number;
test equipment interface identifier and/or "stream" number; and a CRC
over the contents of the test payload or test packet. All these
fields are potential candidates for stuffing.
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5. Control Character Stuffing
5.1. Problem Statement
Link-layer technologies that use HDLC-like framing may insert an
extra bit or byte before each instance of a control character in
traffic. These insertions prevent confusion with control characters,
but they may also introduce significant overhead.
The overhead of these escape sequences is problematic for two
reasons. First, explictly calculating the amount of overhead can be
non-trivial or even impossible for certain types of test traffic. In
such cases, the best testers can do is to characterize the
probability that an escape sequence will occur for a given pattern.
This greatly complicates the requirement of declaring exactly how
much traffic is offered to a DUT/SUT.
Second, in the absence of characterization and compensation for this
overhead, the tester may unwittingly congest the DUT/SUT. For
example, if a tester intends to offer traffic to a DUT at 95 percent
of line rate, but the link-layer protocol introduces an additional 1
percent of overhead to escape control characters, then the aggregate
offered load will be 96 percent of line rate. If the DUT's actual
channel capacity is only 95 percent, congestion will occur and the
DUT will drop traffic even though the tester did not intend this
outcome.
As described in [RFC1661] and [RFC1662], PPP and HDLC-like framing
introduce two kinds of escape sequences: bit and byte stuffing. Bit
stuffing refers to the insertion of an escape bit on bit-synchronous
links. Byte stuffing refers to the insertion of an escape byte on
byte-synchronous links. We discuss each in turn.
5.2. PPP Bit Stuffing
[RFC1662], section 5.2 specifies that any sequence of five contiguous
"1" bits within a frame must be escaped by inserting a "0" bit prior
to the sequence. This escaping is necessary to avoid confusion with
the HDLC control character 0x7E, which contains six "1" bits.
Consider the following PPP frame containing a TCP/IP packet. Not
shown is the 1-byte flag sequence (0x7E), at least one of which must
occur between frames.
The contents of the various frame fields can be described one of
three ways:
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1. Field contents never change over the test duration. An example
would be the IP version number.
2. Field contents change over the test duration. Some of these
changes are known prior to the test duration. An example would
be the use of incrementing IP addresses. Some of these changes
are unknown. An example would be a dynamically calculated field
such as the TCP checksum.
3. Field contents may not be known. An example would be proprietary
payload fields in test packets.
In the diagram below, 30 out of 48 total bytes in the packet headers
are subject to change over the test duration. Additionally, the
payload field could be subject to change both content and size. The
fields containing the changeable bytes are given in ((double
parentheses)).
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0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Address | Control | Protocol |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|Version| IHL |Type of Service| Total Length |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Identification |Flags| Fragment Offset |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Time to Live | Protocol | ((Header Checksum)) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ((Source Address)) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ((Destination Address)) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ((Source Port)) | ((Destination Port)) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ((Sequence Number)) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ((Acknowledgment Number)) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Data | |U|A|P|R|S|F| |
| Offset| Reserved |R|C|S|S|Y|I| ((Window)) |
| | |G|K|H|T|N|N| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ((Checksum)) | Urgent Pointer |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ ((payload)) /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| ((FCS (4 bytes) )) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
None of the other fields are known to contain sequences subject to
bit-stuffing, at least not in their entirety. Note that there is no
payload in this simple example; as noted in section 4.6, the payload
contents of test traffic often will present additional opportunities
for stuffing to occur, and MUST be taken into account when
calculating stuff probability.
Given the information at hand, and assuming static contents for the
rest of the fields, the challenge is to determine the probability
that bit-stuffing will occur.
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5.2.1. Calculating Bit-Stuffing Probability
In order to calculate bit-stuffing probabilities, we assume that for
any string of length L, where b_n represents the "n"th bit of the
string and 1 <= n <= L, the probability of b_n equalling "1" is 0.5
and the probability of b_n equalling "0" is 0.5. Additionally, the
value of b_n is independent of any other bits.
We can calculate the probability of bit-stuffing for both infinite
and finite strings of random bits. We begin with the infinite-string
case. For an infinitely long string of uniformly random bits, we
will need to insert a stuff bit if and only if state 5 is reached in
the following state table.
|--------------------<----------------------|
| |1
_______ __|__ _____ _____ _____ __|__
| | 1 | | 1 | | 1 | | 1 | | 1 | |
| start |--->| 1 |--->| 2 |--->| 3 |--->| 4 |--->| 5 |
|_______| |_____| |_____| |_____| |_____| |_____|
| | | | | | |
| |0 |0 |0 |0 |0 |0
|-<-|----<----|----<-----|----<-----|----<-----|----<-----|
Initially, we begin in the "start" state. A "1" bit moves us into
the next highest state, and a "0" bit returns us to the start state.
From state 5, a "1" bit takes us back to the 1 state and a "0" bit
returns us to "start." From this state table we can build the
following transition matrix:
\ To |
\ |
\ |
From \ | start 1 2 3 4 5
______\|_________________________________________________
start | 0.5 | 0.5 | 0.0 | 0.0 | 0.0 | 0.0
1 | 0.5 | 0.0 | 0.5 | 0.0 | 0.0 | 0.0
2 | 0.5 | 0.0 | 0.0 | 0.5 | 0.0 | 0.0
3 | 0.5 | 0.0 | 0.0 | 0.0 | 0.5 | 0.0
4 | 0.5 | 0.0 | 0.0 | 0.0 | 0.0 | 0.5
5 | 0.5 | 0.5 | 0.0 | 0.0 | 0.0 | 0.0
With this transition matrix we can build the following system of
equations. If P(x) represents the probability of reaching state x,
then:
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P(start) = 0.5 * P(start) + 0.5 * P(1) + 0.5 * P(2) + 0.5 * P(3) +
0.5 * P(4) + 0.5 * P(5)
P(1) = 0.5 * P(start) + 0.5 * P(5)
P(2) = 0.5 * P(1)
P(3) = 0.5 * P(2)
P(4) = 0.5 * P(3)
P(5) = 0.5 * P(4)
P(start) + P(1) + P(2) + P(3) + P(4) + P(5) = 1
Solving this system of equations yields:
P(start) = 0.5
P(1) = 8/31
P(2) = 4/31
P(3) = 2/31
P(4) = 1/31
P(5) = 1/62
Thus, for an infinitely long string of uniformly random bits, the
probability of any individual bit causing a transition to state 5,
and thus causing a stuff, is 1/62.
5.2.2. Bit Stuffing for Finite Strings
For a uniformly random finite bit string of length L, we can
explicitly count the number of bit-stuffs in the set of all possible
strings of length L. This count can then be used to calculate the
expected number of stuffs for the string.
Let f(L) represent the number of bit-stuffs in the set of all
possible strings of length L. Clearly, for 0 <= L <= 4, f(L) = 0 as
there are no strings of length 5. For L >= 5, f(L) = 2^(L-5) + (L-5)
* 2^(L-6) + f(L-5).
A proof of this formula can be found in Appendix A.
Now, the expected number of stuffing events, E[stuffs], can be found
by dividing the total number of stuffs in all possible strings by the
total number of strings. Thus for any L, E[stuffs] = f(L) / 2^L.
Similiarly, the probability that any particular bit is the cause of a
bit-stuff can be calculated by dividing the total number of stuffs in
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the set of all strings of length L by the total number of bits in the
set of all strings of length L. Hence for any L, the probability that
L_n, where 5 <= n <= L, caused a stuff is f(L) / (L * 2^L).
5.2.3. Applied Bit Stuffing
The amount of overhead attributable to bit-stuffing may be calculated
explicitly as long as the expected number of stuff bits per frame,
E[bit-stuffs] is known. For long uniformly random bit-strings,
E[bit-stuffs] may be approximated by multiplying the length of the
string by 1/62.
% overhead = E[bit-stuffs] / framesize (in bits)
Given that the overhead added by bit-stuffing is approximately 1 in
62, or 1.6 percent, it is RECOMMENDED that testers reduce the maximum
intended load by 1.6 percent to avoid introducing congestion when
testing devices using bit-synchronous interfaces (such as T1/E1,
DS-3, and the like).
The percentage given above is an approximation. For greatest
precision, the actual intended load SHOULD be explicitly calculated
from the test traffic.
Note that the DUT/SUT may be able to forward intended loads higher
than the calculated theoretical maximum rate without packet loss.
Such results are the result of queuing on the part of the DUT/SUT.
While a device's throughput may be above this level, delay-related
measurements may be affected. Accordingly, it is RECOMMENDED to
reduce offered levels by the amount of bit-stuffing overhead when
testing devices using bit-synchronous links. This recommendation
applies for all measurements, including throughput.
5.3. POS Byte Stuffing
[RFC1662] requires that "Each Flag Sequence, Control Escape octet,
and any octet which is flagged in the sending Async-Control-
Character-Map (ACCM), is replaced by a two octet sequence consisting
of the Control Escape octet followed by the original octet exclusive-
or'd with hexadecimal 0x20." The practical effect of this is to
insert a stuff byte for instances of up to 34 characters: 0x7E, 0x7D,
or any of 32 ACCM values.
A common implementation of PPP in HDLC-like framing is in PPP over
Sonet/SDH (POS), as defined in [RFC2615].
As with the bit-stuffing case, the requirement in characterizing POS
test traffic is to determine the probability that byte-stuffing will
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occur for a given sequence. This is much simpler to do than with
bit-synchronous links, since there is no possibility of overlap
across byte boundaries.
5.3.1. Nullifying ACCM
Testers can greatly reduce the probability of byte-stuffing by
configuring link partners to negotiate an ACCM value of 0x00. It is
RECOMMENDED that testers configure the test instrument(s) and DUT/SUT
to negotiate an ACCM value of 0x00 unless specific ACCM values are
required.
One instance where nonzero ACCM values are used is in the layer 2
tunneling protocol (L2TP), as defined in [RFC2661], section 4.4.6.
When the default ACCM values are used, the probability of stuffing
for any given random byte is 34 in 256, or approximately 13.3
percent.
5.3.2. Other Stuffed Characters
If an ACCM value of 0x00 is negotiated, the only characters subject
to stuffing are the flag and control escape characters. Thus, we can
say that without ACCM the probability of stuffing for any given
random byte is 2 in 256, or approximately 0.8 percent.
5.3.3. Applied Byte Stuffing
The amount of overhead attributable to byte stuffing may be
calculated explicitly as long as the expected number of stuff bytes
per frame, E[byte-stuffs], is known. For long uniformly random byte-
strings, E[byte-stuffs] may be approximated by multiplying the length
of the string by the probability that any single byte is a stuff
byte.
% overhead = E[byte-stuffs] / framesize (in bytes)
When testing a DUT/SUT that implements PPP in HDLC-like framing and
L2TP (or any other technology that uses nonzero ACCM values), it is
RECOMMENDED that testers reduce the maximum intended load by 13.3
percent to avoid introducing congestion.
When testing a DUT/SUT that implements PPP in HDLC-like framing and
an ACCM value of 0x00, it is RECOMMENDED that testers reduce the
maximum offered load by 0.8 percent to avoid introducing congestion.
Note that the percentages given above are approximations. For
greatest precision, the actual intended load SHOULD be explictly
calculated from the test traffic
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Note also that the DUT/SUT may be able to forward intended loads
higher than the calculated theoretical maximum rate without packet
loss. Such results are the result of queuing on the part of the DUT/
SUT. While a device's throughput may be above this level, delay-
related measurements may be affected. Accordingly, it is RECOMMENDED
to reduce offered levels by the amount of byte-stuffing overhead when
testing devices using byte-synchronous links. This recommendation
applies for all measurements, including throughput.
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6. Security Considerations
This document recommends the use of pseudorandom patterns in test
traffic. The rand() functions of many programming languages produce
output that is pseudorandom rather than truly random. As far as the
authors are aware, pseudorandom patterns are sufficient for
generating test traffic in lab conditions.
[RFC2615], section 6, discusses a denial-of-service attack involving
the intentional transmission of characters that require stuffing.
This attack could consume up to 100 percent of available bandwidth.
However, the test networks described in BMWG documents generally
SHOULD NOT be reachable by anyone other than the tester(s).
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7. IANA Considerations
This document has no actions for IANA.
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8. References
8.1. Normative References
[RFC1661] Simpson, W., "The Point-to-Point Protocol (PPP)", STD 51,
RFC 1661, July 1994.
[RFC1662] Simpson, W., "PPP in HDLC-like Framing", STD 51, RFC 1662,
July 1994.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2544] Bradner, S. and J. McQuaid, "Benchmarking Methodology for
Network Interconnect Devices", RFC 2544, March 1999.
[RFC2615] Malis, A. and W. Simpson, "PPP over SONET/SDH", RFC 2615,
June 1999.
[RFC2661] Townsley, W., Valencia, A., Rubens, A., Pall, G., Zorn,
G., and B. Palter, "Layer Two Tunneling Protocol "L2TP"",
RFC 2661, August 1999.
[RFC2889] Mandeville, R. and J. Perser, "Benchmarking Methodology
for LAN Switching Devices", RFC 2889, August 2000.
8.2. Informative References
[Ca63] Campbell, D. and J. Stanley, "Experimental and Quasi-
Experimental Designs for Research", 1963.
[Go97] Goralski, W., "SONET: A Guide to Synchronous Optical
Networks", 1997.
[Kn97] Knuth, D., "The Art of Computer Programming, Volume 2, Third
Edition", 1997.
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Appendix A. Acknowledgements
The authors gratefully acknowledge reviews and contributions by Len
Ciavattone, Robert Craig, John Dawson, Neil Carter, Glenn Chagnot,
Kevin Dubray, Rafael Francis, Paul Hoffman, David Joyner, Al Morton,
Joe Perches, Scott Poretsky, and Kris Rousey.
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Appendix B. Proof of Formula for Finite Bit Stuffing
We would like to construct a function, f(L), that allows us to
explictly count the total number of bit-stuffs in the set of all
strings of length L. Let S represent a bit string of length L.
Additionally, let b_n be the nth bit of string S where 1 <= n <= L.
Clearly, when 0 <= L <= 4, f(L) = 0, as there can be no possible bit-
stuff if there are < 5 bits.
Suppose L >= 5, then there are some number of strings that will cause
stuffing events. Let us count them.
We begin by counting the number of strings that will cause at least
one bit-stuff. Let us suppose that the first 5 bits, b_1,...,b_5,
cause a stuffing event. Then, there are (L-5) bits that could have
any value, i.e. the bits in position b_6 to b_L. So, there must be
2^(L-5) strings where the first 5 bits cause a stuff.
Now suppose that some other sequence of bits cause a stuff, b_n to
b_(n+4) for some 1 < n <= L-4. In order to guarantee that b_n starts
a stuff sequence, b_(n-1) must be 0, otherwise a stuff could occur at
b_(n+3). Thus, there are a total of 6 bits which must have fixed
values in the string, S, and a total of L-6 bits which do not have
fixed values. Hence, for each value of n, there are 2^(L-6) possible
strings with at least one bit-stuff for a total of (L-5) * 2^(L-6)
So, given a string of length L, where L >= 5, we know that there are
2^(L-5) + (L-5) * 2^(L-6) strings which will be transmitted with at
least one stuffed bit. However, if L >= 10, then there could be more
than one bit-stuff within the string S. Let Z represent a sequence of
5 sequential ones bits. Consider the bit string ..., b_n, b_(n+1),
b_(n+2), Z, b_(n+8), b_(n+9), ... where 1 <= n <= L-9. For the above
sequence of bits to generate two stuffing events, there must be at
least one run of five sequential one's bits in ..., b_n, b_(n+1),
b_(n+2), b_(n+8), b_(n+9), ... Note that the position of Z in the
above squence is irrelevant when looking for bit-stuffs.
Additionally, we've already determined that the number of strings
with at least one stuff in a bit string of length L is 2^(L-5) +
(L-5) * 2^(L-6). Thus, the total number of stuffing events in the
set of all bit strings of length L can be represented as f(L) =
2^(L-5) + (L-5) * 2^(L-6) + f(L-5) for all L >= 5.
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Appendix C. Explicit Calculation of Bit Stuffing Overhead
Consider a scenario where a tester is transmitting test frames across
a bit synchronous link. The test traffic has the following
parameters (values are in decimal):
+----------------------+-----------------------------+
| Field | Value |
+----------------------+-----------------------------+
| IP Version | 4 |
| | |
| IP Header Length | 5 |
| | |
| TOS | 0 |
| | |
| Datagram Length | 1028 |
| | |
| ID | 0 |
| | |
| Flags/Fragments | 0 |
| | |
| TTL | 64 |
| | |
| Protocol | 17 |
| | |
| Source IP | 192.168.13.1-192.168.13.254 |
| | |
| Destination IP | 192.168.1.10 |
| | |
| Source UDP Port | pseudorandom port |
| | |
| Destination UDP Port | pseudorandom port |
| | |
| UDP Length | 1008 |
| | |
| Payload | 1000 pseudorandom bytes |
+----------------------+-----------------------------+
We want to calculate the expected number of stuffs per packet, or
E[packet stuffs].
First, we observe that we have 254 different IP headers to consider,
and secondly, that the changing 4th octet in the IP source addresses
will produce occasional bit-stuffing events, so we must enumerate
these occurances. Additionally, we must take into account that the
3rd octet of the source IP and the first octet of the destination IP
will affect stuffing occurences.
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An exhaustive search shows that cycling through all 254 headers
produces 51 bit stuffs for the destination IP address. This gives us
an expectation of 51/254 stuffs per packet due to the changing source
IP address.
For the IP CRC, we observe that the value will decrement as the
source IP is incremented. A little calculation shows that the CRC
values for these headers will fall in the range of 0xE790 to 0xE88F.
Additionally, both the protocol and source IP address must be
considered, as they provide a source of extra leading and trailing
ones bits.
An exhaustive search shows that cycling through all 254 headers will
produce 102 bit stuffs for the CRC. This gives us an expectation of
102/254 stuffs per packet due to the CRC.
Since our destination IP address is even and the UDP length is less
than 32768, the random source and destination ports provide 32 bits
of sequential random data without forcing us to consider the boundry
bits. Additionally, we will assume that since our payload is
pseudorandom, our UDP CRC will be too. The even UDP length field
again allows us to only consider the bits explicitly contained within
the CRC and data fields. So, using the forumla for the expected
number of stuffs in a finite string from section 5.2.2, we determine
that E[UDP stuffs] = f(32)/2^32 + f(8000+16)/2^(8000+16). Now,
f(32)/2^32 is calculatable without too much difficulty and is
approximately 0.465. However, f(8016)/2^8016 is a little large to
calculate easily, so we will approximate this value by using the
probability value obtained in section 5.2.1. Thus, E[UDP] ~ 0.465 +
8016/62 ~ 129.755.
Hence, E[packet stuffs] = 51/254 + 102/254 + 129.755 = 130.357.
However, since we cannot have a fractional stuff, we round down to
130. Thus, we expect 130 stuffs per packet.
Finally, we can calculate bit-stuffing overhead by dividing the
expected number of stuff bits by the total number of bits in the IP
datagram. So, this example traffic would generate 1.58% overhead.
If our payload had consisted exclusively of zero bits, our overhead
would have been 0.012%. An all ones payload would produce 19.47%
overhead.
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Authors' Addresses
David Newman
Network Test
Email: dnewman@networktest.com
Timmons C. Player
Spirent Communications
Email: timmons.player@spirentcom.com
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