





Network Working Group                                          D. Newman
Request for Comments: 4814                                  Network Test
Category: Informational                                        T. Player
                                                  Spirent Communications
                                                              March 2007


  Hash and Stuffing: Overlooked Factors in Network Device Benchmarking

Status of This Memo

   This memo provides information for the Internet community.  It does
   not specify an Internet standard of any kind.  Distribution of this
   memo is unlimited.

Copyright Notice

   Copyright (C) The IETF Trust (2007).

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
   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.


















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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Requirements . . . . . . . . . . . . . . . . . . . . . . . . .  3
   3.  General Considerations . . . . . . . . . . . . . . . . . . . .  4
     3.1.  Repeatability  . . . . . . . . . . . . . . . . . . . . . .  4
     3.2.  Randomness . . . . . . . . . . . . . . . . . . . . . . . .  4
   4.  Packet Content Variations  . . . . . . . . . . . . . . . . . .  5
     4.1.  Problem Statement  . . . . . . . . . . . . . . . . . . . .  5
     4.2.  IEEE 802 MAC Addresses . . . . . . . . . . . . . . . . . .  7
       4.2.1.  Randomized Sets of MAC Addresses . . . . . . . . . . .  8
     4.3.  MPLS Addressing  . . . . . . . . . . . . . . . . . . . . .  9
     4.4.  Network-layer Addressing . . . . . . . . . . . . . . . . .  9
     4.5.  Transport-Layer Addressing . . . . . . . . . . . . . . . . 10
     4.6.  Application-Layer Patterns . . . . . . . . . . . . . . . . 10
   5.  Control Character Stuffing . . . . . . . . . . . . . . . . . . 11
     5.1.  Problem Statement  . . . . . . . . . . . . . . . . . . . . 11
     5.2.  PPP Bit-Stuffing . . . . . . . . . . . . . . . . . . . . . 12
       5.2.1.  Calculating Bit-Stuffing Probability . . . . . . . . . 14
       5.2.2.  Bit-Stuffing for Finite Strings  . . . . . . . . . . . 15
       5.2.3.  Applied Bit-Stuffing . . . . . . . . . . . . . . . . . 16
     5.3.  POS Byte-Stuffing  . . . . . . . . . . . . . . . . . . . . 16
       5.3.1.  Nullifying ACCM  . . . . . . . . . . . . . . . . . . . 17
       5.3.2.  Other Stuffed Characters . . . . . . . . . . . . . . . 17
       5.3.3.  Applied Byte-Stuffing  . . . . . . . . . . . . . . . . 17
   6.  Security Considerations  . . . . . . . . . . . . . . . . . . . 18
   7.  Normative References . . . . . . . . . . . . . . . . . . . . . 19
   Appendix A.  Acknowledgements  . . . . . . . . . . . . . . . . . . 20
   Appendix B.  Proof of Formula for Finite Bit-Stuffing  . . . . . . 20
   Appendix C.  Explicit Calculation of Bit-Stuffing Overhead for
                IPv4  . . . . . . . . . . . . . . . . . . . . . . . . 21
   Appendix D.  Explicit Calculation of Bit-Stuffing Overhead for
                IPv6  . . . . . . . . . . . . . . . . . . . . . . . . 23
   Appendix E.  Terminology . . . . . . . . . . . . . . . . . . . . . 24

















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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 High-Level Data Link Control (HDLC)-like
   framing.  This stuffing is done to ensure sequences in test traffic
   will not be confused with 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 Point-to-Point Protocol (PPP) and Packet over SONET (POS)
   circuits.  In both areas, we provide recommendations for obtaining
   better repeatability in test results.

   Benchmarking activities as described in this memo are limited to
   technology characterization using controlled stimuli in a laboratory
   environment, using dedicated address space.

   The benchmarking network topology will be an independent test setup
   and MUST NOT be connected to devices that may forward the test
   traffic into a production network, or misroute traffic to the test
   management network.

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 recreated 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 common phenomena.

   While this variability does not necessarily invalidate test results,
   it is important to recognize the existing variation.  Exact bit-for-
   bit repeatability of test traffic is a hard problem.  A simpler
   approach is to acknowledge that some variation exists, characterize
   that variation, and describe it when analyzing test results.

   Another issue related to repeatability is the avoidance of randomness
   in test traffic.  For example, benchmarking experience with some IEEE
   802.11 devices suggests that nonrandom media access control (MAC) and
   IP addresses must be used across multiple trials.  Although this
   would seem to contradict some recommendations made in this document,
   in fact either nonrandom or pseudorandom patterns may be more
   desirable depending on the test setup.  There are also situations
   where it may be desirable to use combinations of the two, for example
   by generating pseudorandom traffic patterns for one test trial and
   then re-using the same pattern across all trials.  The keywords in
   this document are RECOMMENDs and not MUSTs with regard to the use of
   pseudorandom test traffic patterns.

   Note also that this discussion covers only repeatability, which is
   concerned with variability of test results from trial to trial on the
   same test bed.  A separate concern is reproducibility, which refers
   to the precision of test results obtained from different test beds.
   Clearly, reproducibility across multiple test beds requires
   repeatability on a single test bed.

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.




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   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.

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
   upon which path 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.







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   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

   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 capacity.

   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 Benchmarking Working Group (BMWG).

   Therefore, this memo adds a new consideration for benchmarking
   methodologies to select traffic patterns that overcome the effects of
   nonrandomness, 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.



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4.2.  IEEE 802 MAC Addresses

   Test traffic SHOULD use pseudorandom patterns in IEEE 802 MAC
   addresses.  The following source and destination MAC address pattern
   is RECOMMENDED:

      (RR & 0xFC):PP:PP:RR:RR:RR

   where (RR & 0xFC) is a pseudorandom number bitwise ANDed with 0xFC,
   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
   0xFC sets the low-order two bits of that byte to 0, guaranteeing a
   non-multicast address and a non locally administered address.  Note
   that the resulting addresses may violate IEEE 802 standards by using
   organizationally unique identifiers (OUIs) not assigned to the test
   port manufacturer.  However, since these addresses will be used only
   on isolated test networks there should be no possibility of mistaken
   identity.

   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 device under test/system under test
   (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 zero-indexed.  This avoids the low but nonzero probability of an
   all-zeros MAC address.  Some devices will drop frames with all-zeros
   MAC 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.



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   Note also that since only 30 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.

   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.




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   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
   rather than incrementing/decrementing from a starting address.  The
   actual method is an implementation detail; in the end, any method
   that uses multiple addresses with pseudorandom patterns will be
   sufficient.

   Experience with benchmarking of IEEE 802.11 devices suggests
   suboptimal test outcomes may result if different pseudorandom MAC and
   IP addresses are used from trial to trial.  In such cases (not just
   for 802.11 but for any device using IEEE 802 MAC and IP addresses),
   testers MAY generate a pseudorandom set of MAC and IP addresses once,
   or MAY generate a nonrandom set of MAC and IP addresses once.  In
   either case, the same MAC and IP addresses MUST be used in all
   trials.

4.3.  MPLS Addressing

   Similar to L2 switches, multiprotocol label switching (MPLS) devices
   make forwarding decisions based on a 20-bit MPLS label.  Unless
   specific labels are required, it is RECOMMENDED that uniformly random
   values between 16 and 1,048,575 be used for all labels assigned by
   test equipment.  As per [RFC3032], this avoids using reserved MPLS
   labels in the range of 0-15 inclusive.

4.4.  Network-layer Addressing

   When routers make forwarding decisions based solely on the
   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 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 "tie-breaker" 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



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   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 IPv4 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.

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 pseudorandom and
   uniformly 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 49151
   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-



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   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
   cyclic redundancy check (CRC) over the contents of the test payload
   or test packet.  All these fields are potential candidates for
   stuffing.

5.  Control Character Stuffing

5.1.  Problem Statement

   Link-layer technologies that use High-Level Data Link Control (HDLC)-
   like framing may insert an extra bit or byte before each instance of
   a control character in traffic.  These "stuffing" insertions prevent
   confusion with control characters, but they may also introduce
   significant overhead.  Stuffing is data-dependent; thus, selection of
   different payload patterns will result in frames transmitted on the
   media that vary in length, even though the original frames may all be
   of the same length.

   The overhead of these escape sequences is problematic for two
   reasons.  First, explicitly 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.





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   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:

   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.



















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   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)).

    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.





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   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.

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 diagram 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





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   With this transition matrix we can build the following system of
   equations.  If P(x) represents the probability of reaching state x,
   then:

   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 B.

   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.





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   Similarly, the probability that any particular bit is the cause of a
   bit-stuff can be calculated by dividing the total number of stuffs in
   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.
   This results from 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].




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   As with the bit-stuffing case, the requirement in characterizing POS
   test traffic is to determine the probability that byte-stuffing will
   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 intended load by 0.8 percent to avoid introducing congestion.





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   Note that the percentages given above are approximations.  For
   greatest precision, the actual intended load SHOULD be explicitly
   calculated from the test traffic

   Note also that the DUT/SUT may be able to forward intended loads
   higher than the calculated theoretical maximum rate without packet
   loss.  This results from 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.

6.  Security Considerations

   This document recommends the use of pseudorandom patterns in test
   traffic.  This usage requires a uniform distribution, but does not
   have strict predictability requirements.  Although it is not
   sufficient for security applications, the rand() function of many
   programming languages may provide a uniform distribution that is
   usable for testing purposes in lab conditions.  Implementations of
   rand() may vary and provide different properties so test designers
   SHOULD understand the distribution created by the underlying function
   and how seeding the initial state affects its behavior.

   [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.  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.

   [RFC3032]  Rosen, E., Tappan, D., Fedorkow, G., Rekhter, Y.,
              Farinacci, D., Li, T., and A. Conta, "MPLS Label Stack
              Encoding", RFC 3032, January 2001.
























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Appendix A.  Acknowledgements

   The authors gratefully acknowledge reviews and contributions by Tom
   Alexander, Len Ciavattone, Robert Craig, John Dawson, Neil Carter,
   Glenn Chagnot, Kevin Dubray, Diego Dugatkin, Rafael Francis, Paul
   Hoffman, David Joyner, Al Morton, Joe Perches, Jerry Perser, Scott
   Poretsky, Dan Romascanu, and Kris Rousey.

Appendix B.  Proof of Formula for Finite Bit-Stuffing

   We would like to construct a function, f(L), that allows us to
   explicitly 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 is 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 causes 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 "1" 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 sequence 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



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   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.

Appendix C.  Explicit Calculation of Bit-Stuffing Overhead for IPv4

   Consider a scenario where a tester is transmitting IPv4 test packets
   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             |
           | Type of service (TOS) |             0             |
           | Datagram Length       |            1028           |
           | ID                    |             0             |
           | Flags/Fragments       |             0             |
           | Time to live (TTL)    |             64            |
           | Protocol              |             17            |
           | Source IP             | 192.18.13.1-192.18.13.254 |
           | Destination IP        |        192.18.1.10        |
           | 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 occurrences.  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 occurrences.

   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.





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   Additionally, both the protocol and source IP address must be
   considered, as they provide a source of extra leading and trailing
   "1" 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 boundary
   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 formula 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 calculable 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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Appendix D.  Explicit Calculation of Bit-Stuffing Overhead for IPv6

   Consider a scenario where a tester is transmitting IPv6 test packets
   across a bit-synchronous link.  The test traffic has the following
   parameters (values are in decimal except for IPv6 addresses, which
   are in hexadecimal):

        +----------------------+----------------------------------+
        | Field                |               Value              |
        +----------------------+----------------------------------+
        | IP Version           |                 6                |
        | Traffic Class        |                 0                |
        | Flow Label           |        pseudorandom label        |
        | Payload Length       |               1008               |
        | Next Header          |                17                |
        | Hop Limit            |                64                |
        | Source IP            | 2001:DB8:0:1::1-2001:DB8:0:1::FF |
        | Destination IP       |         2001:DB8:0:2::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 255 different IP headers to consider,
   and secondly, that the changing 4th quad in the IP source addresses
   will produce occasional bit-stuffing events, so we must enumerate
   these occurrences.  Additionally, we also note that since the first
   quad of the destination address has a leading zero bit, we do no have
   to consider these adjacent bits when calculating the number of bit-
   stuffs in the source IP address.

   An exhaustive search shows that cycling through all 255 headers
   produces 20 bit-stuffs for the source IP address.  This gives us an
   expectation of 20/255 stuffs per packet due to the changing source IP
   address.

   We also have to consider our pseudorandomly generated flow label.
   However, since our Traffic Class field is 0 and our Payload Length
   field is less than 32768 (and thus the leading bit of the Payload
   Length field is 0), we may consider the flow label as 20 bits of
   random data.  Thus the expectation of a stuff in the flow label is
   f(20)/2^20 ~ .272.





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   Similar to the flow label case above, the fourth quad of our
   destination IP address is even and the UDP length field is less than
   32768, so the random source and destination ports provide 32 bits of
   sequential random data without forcing us to consider the boundary
   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 formula 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 calculable 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 stuffs] ~
   0.465 + 8016/62 ~ 129.755.

   Now we may explicitly calculate that E[packet stuffs] = 20/255 +
   0.272 + 129.755 = 130.105.  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 1.55% overhead.
   If our payload had consisted exclusively of zero bits, our overhead
   would have been 0.010%.  An all-ones payload would produce 19.09%
   overhead.

Appendix E.  Terminology

   Hashing

   Also known as a hash function.  In the context of this document, an
   algorithm for transforming data for use in path selection by a
   networking device.  For example, an Ethernet switch with multiple
   processing elements might use the source and destination MAC
   addresses of an incoming frame as input for a hash function.  The
   hash function produces numeric output that tells the switch which
   processing element to use in forwarding the frame.

   Randomness

   In the context of this document, the quality of having an equal
   probability of any possible outcome for a given pattern space.  For
   example, if an experiment has N randomly distributed outcomes, then
   any individual outcome has a 1 in N probability of occurrence.





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   Repeatability

   The precision of test results obtained on a single test bed, but from
   trial to trial.  See also "reproducibility".

   Reproducibility

   The precision of test results between different setups, possibly at
   different locations.  See also "repeatability".

   Stuffing

   The insertion of a bit or byte within a frame to avoid confusion with
   control characters.  For example, RFC 1662 requires the insertion of
   a "0" bit prior to any sequence of five contiguous "1" bits within a
   frame to avoid confusion with the HDLC control character 0x7E.

Authors' Addresses

   David Newman
   Network Test

   EMail: dnewman@networktest.com


   Timmons C. Player
   Spirent Communications

   EMail: timmons.player@spirent.com






















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Full Copyright Statement

   Copyright (C) The IETF Trust (2007).

   This document is subject to the rights, licenses and restrictions
   contained in BCP 78, and except as set forth therein, the authors
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Acknowledgement

   Funding for the RFC Editor function is currently provided by the
   Internet Society.







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