IP Performance Metrics Working Group                           A.Morton
Internet Draft                                             L.Ciavattone
Document: <draft-ietf-ippm-reordering-00.txt>            G.Ramachandran
Category: Standards Track                                     AT&T Labs

                       Reordering Metric for IPPM

Status of this Memo

   This document is an Internet-Draft and is in full conformance with
   all provisions of Section 10 of RFC2026 [1].

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF), its areas, and its working groups. Note that
   other groups may also distribute working documents as Internet-
   Drafts. Internet-Drafts are draft documents valid for a maximum of
   six months and may be updated, replaced, or made obsolete 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."

   The list of current Internet-Drafts can be accessed at

   The list of Internet-Draft Shadow Directories can be accessed at

1. Abstract

   This memo defines a simple metric to determine if a network has
   maintained packet order. It provides motivations for the new metric,
   suggests a metric definition, and discusses the issues associated
   with measurement. The memo includes sample metrics to quantify the
   extent of reordering in several useful dimensions. Some examples of
   evaluation using the various sample metrics are included.

2. Conventions used in this document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in RFC 2119 [2].
   Although RFC 2119 was written with protocols in mind, the key words
   are used in this document for similar reasons.  They are used to
   ensure the results of measurements from two different
   implementations are comparable, and to note instances when an
   implementation could perturb the network.

Morton, et al.      Standards Track  exp. Dec 2002              Page 1
Reordering Metric for IPPM                                   June 2002

3. Introduction

   Ordered delivery is a property of successful packet transfer
   attempts, where the packet sequence ascends for each arriving packet
   and there are no backward steps.

   An explicit sequence number, such as the sending time of each packet
   or an incrementing message number carried in each packet establishes
   the Source Sequence.

   The presence of reordering at the Destination is based on arrival

   This metric classifies arriving packets with sequence numbers
   smaller than their predecessors as out-of-order, or reordered. For
   example, if arriving packets are numbered 1,2,4,5,3, then packet 3
   is reordered. This is equivalent to Paxon's reordering definition in
   [3], where "late" packets were declared reordered. The alternative
   is to emphasize "premature" packets instead (4 and 5 in the
   example). The metric's construction is very similar to the sequence
   space validation for received segments in RFC793 [4]. Earlier work
   to define ordered delivery includes [5], and more ???.

3.1 Motivation

   A reordering metric is relevant for most applications, especially
   when assessing network support for Real-Time media streams. The
   extent of reordering may be sufficient to cause a received packet to
   be discarded by functions above the IP layer.

   Packet order is not expected to change during transfer, but several
   specific path characteristics can cause their order to change.

   Examples are:
   * When two paths, one with slightly longer transfer time, support a
     single packet stream or flow, then packets traversing the longer
     path may arrive out-of-order. Multiple paths may be used to
     achieve load balancing, or may arise from route instability.
   * To increase capacity, a network device designed with multiple
     processors serving a single port may reorder as a byproduct.
   * A layer 2 retransmission protocol that compensates for an error-
     prone link may cause packet reordering.
   * If for any reason, the packets in a buffer are not serviced in the
     order of their arrival, their order will change.
   * If packets in a flow are assigned to multiple buffers (following
     evaluation of traffic characteristics, for example), and the
     buffers have different occupations and/or service rates, then
     order will likely change.

   The ability to restore order at the destination will likely have
   finite limits.  Practical hosts have receiver buffers with finite

Morton, et al.      Standards Track exp. Dec 2002               Page 2
Reordering Metric for IPPM                                   June 2002

   size in terms of packets, bytes, or time (such as de-jitter
   buffers). Once the initial determination of reordering is made, it
   is useful to quantify the extent of reordering, or lateness, in all
   meaningful dimensions.

3.2 Goals and Objectives

   The definitions below intend to satisfy the goals of:
     1. Determining whether or not packet order is maintained.
     2. Quantifying the extent (achieving this second goal requires
        assumptions of upper layer functions and capabilities to
        restore order, and therefore several solutions).

   Reordering Metrics MUST:

   +  be relevant to one or more known applications
   +  be computable "on the fly"
   +  work with Poisson and Periodic test streams
   +  work even if the stream has duplicate or lost packets

   Reordering Metrics SHOULD:

   +  have concatenating results for segments measured separately
   +  have simplicity for easy consumption and understanding
   +  have relevance to TCP performance
   +  have relevance to Real-time application performance

4. An Ordered Arrival Singleton Metric

   The IPPM framework RFC 2330 [3] gives the definitions of singletons,
   samples, and statistics.

   The evaluation of packet order requires several supporting concepts.
   The first is an incrementing sequence number applied to packets at
   the source (decrementing sequences can be accommodated, and sequence
   roll-over is treated later). The source order may established by a
   simple message number, a byte stream number, or it may be the actual
   time when each packet departs from the Src.

   The second supporting concept is a stored value which is the "next
   expected" packet number. Under normal conditions, the value of Next
   Expected (NextExp) is the sequence number of the previous packet
   (plus 1 for message numbering).  In byte stream numbering, NextExp
   is a value 1 byte greater than the last in-order packet sequence
   number + payload. If Src time is used as the sequence number,
   NextExp is the Src time from the last in-order packet + 1 clock

   Each packet within a packet stream can be evaluated for its order
   singleton metric.

Morton, et al.      Standards Track exp. Dec 2002               Page 3
Reordering Metric for IPPM                                   June 2002

4.1 Metric Name:


4.2 Metric Parameters:

   +  Src, the IP address of a host

   +  Dst, the IP address of a host

   +  SrcTime, the time of packet emission from the Src

   +  SrcNum, the packet sequence number applied at the Src, in units
     of messages or bytes.

   +  NextExp, the Next Expected Sequence number at the Dst, in units
     of messages, time, or bytes.

   +  PayloadSize, the number of bytes contained in the information
     field and referred to when the SrcNum sequence is based on byte

4.3 Definition:

   In-order packets have sequence numbers (or Src times) greater than
   or equal to the value of Next Expected. Each new in-order packet
   will increase the Next Expected (typically by 1 for message
   numbering, or the payload size plus 1 for byte numbering).  The Next
   Expected value cannot decrease, thereby specifying non-reversing
   order as the basis to identify reordered packets.

   A reordered packet outcome occurs when a single IP packet at the Dst
   Measurement Point results in the following:
   The packet has a Src sequence number lower than the Next Expected
   (NextExp), and therefore the packet is reordered. The Next Expected
   value does not change on the arrival of this packet.

   This definition can also be specified in pseudo-code.
   On successful arrival of a packet with sequence number n:
        if n >= NextExp, /* n is in-order */
                NextExp = n + PayloadSize + 1;
        else            /* when n < NextExp */
                designate packet n as reordered;

   When using message-based sequence numbering or Src time,

4.4 Discussion

   Any arriving packet bearing a sequence number from the sequence that
   establishes the Next Expected value can be evaluated to determine if

Morton, et al.      Standards Track exp. Dec 2002               Page 4
Reordering Metric for IPPM                                   June 2002

   it is in-order, or reordered, based on a previous packet's arrival.
   In the case where Next Expected is Undefined (because the arriving
   packet is the first successful transfer), the packet is designated

5. Sample Metrics

   It is highly desirable to assert the degree to which a packet is
   out-of-order with respect to a sample of packets. This section
   defines several metrics that quantify the extent of reordering in
   various units of measure. Each metric highlights a relevant

5.1 N-Reordering

   [Note:  This is a modified definition of N-Reordering.]

   Metric Name: Type-P-packet-N-reordering-Poisson/Periodic-Stream

   Parameter Notation: Let N be a positive integer (a parameter).  Let
   K be a positive integer (sample size, the number of packets sent).
   Let L be a non-negative integer representing the number of packets
   that were received out of the K packets sent.  Assign each sent
   packet a sequence number, 1 to K.  Let <S_1, ..., S_L> be the
   original sequence numbers of the received packets, in the order of
   arrival (duplicates are possible).

   Definition 1: Received packet number I (N < I <= L) is called
   N-reordered IFF for all J such that I-N <= J < I we have S_J > S_I.

   Let M be the number of N-reordered packets in the sample.

   Definition 2: The degree of N-reordering of the sample is M/(K-N).

   Definition 3: The degree of reordering of the sample is its degree
   of 1-reordering.

   Definition 4: A sample is said to have no reordering if its degree
   of reordering is 0.


   The degree of N-reordering may be expressed as a percentage, in
   which case the number from definition 2 is multiplied by 100.

   N-reordering is particularly useful for determining the portion of
   reordered packets which can or cannot be restored to order in a
   typical TCP receiver buffer based on their arrival order alone (and
   without the aid of retransmission).

   [need more on this].

Morton, et al.      Standards Track exp. Dec 2002               Page 5
Reordering Metric for IPPM                                   June 2002

5.2 Reordering Offset

   Any packet whose sequence number causes the Next Expected value to
   increment by more than the usual increment indicates a discontinuity
   in the sequence. From this point on, any packets with sequence
   number less than the Next Expected value can be assigned Offset
   values indicating their position (in packets or bytes) and lateness
   in terms of time of arrival with respect to a sequence
   discontinuity. The various Offset metrics are calculated only on
   reordered packets, as defined in section 4.

5.2.1 Metric Name: Type-P-packet-Position-Offset-Poisson/Periodic-

   Metric Parameters: In addition to the parameters defined for Type-P-
   Non-Reversing-Order, we specify:

   +  DstOrder, numerical order in which each packet in the stream
     arrives at Dst

   Definition:  Reordered packets are associated with a specific
   sequence discontinuity by determining which earlier packet's
   sequence number skipped over them. We calculate all expressions of
   Offset with respect to that packet. Position Offset is calculated
   from a Dst Order number assigned to each packet on arrival:

   Position Offset =
   DstOrder(reordered packet)-DstOrder(packet at discontinuity)

   Using the notation of Section 5.1, an equivalent definition is:
        The Position Offset of Reordered Packet I is M = I-J, for
   min{J|1<=J<I} that satisfies S_J > S_I.

5.2.2 Metric Name: Type-P-packet-Late-Time-Poisson/Periodic-Stream

   Metric Parameters: In addition to the parameters defined for Type-P-
   Non-Reversing-Order, we specify:

   +  DstTime, the time that each packet in the stream arrives at Dst

   Definition: Lateness in time is calculated using Dst times.

   Late Time =
   DstTime(reordered packet)-DstTime(packet at discontinuity)

   Using similar notation to that of Section 5.1, an equivalent
   definition is:
        The Late Time of Reordered Packet I is T = DstTime_I-DstTime_J,
   for min{J|1<=J<I} that satisfies S_J > S_I, or SrcTime_J>SrcTime_I.

5.2.3 Metric Name: Type-P-packet-Byte-Offset-Poisson/Periodic-Stream

Morton, et al.      Standards Track exp. Dec 2002               Page 6
Reordering Metric for IPPM                                   June 2002

   Metric Parameters: We use the same parameters defined above.

   Definition: Byte stream offset can be determined from the payload
   sizes of intervening packets.

   Byte Offset =
   PayloadNum(reordered packet, DstOrder=m)
   - Sum[PayloadSize(packet, DstOrder=m-1),
        PayloadSize(packet, DstOrder=m-2), ...
        PayloadSize(packet at discontinuity)]

5.2.4 Discussion

   The Offset metrics can predict whether reordered packets will be
   useful in a general, limited receiver buffer system.  The limit may
   be the number of bytes or packets the buffer can store, or the time
   of storage prior to a cyclic play-out instant (as with de-jitter

   Note that the One-way IPDV [6] gives the delay variation for a
   packet w.r.t. the preceding packet in the source sequence. Lateness
   and IPDV give an indication of whether a buffer at Dst has
   sufficient storage to accommodate the network's behavior and restore
   order. When an earlier packet in the Src sequence is lost, IPDV will
   necessarily be undefined for adjacent packets, and Late Time may
   provide the only way to evaluate the usefulness of a packet.

   In the case of de-jitter buffers, there are circumstances where the
   receiver employs loss concealment at the intended play-out time of a
   late packet. However, if this packet arrives out of order, the Late
   Time determines whether the packet is still useful. IPDV no longer
   applies, because the receiver establishes a new play-out schedule
   with more buffer delay to accommodate similar events in the future -
   this requires very minimal processing.

   When packets in the stream have variable sizes, it may be most
   useful to characterize Offset in terms of the payload size(s) of
   stored packets (using byte stream numbering).

   For a sample of packets in a stream, results may be reported as a
   ratio of reordered packets to total packets sent by the source
   during the test. If separate reordering events can be distinguished,
   then an event count may also be reported (along with the event
   description, such as the number of reordered packets and their
   offsets).  The distribution of various Offset metrics may also be
   reported and summarized as average, range, etc.

6. Measurement Issues

   The results of sequence tests will be dependent on the time interval
   between measurement packets (both at the Src, and during transport

Morton, et al.      Standards Track exp. Dec 2002               Page 7
Reordering Metric for IPPM                                   June 2002

   where spacing may change).  Clearly, packets launched infrequently
   (e.g., 1 per 10 seconds) are unlikely to be reordered.

   The Non-reversing order criterion remains valid and useful when a
   stream of packets experiences packet loss, or both loss and
   reordering. In other words, losses alone do not cause subsequent
   packets to be declared reordered.

   Assuming that the necessary sequence information (sequence number
   and/or source time stamp) is included in the packet payload
   (possibly in application headers such as RTP), packet sequence may
   be evaluated in a passive measurement arrangement.  Also, it is
   possible to evaluate sequence at a single point along a path, since
   the usual need for synchronized Src and Dst Clocks may be relaxed to
   some extent.

   When the Src sequence is based on byte stream, or payload numbering,
   care must be taken to avoid declaring retransmitted packets out-of-
   sequence. The additional reference of Src Time is one way to avoid
   this ambiguity.

   Since this metric definition may use sequence numbers with finite
   range, it is possible that the sequence numbers could reach end-of-
   range and roll over to zero during a measurement.  By definition,
   the Next Expected value cannot decrease, and all packets received
   after a roll-over would be declared out-of-sequence.  Sequence
   number roll-over can be avoided by using combinations of counter
   size and test duration where roll-over is impossible (and sequence
   is reset to zero at the start). Also, message-based numbering
   results in slower sequence consumption.  There may still be cases
   where methodological mitigation of this problem is desirable (e.g.,
   long-term testing).  The elements of mitigation are:

   1. There must be a test to detect if a roll-over has occurred.  It
   would be nearly impossible for the sequence numbers of successive
   packets to jump by more than half the total range, so these large
   discontinuities are designated as roll-over.

   2. All sequence numbers used in computations are represented in a
   sufficiently large precision.  The numbers have a correction applied
   (equivalent to adding a significant digit) whenever roll-over is

   3. Out-of-order packets coincident with sequence numbers reaching
   end-of-range must also be detected for proper application of
   correction factor.

7. Examples of Order Evaluation

   This section provides some examples to illustrate how the non-
   reversing order criterion works, and the value of viewing reordering
   in both the dimensions of time and position.

Morton, et al.      Standards Track exp. Dec 2002               Page 8
Reordering Metric for IPPM                                   June 2002

   Table 1 gives a simple case of reordering, where one packet (the
   packet with SrcNum=4) arrives out-of-order. Packets are arranged
   according to their arrival, and message numbering is used.

   Table 1 Example with Packet 4 Reordered,
   Sending order(SrcNum@Src): 1,2,3,4,5,6,7,8,9,10
   SrcNum       Src     Dst                     Dst     Posit.  Late
   @Dst NextExp Time    Time    Delay   IPDV    Order   Offset  Time
    1     1       0      68      68              1
    2     2      20      88      68       0      2
    3     3      40     108      68       0      3
    5     4      80     148      68     -82      4
    6     6     100     168      68       0      5
    7     7     120     188      68       0      6
    8     8     140     208      68       0      7
    4     9      60     210     150      82      8      4       62
    9     9     160     228      68       0      9
   10    10     180     248      68       0     10

   Each column gives the following information:

   SrcNum   Packet sequence number at the Source.
   NextExp   The value of NextExp when the packet arrived(before
   SrcTime  Packet time stamp at the Source, ms.
   DstTime  Packet time stamp at the Destination, ms.
   Delay    1-way delay of the packet, ms.
   IPDV     IP Packet Delay Variation, ms
            IPDV = Delay(SrcNum)-Delay(SrcNum-1)
   DstOrder Order in which the packet arrived at the Destination.
   Posit.Offset  The Position Offset of an out-of-order packet.
   LateTime The lateness of an out-of-order packet, ms.

   We can see that when packet 4 arrives, NextExp=9, and it is declared
   reordered. Further, we can compute the Offset of packet 4 in terms
   of position (8-4=4 using DstOrder) and Late Time (210-148=62ms using
   DstTime) compared to packet 5's arrival.  If Dst has a de-jitter
   buffer that holds more than 4 packets, or at least 62 ms storage,
   packet 4 may be useful. Note that 1-way delay and IPDV also indicate
   unusual behavior for packet 4.

   If all packets contained 100 byte payloads, then Byte Offset is
   equal to 500 bytes.

   In the notation of N-reordering, <S_1, ..., S_I, ..., S_L> the
   received packets are represented as:

   1_1, 2_2, 3_3, 5_4, 6_5, 7_6, 8_7, 4_8, 9_9, 10_10

   when N=1, 7<=J<8, and 8_7 > 4_8, so packet I=8 is 1-reordered.

Morton, et al.      Standards Track exp. Dec 2002               Page 9
Reordering Metric for IPPM                                   June 2002

   when N=2, 6<=J<8, and 7_6 > 4_8, so packet I=8 is 2-reordered.
   when N=3, 5<=J<8, and 6_5 > 4_8, so packet I=8 is 3-reordered.
   when N=4, 4<=J<8, and 5_4 > 4_8, so packet I=8 is 4-reordered.

   We note that the Position Offset is equal to the Max(N) with N-

   Table 2 Example with Packets 5 and 6 Reordered,
   Sending order(SrcNum@Src): 1,2,3,4,5,6,7,8,9,10
   SrcNum       Src     Dst                     Dst     Posit.  Late
   @Dst NextExp Time    Time    Delay   IPDV    Order   Offset  Time
    1     1       0      68      68              1
    2     2      20      88      68       0      2
    3     3      40     108      68       0      3
    4     4      60     128      68       0      4
    7     5     120     188      68     -22      5
    5     8      80     189     109      41      6      1       1
    6     8     100     190      90     -19      7      2       2
    8     8     140     208      68       0      8
    9     9     160     228      68       0      9
   10    10     180     248      68       0     10

   [ Remaining examples need to have N-reordering added ]

   Table 2 shows a case where packets 5 and 6 arrive just behind packet
   7, so both 5 and 6 are declared out-of-order. Their positional
   offsets (6-5=1 and 7-5=2, using DstOrder again) and Late times (189-
   188=1, 190-188=2) are small.

   Table 3 Example with Packets 4, 5, and 6 reordered
   Sending order(SrcNum@Src): 1,2,3,4,5,6,7,8,9,10,11
   SrcNum       Src     Dst                     Dst     Posit.  Late
   @Dst NextExp Time    Time    Delay   IPDV    Order   Offset  Time
    1    1        0      68      68              1
    2    2       20      88      68       0      2
    3    3       40     108      68       0      3
    7    4      120     188      68     -68      4
    8    8      140     208      68       0      5
    9    9      160     228      68       0      6
   10   10      180     248      68       0      7
    4   11       60     250     190     122      8      4       62
    5   11       80     252     172     -18      9      5       64
    6   11      100     256     156     -16     10      6       68
   11   11      200     268      68       0     11

   The case in Table 3 is where three packets in sequence have long
   transit times. Delay, Late time, and Offset capture this very well,
   and indicate variation in reordering extent, while IPDV indicates
   that the spacing between packets 4,5,and 6 has changed.

Morton, et al.      Standards Track exp. Dec 2002              Page 10
Reordering Metric for IPPM                                   June 2002

8. Security Considerations [mostly borrowed from npmps]

8.1 Denial of Service Attacks

   This metric requires a stream of packets sent from one host (Src) to
   another host (Dst) through intervening networks.  This method could
   be abused for denial of service attacks directed at Dst and/or the
   intervening network(s).

   Administrators of Src, Dst, and the intervening network(s) should
   establish bilateral or multi-lateral agreements regarding the
   timing, size, and frequency of collection of sample metrics.  Use of
   this method in excess of the terms agreed between the participants
   may be cause for immediate rejection or discard of packets or other
   escalation procedures defined between the affected parties.

8.2 User data confidentiality

   Active use of this method generates packets for a sample, rather
   than taking samples based on user data, and does not threaten user
   data confidentiality. Passive measurement must restrict attention to
   the headers of interest. Since user payloads may be temporarily
   stored for length analysis, suitable precautions MUST be taken to
   keep this information safe and confidential.

8.3 Interference with the metric

   It may be possible to identify that a certain packet or stream of
   packets is part of a sample. With that knowledge at Dst and/or the
   intervening networks, it is possible to change the processing of the
   packets (e.g. increasing or decreasing delay) that may distort the
   measured performance.  It may also be possible to generate
   additional packets that appear to be part of the sample metric.
   These additional packets are likely to perturb the results of the
   sample measurement.

   To discourage the kind of interference mentioned above, packet
   interference checks, such as cryptographic hash, may be used.

9. IANA Considerations

   Since this metric does not define a protocol or well-known values,
   there are no IANA considerations in this memo.

10. References

   1  Bradner, S., "The Internet Standards Process -- Revision 3", BCP
      9, RFC 2026, October 1996.

   2  Bradner, S.,  "Key words for use in RFCs to Indicate Requirement
      Levels", RFC 2119, March 1997.

Morton, et al.      Standards Track exp. Dec 2002              Page 11
Reordering Metric for IPPM                                   June 2002

   3  V.Paxson, "Measurements and Analysis of End-to-End Internet
      Dynamics," Ph.D. dissertation, U.C. Berkeley, 1997,

   4  Postel, J., "Transmission Control Protocol", STD 7, RFC 793,
      September 1981.
      Obtain via: http://www.rfc-editor.org/rfc/rfc793.txt

   5  L.Ciavattone and A.Morton, "Out-of-Sequence Packet Parameter
      Definition (for Y.1540)", Contribution number T1A1.3/2000-047,
      October 30, 2000. ftp://ftp.t1.org/pub/t1a1/2000-A13/0a130470.doc

   6  Demichelis, C., and Chimento, P., "IP Packet Delay Variation
      Metric for IPPM", work in progress.

11. Acknowledgments

   The authors would like to acknowledge the helpful discussions with
   Matt Mathis, and .  We gratefully acknowledge the foundation laid by
   the authors of the IP performance Framework [3].

11. Author's Addresses

   Al Morton
   AT&T Labs
   Room D3 - 3C06
   200 Laurel Ave. South
   Middletown, NJ 07748 USA
   Phone  +1 732 420 1571  Fax +1 732 368 1192

   Len Ciavattone
   AT&T Labs
   Room C4 - 2B29
   200 Laurel Ave. South
   Middletown, NJ 07748 USA
   Phone  +1 732 420 1239

   Gomathi Ramachandran
   AT&T Labs
   Room C4 - 3D22
   200 Laurel Ave. South
   Middletown, NJ 07748 USA
   Phone  +1 732 420 2353

   Stanislav Shalunov
   University Corporation for Advanced Internet Development

Morton, et al.      Standards Track exp. Dec 2002              Page 12
Reordering Metric for IPPM                                   June 2002

   200 Business Park Drive, Suite 307
   Armonk, NY 10504
   Phone: + 1 914 765 1182
   EMail: <shalunov@internet2.edu>

   Jerry Perser
   Spirent Communications
   26750 Agoura Road
   Calabasas, CA 91302  USA
   Phone: + 1 818 676 2300
   EMail: <jerry.perser@spirentcom.com>

Full Copyright Statement

   "Copyright (C) The Internet Society (date). All Rights Reserved.
   This document and translations of it may be copied and furnished to
   others, and derivative works that comment on or otherwise explain it
   or assist in its implmentation may be prepared, copied, published
   and distributed, in whole or in part, without restriction of any
   kind, provided that the above copyright notice and this paragraph
   are included on all such copies and derivative works. However, this
   document itself may not be modified in any way, such as by removing
   the copyright notice or references to the Internet Society or other
   Internet organizations, except as needed for the purpose of
   developing Internet standards in which case the procedures for
   copyrights defined in the Internet Standards process must be
   followed, or as required to translate it into languages other than

   The limited permissions granted above are perpetual and will not be
   revoked by the Internet Society or its successors or assigns.

   This document and the information contained herein is provided on an

Morton, et al.      Standards Track exp. Dec 2002              Page 13