Skip to main content

Datagram PLPMTUD for UDP Options
draft-ietf-tsvwg-udp-options-dplpmtud-04

The information below is for an old version of the document.
Document Type
This is an older version of an Internet-Draft whose latest revision state is "Active".
Authors Gorry Fairhurst , Tom Jones
Last updated 2023-01-10 (Latest revision 2022-09-09)
Replaces draft-fairhurst-tsvwg-udp-options-dplpmtud
RFC stream Internet Engineering Task Force (IETF)
Formats
Additional resources Mailing list discussion
Stream WG state In WG Last Call
Associated WG milestone
Dec 2023
Submit "Datagram PLPMTUD for UDP Options" for publication as a Proposed Standard RFC.
Document shepherd Marten Seemann
IESG IESG state I-D Exists
Consensus boilerplate Yes
Telechat date (None)
Responsible AD (None)
Send notices to martenseemann@gmail.com
draft-ietf-tsvwg-udp-options-dplpmtud-04
Internet Engineering Task Force                             G. Fairhurst
Internet-Draft                                                  T. Jones
Intended status: Standards Track                  University of Aberdeen
Expires: 13 March 2023                                  9 September 2022

                    Datagram PLPMTUD for UDP Options
                draft-ietf-tsvwg-udp-options-dplpmtud-04

Abstract

   This document specifies how a UDP Options sender implements Datagram
   Packetization Layer Path Maximum Transmission Unit Discovery
   (DPLPMTUD) as a robust method for Path Maximum Transmission Unit
   discovery.  This method uses the UDP Options packetization layer.  It
   allows a datagram application to discover the largest size of
   datagram that can be sent across a specific network path.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on 13 March 2023.

Copyright Notice

   Copyright (c) 2022 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.
   Please review these documents carefully, as they describe your rights
   and restrictions with respect to this document.  Code Components
   extracted from this document must include Revised BSD License text as
   described in Section 4.e of the Trust Legal Provisions and are
   provided without warranty as described in the Revised BSD License.

Fairhurst & Jones         Expires 13 March 2023                 [Page 1]
Internet-Draft                UDPO DPLPMTUD               September 2022

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Terminology . . . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  DPLPMTUD for UDP Options  . . . . . . . . . . . . . . . . . .   3
   4.  Sending UDP-Options Probe Packets . . . . . . . . . . . . . .   4
     4.1.  Sending Probe Packets using the Echo Request and Response
           Options . . . . . . . . . . . . . . . . . . . . . . . . .   4
     4.2.  DPLPMTUD Procedures for UDP Options . . . . . . . . . . .   5
       4.2.1.  Confirmation of Connectivity across a Path  . . . . .   5
       4.2.2.  Sending Probe Packets to Increase the PLPMTU  . . . .   6
       4.2.3.  Validating the Path with UDP Options  . . . . . . . .   6
       4.2.4.  Probe Packets that do not include Application Data  .   7
       4.2.5.  Probe Packets that include Application Data . . . . .   7
       4.2.6.  Changes in the Path . . . . . . . . . . . . . . . . .   7
     4.3.  PTB Message Handling for this Method  . . . . . . . . . .   8
   5.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   8
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   8
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .   8
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   9
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .   9
     8.2.  Informative References  . . . . . . . . . . . . . . . . .   9
   Appendix A.  Revision Notes . . . . . . . . . . . . . . . . . . .  10
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   The User Datagram Protocol [RFC0768] offers a minimal transport
   service on top of IP and is frequently used as a substrate for other
   protocols.  Section 3.5 of UDP Guidelines [RFC8085] recommends that
   applications implement some form of Path MTU discovery to avoid the
   generation of IP fragments:

   "Consequently, an application SHOULD either use the path MTU
   information provided by the IP layer or implement Path MTU Discovery
   (PMTUD)".

   The UDP API [RFC8304] offers calls for applications to receive ICMP
   Packet Too Big (PTB) messages and to control the maximum size of
   datagrams that are sent, but does not offer any automated mechanisms
   for an application to discover the maximum packet size supported by a
   path.  Upper layer protocols (which can include applications)
   implement mechanisms for Path MTU discovery above the UDP API.

   Packetization Layer Path MTU Discovery (PLPMTUD) [RFC4821] describes
   a method for a Packetization Layer (PL) (such as UDP Options) to
   search for the largest Packetization Layer PMTU (PLPMTU) supported on
   a path.  Datagram PLPMTUD (DPLPMTUD) [RFC8899] specifies this support

Fairhurst & Jones         Expires 13 March 2023                 [Page 2]
Internet-Draft                UDPO DPLPMTUD               September 2022

   for datagram transports.  PLPMTUD and DPLPMTUD gain robustness by
   using a probing mechanism that does not solely rely on ICMP PTB
   messages and works on paths that drop ICMP PTB messages.

   This document specifies how UDP Options [I-D.ietf-tsvwg-udp-options]
   can be used as a PL to implement DPLPMTUD (see Section 6.1 of
   [RFC8899]).  In summary, UDP Options [I-D.ietf-tsvwg-udp-options]
   supplies functionality that can be used to implement DPLPMTUD within
   the UDP transport service.  Implementing DPLPMTUD using UDP Options
   avoids the need for each upper layer protocol or application to
   implement the DPLPMTUD method.  This provides a standard method for
   applications to discover the current maximum packet size for a path
   and to detect when this changes.

2.  Terminology

   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 BCP 14 [RFC2119]
   [RFC8174] when, and only when, they appear in all capitals, as shown
   here.

   This document uses the terms defined for DPLPMTUD (see Sections 2 and
   5 of [RFC8899]

3.  DPLPMTUD for UDP Options

   There are two ways an upper PL can perform DPLPMTUD:

   *  The UDP Options sender implementing DPLPMTUD uses the method
      specified in [RFC8899] and the upper PL (or application) does not
      perform PMTU discovery.  In this case, UDP Options processing is
      responsible for sending probes to determine a PLPMTU, as described
      in this document.  "An application SHOULD avoid using DPLPMTUD
      when the underlying transport system provides this capability"
      (Section 6.1 of [RFC8899]).  This discovered PLPMTU can be used by
      UDP Options to either:

      -  set the maximum datagram size for the current path (based on
         the discovered largest IP packet that can be received across
         the current path).

      -  set the maximum fragment size when a sender uses the UDP
         Fragmentation Option to divide a datagram into multiple UDP
         fragments for transmission.  Each UDP fragment is then less
         than the discovered largest IP packet that can be received
         across the current path.

Fairhurst & Jones         Expires 13 March 2023                 [Page 3]
Internet-Draft                UDPO DPLPMTUD               September 2022

   *  An upper PL (or application) performs DPLPMTUD (e.g., QUIC
      [RFC9000]).  This upper PL then uses probes to determine a safe
      PLPMTU for the datagrams that it sends.  The format and content of
      any probe is determined by the upper PL.  Such a design should
      avoid performing discovery at multiple levels, so, when
      configurable, this upper PL SHOULD disable DPLPMTUD by UDP
      Options.

   The packet formats and procedures for DPLPMTUD using UDP Options are
   described in this document.

4.  Sending UDP-Options Probe Packets

   DPLPMTUD relies upon the ability of a UDP Options sender to generate
   a probe with a specific size, up to the maximum for the size
   supported by a local interface.  This MUST NOT be constrained by the
   maximum PMTU set by network layer mechanisms (such as PMTUD
   [RFC1191][RFC8201] or the PMTU size held in the IP- layer cache), as
   noted in bullet 2 of Section 3 in [RFC8899]).

   Probe packets consume network capacity and incur endpoint processing
   (see Section 4.1 of [RFC8899]).  Implementations ought to send a
   probe with an REQ Option only when required by their local DPLPMTUD
   state machine, i.e., when confirming the base PMTU for the path,
   probing to increase the PLPMTU or to confirm the current PLPMTU.

4.1.  Sending Probe Packets using the Echo Request and Response Options

   A UDP Options node that supports DPLPMTUD MUST support sending and
   receiving of the REQ Option and the RES Option.  When not supported,
   DPLPMTUD will be unable to confirm the Path or to discover the PMTU.

   [RFC8899] (Section 3, item 2) requires the network interface below
   the PL to provide a way to transmit a probe packet that is larger
   than the PLPMTU without network layer endpoint fragmentation.  This
   document adds to this: UDP datagrams used as DPLPMTUD probes as
   described in this document MUST NOT be fragmented at the UDP layer.

   This section describes a format of probe consisting of an empty UDP
   datagram, UDP Options area and Padding.

   A Probe Packet includes the UDP Options area containing a RES Option
   and any other required options concluded with an EOL Option followed
   by any padding needed to inflate to the required probe size.

   The UDP Options used in this document are described in Section 5.11
   of [I-D.ietf-tsvwg-udp-options]:

Fairhurst & Jones         Expires 13 March 2023                 [Page 4]
Internet-Draft                UDPO DPLPMTUD               September 2022

   *  The REQ Option is set by a sending PL to solicit a response from a
      remote UDP Options receiver.  A four-byte token identifies each
      request.

   *  The RES Option is generated by the UDP Options receiver in
      response to a previously received REQ Option.  Each RES Option
      echoes a previously received four-byte token.

   *  Reception of a RES Option confirms that a specific probe has been
      received by the remote UDP Options receiver.

   The token allows a sender to distinguish between acknowledgements for
   initial probes and acknowledgements confirming receipt of subsequent
   probes (e.g., travelling along alternate paths with a larger round
   trip time).  This needs each probe to be uniquely identifiable by the
   UDP Options sender within the Maximum Segment Lifetime (MSL).  The
   UDP Options sender therefore MUST NOT recycle token values until they
   have expired or have been acknowledged.  A four byte value for the
   token field provides sufficient space for multiple unique probes to
   be made within the MSL.  Since UDP Options operates over UDP, the
   token values only need to be unique for the specific 5-tuple over
   which DPLPMTUD is operating.

   The value of the four byte token field SHOULD be initialised to a
   randomised value to enhance protection from off-path attacks, as
   described in Section 5.1 of [RFC8085]).

   Like other UDP options, each of the two option kinds MUST NOT appear
   more than once in each UDP datagram.

4.2.  DPLPMTUD Procedures for UDP Options

   DPLPMTUD utilises three types of probes.  These are described in the
   following sections:

   *  A probe to confirm the path can support the BASE_PLPMTU (see
      Section 5.1.4 of [RFC8899]).

   *  A probe to detect whether the path can support a larger PLPMTU.

   *  A probe to validate the path supports the current PLPMTU.

4.2.1.  Confirmation of Connectivity across a Path

   The DPLPMTUD method requires a PL to confirm connectivity over the
   path using the BASE_PLPMTU (see Section 5.1.4 of [RFC8899]), but UDP
   does not offer a mechanism for this.

Fairhurst & Jones         Expires 13 March 2023                 [Page 5]
Internet-Draft                UDPO DPLPMTUD               September 2022

   UDP Options can provide this required functionality.  A UDP Options
   sender implementing this specification MUST elicit a positive
   confirmation of connectivity for the path, by sending a probe, padded
   to size BASE_PLPMTU.  This confirmation probe MUST include a UDP
   option that elicits a response from the remote endpoint (e.g., by
   including the RES and REQ Options) to confirm that a packet of the
   size traversed the path.  This also confirms that the remote receiver
   supports use of the RES and REQ Options.

4.2.2.  Sending Probe Packets to Increase the PLPMTU

   From time to time, DPLPMTUD enters the SEARCHING state [RFC8899]
   (e.g., after expiry of the PMTU_RAISE_TIMER) to detect whether the
   current path can support a larger PLPMTU.  When the remote endpoint
   advertises a UDP Maximum Segment Size (MSS) option, this value can be
   used as a hint to initialise this search to increase the PLPMTU.

   Probe packets seeking to increase the PLPMTU SHOULD NOT carry
   application data (see "Probing using padding data" in Section 4.1 of
   [RFC8899]), since they will be lost whenever their size exceeds the
   actual PMTU.

   A probe seeking to increase the PLPMTU needs to elicit a positive
   acknowledgment that the path has delivered a datagram of the specific
   probed size and, therefore, MUST include the REQ Option.

   Received probes that do not carry application data do not form a part
   of the end-to-end transport data and are not delivered to the upper
   layer protocol.

4.2.3.  Validating the Path with UDP Options

   A PL using DPLPMTUD needs to validate that a path continues to
   support the PLPMTU discovered in a previous search for a suitable
   PLPMTU value (see Section 6.1.4 of [RFC8899]).  This validation sends
   probes in the DPLPMTUD SEARCH_COMPLETE state to detect black-holing
   of data (see Section 4.2 of [RFC8899]).

   This function can be implemented within UDP Options, by generating a
   probe of size PLPMTU, which MUST include a REQ Option to elicit a
   positive confirmation whether the path has delivered the probe.  This
   confirmation probe MAY use "Probing using padding data" or "Probing
   using application data and padding data" (see Section 4.1 of
   [RFC8899]) or can construct a probe packet that does not carry any
   application data, as described in a previous section.

Fairhurst & Jones         Expires 13 March 2023                 [Page 6]
Internet-Draft                UDPO DPLPMTUD               September 2022

4.2.4.  Probe Packets that do not include Application Data

   A simple implementation of the method might be designed to only probe
   packets formed of a UDP datagram that include no application data.
   Each probe packet is padded to the required probe size including the
   REQ Option.  This implements "Probing using padding data"
   (Section 4.1 of [RFC8899]), and avoids having to retransmit
   application data when a probe fails.  In this use, the probe packets
   do not form a part of the end-to-end transport data and a receiver
   does not deliver them to the upper layer protocol.

4.2.5.  Probe Packets that include Application Data

   An implementation always uses the format in the previous section when
   DPLPMTUD searches to increase the PLPMTU.

   An alternative format is permitted for a probe that confirms
   connectivity or that validates the path.  These probes are permitted
   to carry application data.  (The data is permitted because these
   probes perform blackhole detection and will therefore usually have a
   higher probability of successful transmission, similar to other
   packets sent by the upper layer protocol.)  Section 4.1 of [RFC8899]
   provides a discussion of the merits and demerits of including
   application data.  For example, this reduces the need to send
   additional datagrams.

   The probe could utilise a control message format defined by the upper
   layer protocol that does not need to be delivered reliably.  The RES
   and REQ Options need to be included by the sending upper layer
   protocol and the values of the tokens need to be coordinated with
   values used for other DPLPMTUD probe packets.  The DPLPMTUD method
   tracks the transmission and reception of these probe packets.  Probes
   with this format form a part of the end-to-end transport data and a
   receiver needs to deliver the RES and REQ Options to the upper layer
   protocol.

4.2.6.  Changes in the Path

   A change in the path or the loss of probe packets can result in a
   change of the PLPMTU.  DPLPMTUD [RFC8899] recommends that methods are
   robust to path changes that could have occurred since the path
   characteristics were last confirmed and to the possibility of
   inconsistent path information being received.  For example, a
   notification that a path could have changed could trigger path
   validation to provide black hole protection Section 4.3 of
   [RFC8899]).

Fairhurst & Jones         Expires 13 March 2023                 [Page 7]
Internet-Draft                UDPO DPLPMTUD               September 2022

   Section 3 of [RFC8899] requires any methods designed to share the
   PLPMTU between PLs (such as updating the IP cache PMTU for an
   interface/destination) to be robust to the wide variety of underlying
   network forwarding behaviors.  For example, an implementation could
   avoid sharing PMTU information that could potentially relate to
   packets sent with the same address over a different interface.

4.3.  PTB Message Handling for this Method

   Support for receiving ICMP PTB messages is OPTIONAL for use with
   DPLPMTUD.  A UDP Options sender can therefore ignore received ICMP
   PTB messages.

   A UDP Options sender that utilises ICMP PTB messages received in
   response to a probe packet MUST use the quoted packet to validate the
   UDP port information in combination with the token contained in the
   UDP Option, before processing the packet using the DPLPMTUD method.
   Section 4.6.1 of [RFC8899] specifies this validation procedure.  An
   implementation unable to support this validation needs to ignore
   received ICMP PTB messages.

5.  Acknowledgements

   Gorry Fairhurst and Tom Jones are supported by funding provided by
   the University of Aberdeen.

6.  IANA Considerations

   This memo includes no requests to IANA.

7.  Security Considerations

   The security considerations for using UDP Options are described in
   [I-D.ietf-tsvwg-udp-options].  The proposed new method does not
   change the integrity protection offered by the UDP options method.

   The security considerations for using DPLPMTUD are described in
   [RFC8899].  On path attackers could maliciously drop or modify probe
   packets to seek to decrease the PMTU, or to maliciously modify probe
   packets in an attempt to blackhole traffic.

   The specification recommends that the nonce value in the REQ Option
   is initialised to a randomised value.  This is designed to enhance
   protection from off-path attacks.  If subsequent probes use a nonce
   value that is easily derived from the initial value, (e.g.,
   incrementing the value) then a misbehaving on-path node could then
   determine the nonce for subsequent probes from that sender, even if
   these probes are not transiting via the misbehaving node.  This would

Fairhurst & Jones         Expires 13 March 2023                 [Page 8]
Internet-Draft                UDPO DPLPMTUD               September 2022

   allow probe packets to be forged, with an impact similar to other on-
   path attacks against probe packets.  This attack could be mitigated
   by using an unpredictable nonce value for each probe.

   The proposed new method does not change the ICMP PTB message
   validation method described by DPLPMTUD: A UDP Options sender that
   utilities ICMP PTB messages received to a probe packet MUST use the
   quoted packet to validate the UDP port information in combination
   with the token contained in the UDP Option, before processing the
   packet using the DPLPMTUD method.

8.  References

8.1.  Normative References

   [I-D.ietf-tsvwg-udp-options]
              Touch, J., "Transport Options for UDP", Work in Progress,
              Internet-Draft, draft-ietf-tsvwg-udp-options-13, 19 June
              2021, <https://www.ietf.org/archive/id/draft-ietf-tsvwg-
              udp-options-13.txt>.

   [RFC0768]  Postel, J., "User Datagram Protocol", STD 6, RFC 768,
              DOI 10.17487/RFC0768, August 1980,
              <https://www.rfc-editor.org/info/rfc768>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [RFC8899]  Fairhurst, G., Jones, T., Tüxen, M., Rüngeler, I., and T.
              Völker, "Packetization Layer Path MTU Discovery for
              Datagram Transports", RFC 8899, DOI 10.17487/RFC8899,
              September 2020, <https://www.rfc-editor.org/info/rfc8899>.

8.2.  Informative References

   [RFC1191]  Mogul, J. and S. Deering, "Path MTU discovery", RFC 1191,
              DOI 10.17487/RFC1191, November 1990,
              <https://www.rfc-editor.org/info/rfc1191>.

   [RFC4821]  Mathis, M. and J. Heffner, "Packetization Layer Path MTU
              Discovery", RFC 4821, DOI 10.17487/RFC4821, March 2007,
              <https://www.rfc-editor.org/info/rfc4821>.

Fairhurst & Jones         Expires 13 March 2023                 [Page 9]
Internet-Draft                UDPO DPLPMTUD               September 2022

   [RFC8085]  Eggert, L., Fairhurst, G., and G. Shepherd, "UDP Usage
              Guidelines", BCP 145, RFC 8085, DOI 10.17487/RFC8085,
              March 2017, <https://www.rfc-editor.org/info/rfc8085>.

   [RFC8201]  McCann, J., Deering, S., Mogul, J., and R. Hinden, Ed.,
              "Path MTU Discovery for IP version 6", STD 87, RFC 8201,
              DOI 10.17487/RFC8201, July 2017,
              <https://www.rfc-editor.org/info/rfc8201>.

   [RFC8304]  Fairhurst, G. and T. Jones, "Transport Features of the
              User Datagram Protocol (UDP) and Lightweight UDP (UDP-
              Lite)", RFC 8304, DOI 10.17487/RFC8304, February 2018,
              <https://www.rfc-editor.org/info/rfc8304>.

   [RFC9000]  Iyengar, J., Ed. and M. Thomson, Ed., "QUIC: A UDP-Based
              Multiplexed and Secure Transport", RFC 9000,
              DOI 10.17487/RFC9000, May 2021,
              <https://www.rfc-editor.org/info/rfc9000>.

Appendix A.  Revision Notes

   XXX Note to RFC-Editor: please remove this entire section prior to
   publication.  XXX

   Individual draft-00.

   *  This version contains a description for consideration and comment
      by the TSVWG.

   Individual draft-01.

   *  Address Nits

   *  Change Probe Request and Probe Reponse options to Echo to align
      names with draft-ietf-tsvwg-udp-options

   *  Remove Appendix B, Informative Description of new UDP Options

   *  Add additional sections around Probe Packet generation

   Individual draft-02.

   *  Address Nits

   Individual draft-03.

   *  Referenced DPLPMTUD RFC.

Fairhurst & Jones         Expires 13 March 2023                [Page 10]
Internet-Draft                UDPO DPLPMTUD               September 2022

   *  Tidied language to clarify the method.

   Individual draft-04

   *  Reworded text on probing with data a little

   *  Removed paragraph on suspending ICMP PTB suspension.

   Working group draft-00

   *  -00 First Working Group Version

   *  RFC8899 call search_done SEARCH_COMPLETE, fix

   Working group draft -01

   *  Update to reflect new fragmentation design in UDP Options.

   *  Add a description of uses of DPLPMTUD with UDP Options.

   *  Add a description on how to form probe packets with padding.

   *  Say that MSS options can be used to initialise the search
      algorithm.

   *  Say that the recommended approach is to not use user data for
      probes.

   *  Attempts to clarify and improve wording throughout.

   *  Remove text saying you can respond to multiple probes in a single
      packet.

   *  Simplified text by removing options that don't yield benefit.

   Working group draft -02

   *  Update to reflect comments from MED.

   *  More consistent description of DPLPMTUD with UDP Options.

   *  Clarify the nonce value (token) is intended per 5-tuple, not
      interface.

   *  BASE_PLPMTU related to RFC8899.

   *  Probes with user data can carry application control data.

Fairhurst & Jones         Expires 13 March 2023                [Page 11]
Internet-Draft                UDPO DPLPMTUD               September 2022

   *  Added that application data uses RES and REQ nonce (token) values
      from the app.

   *  QUIC was intended as an informational reference to an example of
      RFC8899.

   Working group draft -03

   *  Update to reflect more comments from MED.

   *  Again more consistent description of DPLPMTUD with UDP Options.

   *  Clarify token/nonce to use "token".

   *  Clarify any use of application data for blackhole detection.

   *  Minor changes to reflect update to UDP Options base spec.

   Workgin group draft-04.

      Update for WG Last Call

Authors' Addresses

   Godred Fairhurst
   University of Aberdeen
   School of Engineering
   Fraser Noble Building
   Aberdeen
   AB24 3UE
   United Kingdom
   Email: gorry@erg.abdn.ac.uk

   Tom Jones
   University of Aberdeen
   School of Engineering
   Fraser Noble Building
   Aberdeen
   AB24 3UE
   United Kingdom
   Email: tom@erg.abdn.ac.uk

Fairhurst & Jones         Expires 13 March 2023                [Page 12]