Internet Info 1994 March/Internet Info CD-ROM (Walnut Creek) (March 1994).iso/inet/ien/ien-120

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 IEN 120






       INTERNET ROUTING AND THE NETWORK PARTITION PROBLEM
                            IEN #120
                            PRTN #279
                          Radia Perlman
                  Bolt Beranek and Newman, Inc.
                          October, 1979


I. INTRODUCTION

As described in IEN 110, "Internet Addressing and Naming in a
Tactical Environment", a network can become partitioned into two
or more pieces.  Assuming some of these pieces are still
connected to the catenet, we would like the catenet to be able to
efficiently deliver packets to a host in any such piece.  Such a
capability in the catenet could additionally be utilized by a
scheme for delivering intranet traffic across partitions in a
partitioned network.

There are four parts to the solution:
1) detecting that a network is partitioned
2) deriving a name for each partition
3) figuring out which partition a host is in
4) routing packets to the correct partition

The currently implemented gateway routing algorithm is based on
the original ARPANET algorithm.  To efficiently provide for
routing to network partitions, routing must be based on a link
state routing scheme.  I will demonstrate this after first
presenting the design (parts II-VIII), then showing what would be
involved in modifying the original ARPANET algorithm for that
purpose (part IX), and then comparing the two approaches (part
X).


II. TERMINOLOGY

1) neighbor gateways--two gateways attached to the same network

2) functioning neighbor gateways--neighbor gateways able to
communicate with each other over their common network

3) attached network--a network physically attached to a gateway,
and with which the gateway can communicate directly (not through
another gateway)

4) neighbor network of gateway G--an attached network of a
functioning neighbor gateway of G, excluding attached networks of
G.


                              - 1 -



III. TABLES TO BE MAINTAINED BY EACH GATEWAY

1) a list of attached networks--This list is relatively constant
and is updated by a gateway when it notices a network interface
is down or for some other reason the gateway is incapable of
communicating with an attached network.  Keeping this table
updated is solely the responsibility of each gateway, and does
not require intergateway communication.

2) a table of all gateways and their attached networks--This
table is maintained by intergateway communication -- gateways
give copies of their table 1 to all other gateways.  The table of
all gateways never shrinks (a down gateway is assumed to exist
but be unreachable).

3) a table of link states to neighbor gateways--This table in
gateway G specifies, for each neighbor gateway G1, over which
common networks G and G1 can communicate.  This table is updated
by G periodically bouncing packets off each neighbor gateway from
which it has not recently received traffic.  Note that I refer to
two gateways as neighbor gateways even if they cannot
(temporarily, hopefully) communicate with each other.

4) a list of neighbor networks--This list is derived from the
table of link states to neighbor gateways and the list of
gateways with attached networks (tables 3 and 2).

5) total link state--This is a table of all gateways and the
state of their links to their neighbor gateways.  This table is
compiled from intergateway communication.  When a gateway notices
that its table of attached networks, or its table of link states
to neighbor gateways (tables 2 and 3) changes, that gateway
efficiently broadcasts this information to all other gateways in
the catenet.  To minimize numbers of reports when a link is
flaky, a link on an attached network must be up continuously for
some amount of time before its state is considered to change from
down to up and trigger a link state report.

6) shortest distance matrix--This is a data structure from which
routing decisions can be made directly.  It is computed from the
other tables.  It is described more fully in part IV.


IV. ROUTING COMPUTATION

A gateway, using the tables described above, constructs a
connectivity matrix whose rows and columns represent networks,
and whose entries are 1 if any gateways claim to be attached to
both networks, and infinity otherwise.  Then the gateway *'s that
matrix to construct a shortest distance matrix.  (The operation
"*" consists of "multiplying" a matrix by itself, using the
operations min and plus instead of plus and times, until the
result stabilizes.  This is a well-known algorithm.)  The gateway


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then looks in the shortest distance matrix for the neighbor
network (or set of such) closest to the destination network, and
chooses a functioning neighbor gateway (or set of such) attached
to that neighbor network, to forward packets to for that
destination network.

When a link state report changes the state of an entry in the
connectivity matrix (remember, all gateways connecting two
networks have to go down before a 1 changes to infinity), a
gateway must recompute the distance matrix.

This design is a slight modification of the design presented in
"Gateway Routing", by Radia Perlman (PRTN #242, PSPWN #99).  The
modification is that the indices of the matrix are networks, not
gateways.  The purpose of this modification is to make the size
of the matrix smaller, an important modification given that in
the catenet there are many more gateways than networks.  There
are aspects to the scheme that are irrelevant to a discussion of
how to solve the network partition problem, such as sequence
numbers for link state reports, etc.  The purpose of this paper
is to direct a correct approach to the design, and not to present
an implementation specification.  Thus an implementer should read
PRTN 242 to discover the details of a link state algorithm that
were not relevant for presentation here.

Note that an alternative to *'ing the matrix is to use the scheme
that the ARPANET has switched over to, which is a link state
scheme in which a shortest path routing tree is constructed from
the connectivity information.  The new ARPANET scheme is less
costly to maintain as links change state.  Its disadvantages are
that it precludes load splitting, probably a very important
problem in the case of the catenet, and is probably a little
harder to implement.  Since links will not change state very
often, the author favors the overhead of the matrix *'ing scheme
over the disadvantages of the ARPANET scheme.  However, this
decision is separable from the rest of the design and can be
decided either way at a later time.


V. DETECTING THAT A NETWORK HAS PARTITIONED

Now we look at the problem of network partitions.  In the design
presented so far there is enough information for any gateway to
detect a partitioned network and to isolate groups of gateways on
each partition:  A gateway G knows that network N is partitioned
if there are two sets of gateways, set Q and set R, such that all
gateways in both sets report they are attached to network N, but
there are no two-way links between a member of set Q and a member
of set R via network N.  This information is derived
independently by each gateway from the table of all gateways and
their attached networks, and from the table of total link state
(tables 2 and 5).



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VI. DERIVING A NAME FOR EACH PARTITION

It is necessary to expand the internet header to allow a field
for identifying a network partition.  The reason for this is to
avoid the necessity for every gateway on a packet's route to
discover to which partition the packet should be sent.

The partition name must give sufficient information so that every
gateway can make the proper routing decisions to send a packet to
that partition, based on its tables of total link state and
gateways/attached nets (tables 5 and 2).

The following schemes for naming a partition are all done
independently by all gateways, as opposed to having some central
authority choose a name and inform all gateways, or having a
group of gateways decide on a name "by committee".

One method of identifying a partition is to use the name of any
member gateway of the partition.  It will not matter if two
gateways choose different names for the same partition.  Since
the sets of gateways involved in the network partitions are
disjoint, any member of the set identifies the set.

Another method is to list (either by an explicit list or a bit
table) the set of gateways that make up that partition.  This is
unnecessarily descriptive, since the list of gateways is
derivable from a single member of the set.  And it is a less
robust scheme, because any change to the partition (a gateway
going down, coming up, or the net partitioning into more pieces)
can confuse a gateway trying to route to that set of gateways.
In the first method, if the partition changes, the packet will be
routed unambiguously to whatever partition the named gateway is
in.  Of course, if the named gateway goes down, the packet
becomes undeliverable, but that is easier to deal with than
trying to deliver a packet to a set of gateways that overlaps two
partitions.

A third method is for each gateway to number partitions from 1 to
the number of partitions, ordered by, say, the highest numbered
gateway in each partition.  This method uses fewer bits in the
packet header but is a much less robust scheme.  With gateways
having slightly differing information, partition names have
different meanings.  Also, partitions can switch names suddenly.
For instance, a net can be partitioned into 2 pieces, numbered 1
and 2, and, assuming the highest numbered gateway was down, and
comes up in partition 2, partitions 1 and 2 now switch
identities.

Thus the recommended method of identifying a partition is the
first method.





                              - 4 -



VII. FIGURING OUT WHICH PARTITION A HOST IS IN

Now we will examine several schemes for having the correct
partition identified in a packet.  It is the responsibility of
either the source host or first gateway to do this.  By examining
the alternative schemes we can also determine whose
responsibility it should be.

a) Source host determines correct partition by trial and error --
The source host does not know about the structure of the catenet
and does not know that the destination net is partitioned.  When
it sends a packet to that net with no partition name filled in,
the first gateway to receive the packet sends back a message that
that network is partitioned, and lists the partition names.
Assuming there are k partitions, the source host sends k packets
requiring ACKs to the destination, each packet addressed to a
different partition.  The packet that receives an ACK is the one
addressed to the correct partition.

If a gateway receives a packet with an incorrectly filled in
partition name field, that gateway will send back the same kind
of notification as for a packet with a blank field -- it will
notify the host that the net is partitioned and list the
partition names, or if the net is no longer partitioned, give
that information.

If the source host is sending packets that require
acknowledgments, it will notice quickly if its packets stop
getting successfully delivered to the destination.  Then it can
redetermine the host's partition.

b) The first gateway, using trial and error -- If it is the first
gateway that has the responsibility, it can do the same thing as
the source host in scheme a, sending packets to the destination
addressed to each partition to discover from which partition it
receives an ACK.  Since a network is unlikely to be partitioned
into very many pieces, it is not costly to try all partitions.
Either the correct partition will be found or no ACK will return
(in which case presumably the host is down or the network is
partitioned in such a way that some hosts are unreachable from
all gateways).  The disadvantage of having the first gateway do
the work in this scheme is that a gateway does not know whether
packets it is forwarding successfully reach their destination.
Thus it must either keep a cache of host/partition
correspondence, which can be out of date for some amount of time
during which the gateway will misaddress packets to a
destination, or the gateway must rediscover the correct partition
on a packet by packet basis, which is of course unacceptably
expensive.  Also, assuming it is common for a source host to
split its traffic among several gateways on the source net, after
a gateway discovers the correct partition for a destination host
it should inform all other gateways on the source net of the
correct partition, to prevent the necessity of them rediscovering
that fact.

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c) gateways on a partitioned net could keep track of
host/partition correspondence for their net -- Another method is
for gateways on a partitioned net to find out which hosts they
can reach, and exchange that information with the other gateways
on that partitioned network.  Then a gateway could respond more
intelligently to a packet addressed to the incorrect partition by
sending back a message giving the correct partition (to the
packet source if that is who fills in the partition field in the
packet header, or to all gateways on the source net otherwise).
In addition, a gateway on the partitioned network can forward the
misaddressed packet to the correct partition.

This method requires gateways on the partitioned network either
to keep a complete list of the hosts on the net, marked as to
partition, or to keep a cache of hosts, adding hosts to the cache
by querying the gateways on other partitions at the time the
necessity of locating that host arises.  In the complete list
case, gateways on a partitioned net would periodically send
packets requiring ACKs to all hosts on that net in order to keep
their lists up-to-date.  In the cache case, gateways would poke a
host only when the need to know its location arose (when the
gateway received a packet for that host, and the host was not
already in its cache, or when a query from a gateway on a
different partition of the net arrived, asking for that host's
location).

This method suffers from the same problem as method b, with the
first gateway having responsibility for determining
host/partition correspondence -- the tables in the gateways on
the partitioned net can become out of date, during which time
they will misdirect traffic, and they cannot constantly be
checking their tables.

Thus I recommend method a, having the source host fill in the
partition field using the trial and error method of discovering
host/partition correspondence.


VIII. ROUTING PACKETS TO THE CORRECT PARTITION

As stated above, a gateway G, distant from partitioned network N,
must know which gateways are involved in a partition before G can
correctly route a packet -- it might have to make a different
routing decision for one partition than for another one.

When G detects a network has become partitioned into n pieces, G
must add n-1 rows and columns to its shortest distance matrix,
i.e., it treats each partition as a separate network.  It is an
implementation detail, and not a difficult one, to ensure that
the gateway understands the meaning of each row and column.  And
given that the gateway understands the meaning of each row and
column, it is easy for it to fill in the connectivity matrix from
its table of total link state.  The computation is done exactly
as in the nonpartitioned case.

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IX. MODIFYING THE ORIGINAL ARPANET ROUTING FOR PARTITIONS

The original ARPANET routing is the currently implemented routing
algorithm in the gateways.  The basic design is that gateways
report their distance vector to all their neighbor gateways
(their distance vector gives their distance to all destination
nets).  They derive their distance vector from their neighbors'
distance vectors. (A gateway's distance to a destination net is 0
if the gateway is directly attached to the destination net.
Otherwise, it is 1 hop further than the neighbor closest to the
destination.)

The major modifications that are necessary to handle partitioning
are:

1) Currently distance vectors are just a list of numbers, and
gateways have an assembled-in offset/net number correspondence.
Thus the vectors do not need labels for each entry.  If networks
became partitioned, more destinations would need to be reported
in the distance vector.  Either some (very complicated)
negotiation process would need to be carried out so that all
gateways would agree, when nets became more or less partitioned,
on a new offset/net number correspondence, or the distance
vectors would need labels identifying the destination whose
distance is being reported.  The problems associated with a
negotiation process make that scheme unworkable.  Thus we can
assume the vectors would be expanded to have an identifying label
for each destination.  The label would include net number and
partition name.

2) Gateways do not have global knowledge of the structure of the
catenet, in contrast to a link state scheme.  Thus it is the
responsibility of the gateways on a partitioned network to notice
that the net has become partitioned and start a routing update.

In the current implementation, there is no way for gateways on a
partitioned net to tell the difference between having their net
partitioned and having several gateways on their net go down,
since they do not receive information about individual gateways
-- they only receive distance vectors from their neighbors.  They
will no longer receive distance vectors from their neighbors on a
partitioned net, or from neighbors who have gone down, so lack of
response from neighbors does not distinguish between dead
neighbors and a partitioned network.

Thus either distance vectors would have to contain information
about all catenet gateways (which adds a great deal of overhead
since there are many more gateways than nets, and the only
purpose of doing that is to detect partitions) or gateways on a
network would report that the network has become partitioned
every time a gateway goes down.




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3) Gateways in a partition must agree on a partition name, since
if two of them started a routing update with two different names
for the same partition, the rest of the catenet can draw no
conclusion except that the two partition names refer to distinct
destination partitions.  Agreeing on a name is not that easy.  If
some simple algorithm is chosen, such as highest numbered gateway
in that partition, the name of a partition can change.  Suppose
the old partition name was 5 and it changes to 12.  A source host
(or distant gateway) has gone through the overhead of determining
that the proper partition for a destination host was 5.  When the
name of the partition changes, this overhead must be repeated.
Also, when the name of a partition changes, the rest of the
gateways on the catenet must be informed of that fact so that
they will stop reporting about obsolete partition names in their
distance vectors.


X. COMPARISON OF LINK STATE AND ORIGINAL ARPANET SCHEMES

The link state scheme is far more robust.  Because gateways have
global knowledge, routing is more likely to proceed calmly while
routing updates are percolating throughout the catenet.
Partition names are not as important in the link state scheme --
gateways do not have to agree on a single name for a partition.

As stated above, because in the currently implemented scheme
gateways report only their distances to destination networks, and
not to individual gateways, either gateways would report network
partitions whenever gateways went down, or the distance vectors
would have to be expanded to include reports about all gateways.
This is a further disadvantage of the original ARPANET scheme to
this application.

Another disadvantage of the original ARPANET routing, not related
to partitioning, is that, because nodes do not have global
knowledge of network connectivity, there are types of routing
loops which they cannot distinguish from degradation of best
routes due to connectivity changes.  As currently implemented in
the catenet, nodes report their distance to a destination as
"infinity" (a number higher than the maximum possible distance in
the catenet) when reporting to downstream neighbors.  This fixes
many kinds of routing loops.  However, neither this scheme nor
any variant (such as hold-down, the scheme chosen by the ARPANET
as a modification of the original algorithm) can distinguish all
kinds of routing loops from connectivity changes.  Thus there are
cases when a group of nodes will have to count up their distance
to a destination until it reaches "infinity" before discovering
the destination is unreachable.  This does not make the scheme
unworkable for the current catenet, since the longest possible
path in the catenet is less than 10 hops.  However, it is again a
further disadvantage of the original ARPANET scheme.




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Another important consideration is the link state scheme's
flexibility.  There are new features that the catenet is
scheduled to provide, most notably extended routing, in which the
functional differences between links are recognized and accounted
for.  As described in IEN #86 "Extended Internet Routing", by
Radia Perlman, a link state scheme must be adopted eventually in
order for the catenet to provide this service.

Thus the link state approach should be adopted to provide for
network partitioning.


XI. CONCLUSIONS

A link state scheme, as originally presented in PRTN 242,
modified as presented in part IV of this paper should be the
basis of internet routing.

The internet header should include a field long enough for a
gateway ID, for the purpose of specifying a partition name.  A
partition name is the ID of any member gateway on that partition.

The first gateway that handles a packet checks to see if it is
addressed to a partitioned network.  If so, and if the partition
name field in the internet header is blank, the gateway sends
back a special packet to the source host informing it that the
network is partitioned and giving it a name for each partition of
that network.  When a gateway on the source net handles a packet
for an unpartitioned network in which the partition name field is
not blank, it erases that field and informs the source that that
network is no longer partitioned.

When a source host receives notice that a network is partitioned,
it stores the partition names for that network, and when it
wishes to send a packet to a host on that net, it first tries all
partitions to determine the correct one.  It keeps a cache of
host/partition correspondence.  When packets for a host in its
cache no longer reach the destination, the source host should
again attempt to determine the correct partition for that host.
















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                            APPENDIX
               COMBINING USUALLY SEPARATE NETWORKS

In IEN 110, Dr. Vinton Cerf raises the possibility of combining
nets, given that the catenet could handle a partitioned network.
In general if the networks in question are usually partitioned,
this is a bad idea, since there is overhead involved in having a
partitioned network.  Every time a source wishes to send a packet
to a destination, someone must discover which partition to send
the packet to.

However, the specific example discussed in IEN 110 is an example
where there is also a cost associated with not combining
networks.  In the example there are two ground PR nets, A and B.
There are also a number of PRs on airplanes, call them P1, P2,
... Pn.  When Pi is within range of a PR in net A, Pi
automatically becomes a part of network A.  When Pi is within
range of both PR nets, the nets become a single PR net.

Keeping the two nets separate leads to problems of addressing the
airplane PRs, since the net on which they reside changes.
Combining the two nets into a single network has the overhead of
introducing a usually partitioned network into the catenet.

There is a third solution to the particular case involved here.
That is to keep networks A and B as separate logical networks,
and to have P1, P2, ... Pn also as separate logical networks on
the internet level.  On the packet radio level there might be
only one net, because one of the Pi connects nets A and B.  But
on the internet level there will be n+2 nets.

A gateway on net A, called G1, will have a half gateway
associated with each of the nets it might be "directly connected
to" in the internet sense.  In other words, it will have a half
gateway for A, P1, ... Pn.  The half gateway associated with
network A determines whether its interface to net A is up or down
depending on the state of the hardware ready line, etc., as is
now done.  The half gateway associated with "network" Pi must
determine whether it is "connected" to its "network" by some
other means.  One method is to have a special querying packet
containing the number i.  The packet would be addressed, with a
local header only, to Pi, and sent out the interface to network
A.  Pi's responsibility, upon seeing this querying packet, is to
send back a special answering packet, also containing the number
i.  The half gateway associated with network A, upon receiving
one of these special answering packets, uses the number contained
in the packet to dispatch the packet to the half gateway
associated with Pi.  The half gateway associated with Pi, upon
receiving this special answering packet, knows that its "network"
is up.

G1's list of neighbor gateways will include, besides all the
gateways on net A, all the gateways on net B, since a gateway on


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net B also has the Pi as potential attached networks.  If some Pi
connects nets A and B, then the gateways on A and B will all
consider each other functional neighbors, and A, B, and the
connected Pi, which have formed themselves into a single
functional PR net, will function as a single net on the internet
level, too.  If one of the Pi is not within reach of either net A
or net B, then all the gateways on nets A and B will report that
they are not attached to net Pi, and all the gateways in the
catenet will know Pi is unreachable.  If A and B have not merged
into one net (none of the Pi are in both nets), then the gateways
on each will report which Pi are reachable from them, so the
catenet will automatically route packets for Pi to the correct
ground PR net.

[It would be reasonable to include, in gateway G1, a half gateway
for net B also, since if nets A and B merged, G1 would be
connected to net B.  However, it is not necessary to and is
slightly more efficient not to, since even if nets A and B are
merged, PRs in B are probably physically closer to the gateways
on net B, so the catenet should route packets for PRs in B to the
gateways that "really" are on ground net B.  The advantage of
including a half gateway for B in G1 is that net B could
potentially partition in such a way that some partition included
no gateways from B, but was reachable in the catenet via net A
and some Pi.  It is not obvious, however, what algorithm a half
gateway for B should use to determine whether its "network" is
up.]

The airplane PR Pi does not think of itself as a network.  From
its point of view it is an ordinary PR.  The only difference
between Pi and an ordinary PR on net A is that Pi (or the TIU
attached to Pi, if we want to strictly adhere to packet radio
terminology) has stored as its internet address, Pi for its net
number.  It also has a list of possible gateways to use for
internet packets.  This list includes all the gateways on nets A
and B.  In the current PR net there is only one gateway, and all
PRs know the ID of the gateway.  This will change such that there
will either be a special ID for an information service that will
give out the ID of a gateway on the net (so that Pi, instead of
keeping a list of gateways, could ask for a gateway address, as
would the rest of the PRs on nets A and B) or all PRs will have
assembled in a list of gateways, and they will need to probe each
in turn until they find one that responds.  Thus the only
difference in Pi's finding a gateway and in an ordinary PR on net
A finding a gateway, is that (assuming the assembled-in gateway
list scheme is used) Pi's list will be longer, since it will also
include the gateways on net B.

There is obviously a cost associated with this solution, too.  If
the number of Pi are small, then this is a reasonable solution.
If there are enough Pi, then the cost of having all those logical
nets becomes greater than the cost of having an often partitioned
network, so the solution of combining A, B, and all the Pi into
one logical net in the catenet is a more practical solution.

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