Babel RTT metric: Delay-Based Metric Extension for the Babel Routing Protocol

Internet Engineering Task Force (IETF)                        B. Jonglez
Request for Comments: 9616                                      ENS Lyon
Category: Standards Track                                  J. Chroboczek
ISSN: 2070-1721                              IRIF, Université Paris Cité
                                                          September 2024


      Delay-Based Metric Extension for the Babel Routing Protocol

Abstract

   This document defines an extension to the Babel routing protocol that
   measures the round-trip time (RTT) between routers and makes it
   possible to prefer lower-latency links over higher-latency ones.

Status of This Memo

   This is an Internet Standards Track document.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Further information on
   Internet Standards is available in Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   https://www.rfc-editor.org/info/rfc9616.

Copyright Notice

   Copyright (c) 2024 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.

Table of Contents

   1.  Introduction
     1.1.  Applicability
   2.  Specification of Requirements
   3.  RTT Sampling
     3.1.  Data Structures
     3.2.  Protocol Operation
     3.3.  Wrap-Around and Node Restart
     3.4.  Implementation Notes
   4.  RTT-Based Route Selection
     4.1.  Smoothing
     4.2.  Cost Computation
     4.3.  Hysteresis
   5.  Backwards and Forwards Compatibility
   6.  Packet Format
     6.1.  Timestamp Sub-TLV in Hello TLVs
     6.2.  Timestamp Sub-TLV in IHU TLVs
   7.  IANA Considerations
   8.  Security Considerations
   9.  References
     9.1.  Normative References
     9.2.  Informative References
   Acknowledgements
   Authors' Addresses

1.  Introduction

   The Babel routing protocol [RFC8966] does not mandate a specific
   algorithm for computing metrics; existing implementations use a
   packet-loss-based metric on wireless links and a simple hop-count
   metric on all other types of links.  While this strategy works
   reasonably well in many networks, it fails to select reasonable
   routes in some topologies involving tunnels or VPNs.

                      +------------+
                      | A (Paris)  +---------------+
                      +------------+                \
                     /                               \
                    /                                 \
                   /                                   \
     +------------+                                     +------------+
     | B  (Paris) |                                     | C  (Tokyo) |
     +------------+                                     +------------+
                   \                                   /
                    \                                 /
                     \                               /
                      +------------+                /
                      | D (Paris)  +---------------+
                      +------------+

                Figure 1: Four Routers in a Diamond Topology

   For example, consider the topology described in Figure 1, with three
   routers A, B, and D located in Paris and a fourth router C located in
   Tokyo, connected through tunnels in a diamond topology.  When routing
   traffic from A to D, it is obviously preferable to use the local
   route through B as this is likely to provide better service quality
   and lower monetary cost than the distant route through C.  However,
   the existing implementations of Babel consider both routes as having
   the same metric; therefore, they will route the traffic through C in
   roughly half the cases.

   In the first part of this document (Section 3), we specify an
   extension to the Babel routing protocol that produces a sequence of
   accurate measurements of the round-trip time (RTT) between two Babel
   neighbours.  These measurements are not directly usable as an input
   to Babel's route selection procedure since they tend to be noisy and
   to cause a negative feedback loop, which might give rise to frequent
   oscillations.  In the second part (Section 4), we define an algorithm
   that maps the sequence of RTT samples to a link cost that can be used
   for route selection.

1.1.  Applicability

   The extension defined in Section 3 provides a sequence of accurate
   but potentially noisy RTT samples.  Since the RTT is a symmetric
   measure of delay, this protocol is only applicable in environments
   where the symmetric delay is a good predictor of whether a link
   should be taken by routing traffic, which might not necessarily be
   the case in networks built over exotic link technologies.

   The extension makes minimal requirements on the nodes.  In
   particular, it does not assume synchronised clocks, and only requires
   that clock drift be negligible during the time interval between two
   Hello TLVs.  Since that is on the order of a few seconds, this
   requirement is met even with cheap crystal oscillators, such as the
   ones used in consumer electronics.

   The algorithm defined in Section 4 depends on a number of assumptions
   about the network.  The assumption with the most severe consequences
   is that all links below a certain RTT (rtt-min in Section 4.2) can be
   grouped in a single category of "good" links.  While this is the case
   in wide-area overlay networks, it makes the algorithm inapplicable in
   networks where distinguishing between low-latency links is important.

   There are other assumptions, but they are less likely to limit the
   algorithm's applicability.  The algorithm assumes that all links
   above a certain RTT (rtt-max in Section 4.2) are equally bad, and
   they will only be used as a last resort.  In addition, in order to
   avoid oscillations, the algorithm is designed to react slowly to RTT
   variations, thus causing suboptimal routing for seconds or even
   minutes after an RTT change; while this is a desirable property in
   fixed networks, as it avoid excessive route oscillations, it might be
   an issue with networks with high rates of node mobility.

2.  Specification of Requirements

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "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.

3.  RTT Sampling

3.1.  Data Structures

   We assume that every Babel speaker maintains a local clock that
   counts microseconds from an arbitrary origin.  We do not assume that
   clocks are synchronised: clocks local to distinct nodes need not
   share a common origin.  The protocol will eventually recover if the
   clock is stepped, so clocks need not persist across node reboots.

   Every Babel speaker maintains a Neighbour Table, described in
   Section 3.2.4 of [RFC8966].  This extension extends every entry in
   the Neighbour Table with the following data:

   *  the Origin Timestamp, a 32-bit timestamp (modulo 2^32) according
      to the neighbour's clock;

   *  the Receive Timestamp, a 32-bit timestamp (modulo 2^32) according
      to the local clock.

   Both values are initially undefined.

3.2.  Protocol Operation

   The RTT to a neighbour is estimated using an algorithm due to Mills
   [RFC891], originally developed for the HELLO routing protocol and
   later used in NTP [RFC5905].

   A Babel speaker periodically sends Hello messages to its neighbours
   (Section 3.4.1 of [RFC8966]).  Additionally, it occasionally sends a
   set of IHU ("I Heard You") messages, at most one per neighbour
   (Section 3.4.2 of [RFC8966]).

      A          B
        |      |
     t1 +      |
        |\     |
        | \    |
        |  \   |  Hello(t1)
        |   \  |
        |    \ |
        |     \|
        |      + t1'
        |      |
        |      |               RTT = (t2 - t1) - (t2' - t1')
        |      |
        |      + t2'
        |     /|
        |    / |
        |   /  |
        |  /   |  Hello(t2')
        | /    |  IHU(t1, t1')
        |/     |
     t2 +      |
        |      |
        v      v

                         Figure 2: Mills' Algorithm

   In order to enable the computation of RTTs, a node A MUST include, in
   every Hello that it sends, a timestamp t1 (according to A's local
   clock), as illustrated in Figure 2.  When a node B receives A's
   timestamped Hello, it computes the time t1' at which the Hello was
   received (according to B's local clock).  It then MUST record the
   value t1 in the Origin Timestamp field of the Neighbour Table entry
   corresponding to A and the value t1' in the Receive Timestamp field
   of the Neighbour Table entry.

   When B sends an IHU to A, it checks whether both timestamps are
   defined in the Neighbour Table.  If that is the case, then it MUST
   ensure that its IHU TLV is sent in a packet that also contains a
   timestamped Hello TLV (either a normally scheduled Hello or an
   unscheduled Hello, see Section 3.4.1 of [RFC8966]).  It MUST include
   in the IHU both the Origin Timestamp and the Receive Timestamp stored
   in the Neighbour Table.

   Upon receiving B's packet, A computes the time t2 (according to its
   local clock) at which it was received.  Node A MUST then verify that
   it contains both a Hello TLV with timestamp t2' and an IHU TLV with
   two timestamps t1 and t1'.  If that is the case, A computes the
   value:

   RTT = (t2 - t1) - (t2' - t1')

   (where all computations are done modulo 2^32), which is a measurement
   of the RTT between A and B.  (A then stores the values t2' and t2 in
   its Neighbour Table, as B did before.)

   This algorithm has a number of desirable properties:

   1.  The algorithm is symmetric: A and B use the same procedures for
       timestamping packets and computing RTT samples, and both nodes
       produce one RTT sample for each received (Hello, IHU) pair.

   2.  Since there is no requirement that t1' and t2' be equal, the
       protocol is asynchronous: the only change to Babel's message
       scheduling is the requirement that a packet containing an IHU
       also contain a Hello.

   3.  Since the algorithm only ever computes differences of timestamps
       according to a single clock, it does not require synchronised
       clocks.

   4.  The algorithm requires very little additional state: a node only
       needs to store the two timestamps associated with the last hello
       received from each neighbour.

   5.  Since the algorithm only requires piggybacking one or two
       timestamps on each Hello and IHU TLV, it makes efficient use of
       network resources.

   In principle, this algorithm is inaccurate in the presence of clock
   drift (i.e., when A's clock and B's clock are running at different
   frequencies).  However, t2' - t1' is usually on the order of a few
   seconds, and significant clock drift is unlikely to happen at that
   time scale.

   In order for RTT values to be consistent between implementations,
   timestamps need to be computed at roughly the same point in the
   network stack.  Transmit timestamps SHOULD be computed just before
   the packet is passed to the network stack (i.e., before it is
   subjected to any queueing delays); receive timestamps SHOULD be
   computed just after the packet is received from the network stack.

3.3.  Wrap-Around and Node Restart

   Timestamp values are a count of microseconds stored as a 32-bit
   unsigned integer; thus, they wrap around every 71 minutes or so.
   What is more, a node may occasionally reboot and restart its clock at
   an arbitrary origin.  For these reasons, very old timestamps or
   nonsensical timestamps MUST NOT be used to yield RTT samples.

   The following algorithm can be used to discard obsolete samples.
   When a node receives a packet containing a Hello and an IHU, it
   compares the current local time t2 with the Origin Timestamp
   contained in the IHU; if the Origin Timestamp appears to be in the
   future, or if it is in the past by more than a time T (the value T =
   3 minutes is recommended), then the timestamps are still recorded in
   the Neighbour Table, but they are not used for computation of an RTT
   sample.

   Similarly, the node compares the Hello's timestamp with the Receive
   Timestamp recorded in the Neighbour Table; if the Hello's timestamp
   appears to be older than the recorded timestamp, or if it appears to
   be more recent by an interval larger than the value T, then the
   timestamps are not used for computation of an RTT sample.

3.4.  Implementation Notes

   The accuracy of the computed RTT samples depends on Transmit
   Timestamps being computed as late as possible before a packet
   containing a Hello TLV is passed to the network stack, and Receive
   Timestamps being computed as early as possible after reception of a
   packet containing a (Hello, IHU) pair.  We have found the following
   implementation strategy to be useful.

   When a Hello TLV is buffered for transmission, we insert a PadN sub-
   TLV (Section 4.7.2 of [RFC8966]) with a length of 4 octets within the
   TLV.  When the packet is ready to be sent, we check whether it
   contains a 4-octet PadN sub-TLV; if that's the case, we overwrite the
   PadN sub-TLV with a Timestamp sub-TLV with the current time, and send
   out the packet.

   Conversely, when a packet is received, we immediately compute the
   current time and record it with the received packet.  We then process
   the packet as usual and use the recorded timestamp in order to
   compute an RTT sample.

   The protocol is designed to survive the clock being reset when a node
   reboots; on POSIX systems, this makes it possible to use the
   CLOCK_MONOTONIC clock for computing timestamps.  If CLOCK_MONOTONIC
   is not available, CLOCK_REALTIME may be used, since the protocol is
   able to survive the clock being occasionally stepped.

4.  RTT-Based Route Selection

   The protocol described above yields a series of RTT samples.  While
   these samples are fairly accurate, they are not directly usable as an
   input to the route selection procedure, for at least three reasons:

   1.  In the presence of bursty traffic, routers experience transient
       congestion, which causes occasional spikes in the measured RTT.
       Thus, the RTT signal may be noisy and require smoothing before it
       can be used for route selection.

   2.  Using the RTT signal for route selection gives rise to a negative
       feedback loop.  When a route has a low RTT, it is deemed to be
       more desirable; this causes it to be used for more data traffic,
       which may lead to congestion, which in turn increases the RTT.
       Without some form of hysteresis, using RTT for route selection
       would lead to oscillations between parallel routes, which would
       lead to packet reordering and negatively affect upper-layer
       protocols (such as TCP).

   3.  Even in the absence of congestion, the RTT tends to exhibit some
       variation.  If the RTTs of two parallel routes oscillate around a
       common value, using the RTT as input to route selection will
       cause frequent routing oscillations, which, again, indicates the
       need for some form of hysteresis.

   In this section, we describe an algorithm that integrates smoothing
   and hysteresis.  It has been shown to behave well both in simulation
   and experimentally over the Internet [DELAY-BASED] and is RECOMMENDED
   when RTT information is being used for route selection.  The
   algorithm is structured as follows:

   *  the RTT values are first smoothed in order to avoid instabilities
      due to outliers (Section 4.1);

   *  the resulting smoothed samples are mapped to a cost using a
      bounded, non-linear mapping, which avoids instabilities at the
      lower and upper end of the RTT range (Section 4.2);

   *  a hysteresis filter is applied in order to limit the amount of
      oscillation in the middle of the RTT range (Section 4.3).

4.1.  Smoothing

   The RTT samples provided by Mills' algorithm are fairly accurate, but
   noisy: experiments indicate the occasional presence of individual
   samples that are much larger than the expected value.  Thus, some
   form of smoothing SHOULD be applied in order to avoid instabilities
   due to occasional outliers.

   An implementation MAY use the exponential average algorithm, which is
   simple to implement and appears to yield good results in practice
   [DELAY-BASED].  The algorithm is parameterised by a constant α, where
   0 < α < 1, which controls the amount of smoothing being applied.  For
   each neighbour, it maintains a smoothed value RTT, which is initially
   undefined.  When the first sample RTT0 is measured, the smoothed
   value is set to the value of RTT0.  At each new sample RTTn, the
   smoothed value is set to a weighted average of the previous smoothed
   value and the new sample:

       RTT := α RTT + (1 - α) RTTn

   The smoothing constant α SHOULD be between 0.8 and 0.9; the value
   0.836 is the RECOMMENDED default.

4.2.  Cost Computation

   The smoothed RTT value obtained in the previous step needs to be
   mapped to a link cost, suitable for input to the metric computation
   procedure (Section 3.5.2 of [RFC8966]).  Obviously, the mapping
   should be monotonic (larger RTTs imply larger costs).  In addition,
   the mapping should be constant beyond a certain value (all very bad
   links are equally bad) so that congested links do not contribute to
   routing instability.  The mapping should also be constant around 0,
   so that small oscillations in the RTT of low-RTT links do not
   contribute to routing instability.

     cost
       ^
       |
       |
       |                           C + max-rtt-penalty
       |                       +---------------------------
       |                      /.
       |                     / .
       |                    /  .
       |                   /   .
       |                  /    .
       |                 /     .
       |                /      .
       |               /       .
       |              /        .
       |             /         .
     C +------------+          .
       |            .          .
       |            .          .
       |            .          .
       |            .          .
     0 +---------------------------------------------------->
       0         rtt-min    rtt-max                          RTT

                  Figure 3: Mapping from RTT to Link Cost

   Implementations SHOULD use the mapping described in Figure 3, which
   is parameterised by three parameters: rtt-min, rtt-max, and max-rtt-
   penalty.  For RTT values below rtt-min, the link cost is just the
   nominal cost C of a single hop.  Between rtt-min and rtt-max, the
   cost increases linearly; above rtt-max, the constant value max-rtt-
   penalty is added to the nominal cost.

   The value rtt-min should be slightly larger than the RTT of a local,
   uncongested link.  The value rtt-max should be the RTT above which a
   link should be avoided if possible, either because it is a long-
   distance link or because it is congested; reducing the value of rtt-
   max improves stability, but prevents the protocol from discriminating
   between high-latency links.  As for max-rtt-penalty, it controls how
   much the protocol will penalise long-distance links.  The default
   values rtt-min = 10 ms, rtt-max = 120 ms, and max-rtt-penalty = 150
   are RECOMMENDED.

4.3.  Hysteresis

   Even after applying a bounded mapping from smoothed RTT to a cost
   value, the cost may fluctuate when a link's RTT is between rtt-min
   and rtt-max.  Implementations SHOULD use a robust hysteresis
   algorithm, such as the one described in Appendix A.3 of [RFC8966].

5.  Backwards and Forwards Compatibility

   This protocol extension stores the data that it requires within sub-
   TLVs of Babel's Hello and IHU TLVs.  As discussed in Appendix D of
   [RFC8966], implementations that do not understand this extension will
   silently ignore the sub-TLVs while parsing the rest of the TLVs that
   they contain.  In effect, this extension supports building hybrid
   networks consisting of extended and unextended routers; while such
   networks might suffer from sub-optimal routing, they will not suffer
   from routing loops or other pathologies.

   If a sub-TLV defined in this extension is longer than expected, the
   additional data is silently ignored.  This provision is made in order
   to allow a future version of this protocol to extend the packet
   format with additional data, for example high-precision or absolute
   timestamps.

6.  Packet Format

   This extension defines the Timestamp sub-TLV whose Type field has the
   value 3.  This sub-TLV can be contained within a Hello sub-TLV, in
   which case it carries a single timestamp, or within an IHU sub-TLV,
   in which case it carries two timestamps.

   Timestamps are encoded as 32-bit unsigned integers (modulo 2^32),
   expressed in units of one microsecond, counting from an arbitrary
   origin.  Timestamps wrap around every 4295 seconds, or roughly 71
   minutes (see also Section 3.3).

6.1.  Timestamp Sub-TLV in Hello TLVs

   When contained within a Hello TLV, the Timestamp sub-TLV has the
   following format:

    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |   Type = 3    |    Length     |      Transmit Timestamp       |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |          (continued)          |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   Type:     Set to 3 to indicate a Timestamp sub-TLV.

   Length:   The length of the body in octets, exclusive of the Type and
             Length fields.

   Transmit Timestamp:  The time at which the packet containing this
             sub-TLV was sent, according to the sender's clock.

   If the Length field is larger than the expected 4 octets, the sub-TLV
   MUST be processed normally (the first 4 octets are interpreted as
   described above) and any extra data contained in this sub-TLV MUST be
   silently ignored.  If the Length field is smaller than the expected 4
   octets, then this sub-TLV MUST be ignored (and the remainder of the
   enclosing TLV processed as usual).

6.2.  Timestamp Sub-TLV in IHU TLVs

   When contained in an IHU TLV, the Timestamp sub-TLV has the following
   format:

    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |   Type = 3    |    Length     |        Origin Timestamp       |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |          (continued)          |        Receive Timestamp      |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |          (continued)          |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   Type:     Set to 3 to indicate a Timestamp sub-TLV.

   Length:   The length of the body in octets, exclusive of the Type and
             Length fields.

   Origin Timestamp:  A copy of the Transmit Timestamp of the last
             Timestamp sub-TLV contained in a Hello TLV received from
             the node to which the enclosing IHU TLV applies.

   Receive Timestamp:  The time, according to the sender's clock, at
             which the last timestamped Hello TLV was received from the
             node to which the enclosing IHU TLV applies.

   If the Length field is larger than the expected 8 octets, the sub-TLV
   MUST be processed normally (the first 8 octets are interpreted as
   described above), and any extra data contained in this sub-TLV MUST
   be silently ignored.  If the Length field is smaller than the
   expected 8 octets, then this sub-TLV MUST be ignored (and the
   remainder of the enclosing TLV processed as usual).

7.  IANA Considerations

   IANA has added the following entry to the "Babel Sub-TLV Types"
   registry:

                     +======+===========+===========+
                     | Type | Name      | Reference |
                     +======+===========+===========+
                     | 3    | Timestamp | RFC 9616  |
                     +------+-----------+-----------+

                                 Table 1

8.  Security Considerations

   This extension adds timestamping data to two of the TLVs sent by a
   Babel router.  By broadcasting the value of a reasonably accurate
   local clock, these additional data might make a node more susceptible
   to timing attacks.

   Broadcasting an accurate time raises privacy issues.  The timestamps
   used by this protocol have an arbitrary origin; therefore, they do
   not leak a node's boot time or time zone.  However, having access to
   accurate timestamps could allow an attacker to determine the physical
   location of a node.  Nodes might avoid disclosure of location
   information by not including Timestamp sub-TLVs in the TLVs that they
   send, which will cause their neighbours to fall back to hop-count
   routing.

9.  References

9.1.  Normative References

   [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>.

   [RFC8966]  Chroboczek, J. and D. Schinazi, "The Babel Routing
              Protocol", RFC 8966, DOI 10.17487/RFC8966, January 2021,
              <https://www.rfc-editor.org/info/rfc8966>.

9.2.  Informative References

   [DELAY-BASED]
              Jonglez, B., Boutier, M., and J. Chroboczek, "A delay-
              based routing metric", DOI 10.48550/arXiv.1403.3488, March
              2014, <http://arxiv.org/abs/1403.3488>.

   [RFC891]   Mills, D., "DCN Local-Network Protocols", STD 44, RFC 891,
              DOI 10.17487/RFC0891, December 1983,
              <https://www.rfc-editor.org/info/rfc891>.

   [RFC5905]  Mills, D., Martin, J., Ed., Burbank, J., and W. Kasch,
              "Network Time Protocol Version 4: Protocol and Algorithms
              Specification", RFC 5905, DOI 10.17487/RFC5905, June 2010,
              <https://www.rfc-editor.org/info/rfc5905>.

Acknowledgements

   The authors are indebted to Jean-Paul Smets, who prompted the
   investigation that originally lead to this protocol.  We are also
   grateful to Donald Eastlake, 3rd, Toke Høiland-Jørgensen, Maria
   Matejka, David Schinazi, Pascal Thubert, Steffen Vogel, and Ondřej
   Zajiček.

Authors' Addresses

   Baptiste Jonglez
   ENS Lyon
   France
   Email: baptiste.jonglez@ens-lyon.org


   Juliusz Chroboczek
   IRIF, Université Paris Cité
   Case 7014
   75205 Paris Cedex 13
   France
   Email: jch@irif.fr