rfc2498.txt

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Network Working Group                                        J. Mahdavi
Request for Comments: 2498             Pittsburgh Supercomputing Center
Category: Experimental                                        V. Paxson
                                  Lawrence Berkeley National Laboratory
                                                           January 1999


                IPPM Metrics for Measuring Connectivity

Status of this Memo

   This memo defines an Experimental Protocol for the Internet
   community.  It does not specify an Internet standard of any kind.
   Discussion and suggestions for improvement are requested.
   Distribution of this memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (1999).  All Rights Reserved.

1. Introduction

   Connectivity is the basic stuff from which the Internet is made.
   Therefore, metrics determining whether pairs of hosts (IP addresses)
   can reach each other must form the base of a measurement suite.  We
   define several such metrics, some of which serve mainly as building
   blocks for the others.

   This memo defines a series of metrics for connectivity between a pair
   of Internet hosts.  It builds on notions introduced and discussed in
   RFC 2330, the IPPM framework document.  The reader is assumed to be
   familiar with that document.

   The structure of the memo is as follows:

 +    An analytic metric, called Type-P-Instantaneous-Unidirectional-
      Connectivity, will be introduced to define one-way connectivity at
      one moment in time.
 +    Using this metric, another analytic metric, called Type-P-
      Instantaneous-Bidirectional-Connectivity, will be introduced to
      define two-way connectivity at one moment in time.
 +    Using these metrics, corresponding one- and two-way analytic
      metrics are defined for connectivity over an interval of time.








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 +    Using these metrics, an analytic metric, called Type-P1-P2-
      Interval-Temporal-Connectivity, will be introduced to define a
      useful notion of two-way connectivity between two hosts over an
      interval of time.
 +    Methodologies are then presented and discussed for estimating
      Type-P1-P2-Interval-Temporal-Connectivity in a variety of
      settings.

   Careful definition of Type-P1-P2-Interval-Temporal-Connectivity and
   the discussion of the metric and the methodologies for estimating it
   are the two chief contributions of the memo.

2. Instantaneous One-way Connectivity

2.1. Metric Name:

   Type-P-Instantaneous-Unidirectional-Connectivity

2.2. Metric Parameters:

 +    Src, the IP address of a host
 +    Dst, the IP address of a host
 +    T, a time

2.3. Metric Units:

   Boolean.

2.4. Definition:

   Src has *Type-P-Instantaneous-Unidirectional-Connectivity* to Dst at
   time T if a type-P packet transmitted from Src to Dst at time T will
   arrive at Dst.

2.5. Discussion:

   For most applications (e.g., any TCP connection) bidirectional
   connectivity is considerably more germane than unidirectional
   connectivity, although unidirectional connectivity can be of interest
   for some security applications (e.g., testing whether a firewall
   correctly filters out a "ping of death").  Most applications also
   require connectivity over an interval, while this metric is
   instantaneous, though, again, for some security applications
   instantaneous connectivity remains of interest.  Finally, one might
   not have instantaneous connectivity due to a transient event such as
   a full queue at a router, even if at nearby instants in time one does
   have connectivity.  These points are addressed below, with this
   metric serving as a building block.



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   Note also that we have not explicitly defined *when* the packet
   arrives at Dst.  The TTL field in IP packets is meant to limit IP
   packet lifetimes to 255 seconds (RFC 791).  In practice the TTL field
   can be strictly a hop count (RFC 1812), with most Internet hops being
   much shorter than one second.  This means that most packets will have
   nowhere near the 255 second lifetime.  In principle, however, it is
   also possible that packets might survive longer than 255 seconds.
   Consideration of packet lifetimes must be taken into account in
   attempts to measure the value of this metric.

   Finally, one might assume that unidirectional connectivity is
   difficult to measure in the absence of connectivity in the reverse
   direction.  Consider, however, the possibility that a process on
   Dst's host notes when it receives packets from Src and reports this
   fact either using an external channel, or later in time when Dst does
   have connectivity to Src.  Such a methodology could reliably measure
   the unidirectional connectivity defined in this metric.

3. Instantaneous Two-way Connectivity

3.1. Metric Name:

   Type-P-Instantaneous-Bidirectional-Connectivity

3.2. Metric Parameters:

 +    A1, the IP address of a host
 +    A2, the IP address of a host
 +    T, a time

3.3. Metric Units:

   Boolean.

3.4. Definition:

   Addresses A1 and A2 have *Type-P-Instantaneous-Bidirectional-
   Connectivity* at time T if address A1 has Type-P-Instantaneous-
   Unidirectional-Connectivity to address A2 and address A2 has Type-P-
   Instantaneous-Unidirectional-Connectivity to address A1.

3.5. Discussion:

   An alternative definition would be that A1 and A2 are fully connected
   if at time T address A1 has instantaneous connectivity to address A2,
   and at time T+dT address A2 has instantaneous connectivity to A1,
   where T+dT is when the packet sent from A1 arrives at A2.  This
   definition is more useful for measurement, because the measurement



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   can use a reply from A2 to A1 in order to assess full connectivity.
   It is a more complex definition, however, because it breaks the
   symmetry between A1 and A2, and requires a notion of quantifying how
   long a particular packet from A1 takes to reach A2.  We postpone
   discussion of this distinction until the development of interval-
   connectivity metrics below.

4. One-way Connectivity

4.1. Metric Name:

   Type-P-Interval-Unidirectional-Connectivity

4.2. Metric Parameters:

 +    Src, the IP address of a host
 +    Dst, the IP address of a host
 +    T, a time
 +    dT, a duration
   {Comment:  Thus, the closed interval [T, T+dT] denotes a time
   interval.}

4.3. Metric Units:

   Boolean.

4.4. Definition:

   Address Src has *Type-P-Interval-Unidirectional-Connectivity* to
   address Dst during the interval [T, T+dT] if for some T' within [T,
   T+dT] it has Type-P-instantaneous-connectivity to Dst.

5. Two-way Connectivity

5.1. Metric Name:

   Type-P-Interval-Bidirectional-Connectivity

5.2. Metric Parameters:

 +    A1, the IP address of a host
 +    A2, the IP address of a host
 +    T, a time
 +    dT, a duration
   {Comment:  Thus, the closed interval [T, T+dT] denotes a time
   interval.}





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5.3. Metric Units:

   Boolean.

5.4. Definition:

   Addresses A1 and A2 have *Type-P-Interval-Bidirectional-Connectivity*
   between them during the interval [T, T+dT] if address A1 has Type-P-
   Interval-Unidirectional-Connectivity to address A2 during the
   interval and address A2 has Type-P-Interval-Unidirectional-
   Connectivity to address A1 during the interval.

5.5. Discussion:

   This metric is not quite what's needed for defining "generally
   useful" connectivity - that requires the notion that a packet sent
   from A1 to A2 can elicit a response from A2 that will reach A1.  With
   this definition, it could be that A1 and A2 have full-connectivity
   but only, for example, at time T1 early enough in the interval [T,
   T+dT] that A1 and A2 cannot reply to packets sent by the other.  This
   deficiency motivates the next metric.

6. Two-way Temporal Connectivity

6.1. Metric Name:

   Type-P1-P2-Interval-Temporal-Connectivity

6.2. Metric Parameters:

 +    Src, the IP address of a host
 +    Dst, the IP address of a host
 +    T, a time
 +    dT, a duration
   {Comment:  Thus, the closed interval [T, T+dT] denotes a time
   interval.}

6.3. Metric Units:

   Boolean.

6.4. Definition:

   Address Src has *Type-P1-P2-Interval-Temporal-Connectivity* to
   address Dst during the interval [T, T+dT] if there exist times T1 and
   T2, and time intervals dT1 and dT2, such that:





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