rfc3357.txt

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RFC 3357          One-way Loss Pattern Sample Metrics        August 2002


5.4. Definitions

5.4.1. Type-P-One-Way-Loss-Distance-Stream

   When a packet is considered lost (using the definition in [1]), we
   look at its sequence number and compare it with that of the
   previously lost packet.  The difference is the loss distance between
   the lost packet and the previously lost packet.  The sample would
   consist of <loss distance, loss> pairs.  This definition assumes that
   sequence numbers of successive test packets increase monotonically by
   one.  The loss distance associated with the very first packet loss is
   considered to be zero.

   The sequence number of a test packet can be derived from the
   timeseries sample collected by performing the loss measurement
   according to the methodology in [1].  For example, if a loss sample
   consists of <T0,0>, <T1,0>, <T2,1>, <T3,0>, <T4,0>, the sequence
   numbers of the five test packets sent at T0, T1, T2, T3, and T4 can
   be 0, 1, 2, 3 and 4 respectively, or 100, 101, 102, 103 and 104
   respectively, etc.

5.4.2. Type-P-One-Way-Loss-Period-Stream

   We start a counter 'n' at an initial value of zero.  This counter is
   incremented by one each time a lost packet satisfies the definition
   outlined in 4.  The metric is defined as <loss period, loss> where
   "loss" is derived from the sequence of <time, loss> in Type-P-One-
   Way-Loss-Stream [1], and loss period is set to zero when "loss" is
   zero in Type-P-One-Way-Loss-Stream, and loss period is set to 'n'
   (above) when "loss" is one in Type-P-One-Way-Loss-Stream.

   Essentially, when a packet is lost, the current value of "n"
   indicates the loss period to which this packet belongs.  For a packet
   that is received successfully, the loss period is defined to be zero.

5.4.3. Examples

   Let the following set of pairs represent a Type-P-One-Way-Loss-
   Stream.

   {<T1,0>,<T2,1>,<T3,0>,<T4,0>,<T5,1>,<T6,0>,<T7,1>,<T8,0>,
    <T9,1>,<T10,1>}

   where T1, T2,..,T10 are in increasing order.







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   Packets sent at T2, T5, T7, T9, T10 are lost.  The two derived
   metrics can be obtained from this sample as follows.

   (i) Type-P-One-Way-Loss-Distance-Stream:

   Since packet 2 is the first lost packet, the associated loss distance
   is zero.  For the next lost packet (packet 5), loss distance is 5-2
   or 3.  Similarly, for the remaining lost packets (packets 7, 9, and
   10) their loss distances are 2, 2, and 1 respectively.  Therefore,
   the Type-P-One-Way-Loss-Distance-Stream is:

   {<0,0>,<0,1>,<0,0>,<0,0>,<3,1>,<0,0>,<2,1>,<0,0>,<2,1>,<1,1>}

   (ii) The Type-P-One-Way-Loss-Period-Stream:

   The packet 2 sets the counter 'n' to 1, which is incremented by one
   for packets 5, 7 and 9 according to the definition in 4.  However,
   for packet 10, the counter remains at 4, again satisfying the
   definition in 4.  Thus, the Type-P-One-Way-Loss-Period-Stream is:

   {<0,0>,<1,1>,<0,0>,<0,0>,<2,1>,<0,0>,<3,1>,<0,0>,<4,1>,<4,1>}

5.5. Methodologies

   The same methodology outlined in [1] can be used to conduct the
   sample experiments.  A synopsis is listed below.

   Generally, for a given Type-P, one possible methodology would proceed
   as follows:

   -  Assume that Src and Dst have clocks that are synchronized with
      each other.  The degree of synchronization is a parameter of the
      methodology, and depends on the threshold used to determine loss
      (see below).

   -  At the Src host, select Src and Dst IP addresses, and form a test
      packet of Type-P with these addresses.

   -  At the Dst host, arrange to receive the packet.

   -  At the Src host, place a timestamp in the prepared Type-P packet,
      and send it towards Dst.

   -  If the packet arrives within a reasonable period of time, the
      one-way packet-loss is taken to be zero.






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   -  If the packet fails to arrive within a reasonable period of time,
      the one-way packet-loss is taken to be one.  Note that the
      threshold of "reasonable" here is a parameter of the methodology.

5.6. Discussion

   The Loss-Distance-Stream metric allows one to study the separation
   between packet losses.  This could be useful in determining a "spread
   factor" associated with the packet loss rate.  In conjunction, the
   Loss-Period-Stream metric allows the study of loss burstiness for
   each occurrence of loss.  A single loss period of length 'n' can
   account for a significant portion of the overall loss rate.  Note
   that it is possible to measure distance between loss bursts separated
   by one or more successfully received packets.  (Refer to Sections 6.4
   and  6.5).

5.7. Sampling Considerations

   The proposed metrics can be used independent of the particular
   sampling method used.  We note that Poisson sampling may not yield
   appropriate values for these metrics for certain real-time
   applications such as voice over IP, as well as to TCP-based
   applications.  For real-time applications, it may be more appropriate
   to use the ON-OFF [10] model, in which an ON period starts with a
   certain probability 'p', during which a certain number of packets are
   transmitted with mean 'lambda-on' according to geometric distribution
   and an OFF period starts with probability '1-p' and lasts for a
   period of time based on exponential distribution with rate 'lambda-
   off'.

   For TCP-based applications, one may use the model proposed in [8].
   See [9] for an application of the model.

5.8. Errors and Uncertainties

   The measurement aspects, including the packet size, loss threshold,
   type of the test machine chosen etc, invariably influence the packet
   loss metric itself and hence the derived metrics described in this
   document.  Thus, when making an assessment of the results pertaining
   to the metrics outlined in this document, attention must be paid to
   these matters.  See [1] for a detailed consideration of errors and
   uncertainties regarding the measurement of base packet loss metric.









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6. Statistics

6.1. Type-P-One-Way-Loss-Noticeable-Rate

   Define loss of a packet to be "noticeable" [7] if the distance
   between the lost packet and the previously lost packet is no greater
   than delta, a positive integer, where delta is the "loss constraint".

   Example:  Let delta = 99.  Let us assume that packet 50 is lost
   followed by a bursty loss of length 3 starting from packet 125.  All
   the three losses starting from packet 125 are noticeable.

   Given a Type-P-One-Way-Loss-Distance-Stream, this statistic can be
   computed simply as the number of losses that violate some constraint
   delta, divided by the number of losses.  (Alternatively, it can also
   be defined as the number of "noticeable losses" to the number of
   successfully received packets).  This statistic is useful when the
   actual distance between successive losses is important.  For example,
   many multimedia codecs can sustain losses by "concealing" the effect
   of loss by making use of past history information.  Their ability to
   do so degrades with poor history resulting from losses separated by
   close distances.  By choosing delta based on this sensitivity, one
   can measure how "noticeable" a loss might be for quality purposes.
   The noticeable loss requires a certain "spread factor" for losses in
   the timeseries.  In the above example where loss constraint is equal
   to 99, a loss rate of one percent with a spread of 100 between losses
   (e.g., 100, 200, 300, 400, 500 out of 500 packets) may be more
   desirable for some applications compared to the same loss rate with a
   spread that violates the loss constraint (e.g., 100, 175, 275, 290,
   400:  losses occurring at 175 and 290 violate delta = 99).

6.2. Type-P-One-Way-Loss-Period-Total

   This represents the total number of loss periods, and can be derived
   from the loss period metric Type-P-One-Way-Loss-Period-Stream as
   follows:

   Type-P-One-Way-Loss-Period-Total = maximum value of the first entry
   of the set of pairs, <loss period, loss>, representing the loss
   metric Type-P-One-Way-Loss-Period-Stream.

   Note that this statistic does not describe the duration of each loss
   period itself.  If this statistic is large, it does not mean that the
   losses are more spread out than they are otherwise; one or more loss
   periods may include bursty losses.  This statistic is generally
   useful in gathering first order approximation of loss spread.





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6.3. Type-P-One-Way-Loss-Period-Lengths

   This statistic is a sequence of pairs <loss period, length>, with the
   "loss period" entry ranging from 1 - Type-P-One-Way-Loss-Period-
   Total.  Thus the total number of pairs in this statistic equals
   Type-P-One-Way-Loss-Period-Total.  In each pair, the "length" is
   obtained by counting the number of pairs, <loss period, loss>, in the
   metric Type-P-One-Way-Loss-Period-Stream which have their first entry
   equal to "loss period."

   Since this statistic represents the number of packets lost in each
   loss period, it is an indicator of burstiness of each loss period.
   In conjunction with loss-period-total statistic, this statistic is
   generally useful in observing which loss periods are potentially more
   influential than others from a quality perspective.

6.4. Type-P-One-Way-Inter-Loss-Period-Lengths

   This statistic measures distance between successive loss periods.  It
   takes the form of a set of pairs <loss period, inter-loss-period-
   length>, with the "loss period" entry ranging from 1 - Type-P-One-
   Way-Loss-Period-Total, and "inter-loss-period-length" is the loss
   distance between the last packet considered lost in "loss period"
   'i-1', and the first packet considered lost in "loss period" 'i',
   where 'i' ranges from 2 to Type-P-One-Way-Loss-Period-Total.  The
   "inter-loss-period-length" associated with the first "loss period" is
   defined to be zero.

   This statistic allows one to consider, for example, two loss periods
   each of length greater than one (implying loss burst), but separated
   by a distance of 2 to belong to the same loss burst if such a
   consideration is deemed useful.  When the Inter-Loss-Period-Length
   between two bursty loss periods is smaller, it could affect the loss
   concealing ability of multimedia codecs since there is relatively
   smaller history.  When it is larger, an application may be able to
   rebuild its history which could dampen the effect of an impending
   loss (period).

6.5. Examples

   We continue with the same example as in Section 5.4.3.  The three
   statistics defined above will have the following values.

   -  Let delta = 2.  In Type-P-One-Way-Loss-Distance-Stream

         {<0,0>,<0,1>,<0,0>,<0,0>,<3,1>,<0,0>,<2,1>,<0,0>,<2,1>,<1,1>},





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RFC 3357          One-way Loss Pattern Sample Metrics        August 2002