+====+           +====+           +====+           +====+
          |  H |   <---    |  I |    --->   |  J |    --->   |  K | 	
             |     \__                         |        ___/    |
             |        \                        |       /        |
             V         _|                      V     |_         V
          +====+           +====+           +====+           +====+
          |  D |           |  E |           |  F |  <---     |  G |
             \  \         __/  \__         __/  \__        /  / 
              \  \       /         \      /        \      /  / 
               _| _|   |_           _|  |_          _|  |_ |_  
                  +====+            +====+           +====+
                  |  B |    --->    |  A |   <---    |  C |    
                     |                | |               |
                     V                V V               V
 ------------------------------------------------------------------Omega

				
			

Figure 6: ARC DAG

An ARC Set can be represented in a number of fashions:

Graph View:

ARC View:

Collapsed DAG view:

4. Applicability

This section has to be refined. ARCs probably apply to both unicast and multicast and the authors expect further documents to explain how that is done. The examples below are provided as an indication but is not limiting the field of applications.

4.1. Load Balancing

In normal conditions, only the Cursor may distribute its traffic between the two Edge Nodes. If an Edge Node is still congested after the Cursor forwards all its traffic towards the other Edge Node, then the Cursor can be moved towards the congested Edge in order to derive even more traffic towards the other Edge. If both Edges are congested, then a back-pressure can be applied on the incoming ARCs so that they move their own traffic towards their own alternate Edge. The process may recurse.

It is expected that control frames similar to those defined for MPLS Fault Management Operations, Administration, and Maintenance (OAM) [RFC6291] will echo from Edge Node to Edge Node provide information such as liveliness and load. In order to establish a control loop between the Edge Nodes and the Cursor, the OAM frame would carry at least a logical information whether:

• The Edge Node is capable of forwarding data down to the next ARC
• the load may be increased (e.g. rate below threshold including hysteresis)
• the load should be decreased (e.g. congestion observed as increased latency or buffer bloat)

If the load should be decreased towards of congested Edge Node and the load may be increased towards the other then the Cursor may adjust its balancing of the load, or move Cursor ownership towards the congested Edge if it is already redirecting all the traffic towards the non-congested Edge.

If the Cursor is balancing traffic away from the default position due to a past congestion notification and the Edge that was congested now reports that the load may be increased, then the reverse operation can happen and the Cursor may rebalance the load back to the original position taking the reverse steps as above.

If the OAM can not be forwarded due to a link or a node failure, then the last node towards the broken Edge becomes Cursor and echoes the OAM frames advertising that it is an Edge node that is blocked, not capable of forwarding data down to the next ARC.

If both Edges are experiencing a congestion then the condition should be reported to the Edge Nodes of all incoming ARCs. Same goes when both Edges are blocked.

4.1.1. Routing Hierarchies

The ARC methods may be used to build and/or leverage routing hierarchies, allowing high availability at multiple hierarchical levels. In one hand, the view of an ARC Set can be simplified by abstracting an ARC as a node in a DAG. The view of the routing topology is thus simplified, as illustrated in Figure 6. In the other hand, ARCs may be used inside a sub-topology, such as a ring, to enable forwarding inside a ring towards a next ring. Then, abstracting a full ring as a node, ARCs can be applied to a graph of rings, providing another level of redundancy and an abstract end to end path computation that is represented as a cascade of ARCs of rings.

5. Lowest ARC First

The open Lowest ARC First(oLAF) algorithm is presented below in such a way as to help the reader figure how an ARC Set can be obtained but not in a computer-optimized fashion that is left to be determined. oLAF is based on Dijkstra's algorithm for Shortest Path First (SPF) computation, and is designed in such a fashion that the reverse SPF tree towards a destination is conserved and preferred for forwarding along the resulting ARC Set.

We make the computation on behalf of Omega, that is an abstraction, but could represent the node or the set of nodes that we want to reach with an ARC Set. If Omega is instantiated as an actual destination node, then that node may be a fine location for an ARC Computing Engine.

5.1. Init

So we start with an proverbial Initial Set of Nodes that are interconnected by Links, and Omega that is the destination that we want to reach with an ARC Set.

If there is no Heir, we're done. If there is a single Heir then the graph is monoconnected, so we restart the computation taking that Heir off the Set of Nodes and making it Omega.

Else, if Omega is a single Node, or if Omega is composed of multiple nodes but we are willing to accept that both ends of an ARC terminate in a same node in Omega, then we create virtual Omega nodes, a minimum of two and at most one per Heir, and we make them the new Omega. Note: we need at least two destinations because both ends of an ARC cannot terminate in a same node.

Now we can start building an ARC Set towards the resulting Omega.

In this process, we create so-called Dependent Sets of nodes, each owned by a Safe Node S, DSet(S). DSet(S) contains nodes that are not determined to be Safe at the current stage of the computation and for which S, the owner Safe Node, is the last single point of failure on the shortest path tree to Omega. It results that a given node can be at most in one DSet, and that a Safe Node belongs to its own DSet.

For each node S in Omega we create a DSet(S) in which we place S.

5.2. Growing Trees

And then the process goes like this:

We select the node in the Set of Nodes that is closest to Omega using the cost towards Omega as if we were building a traditional reverse SPF tree and we place the selected node in the same Dependent Set as its parent in the reverse SPF tree. Note that for a Heir, the parent might be a real node in Omega, or a virtual Omega node.

If we kept it at that, we would be building subtrees that are hanging off a Safe Node and together would represent the reverse shortest path tree towards Omega, each subtree being grown separately inside DSet(S) where S is the (virtual) Safe node that is the root of the subtree.

5.3. Being Safe

But once we have placed the selected node in a DSet, we consider its neighbors one by one. If at least one of the neighbors is already in a different DSet than this node, we select the neighbor that provides the shortest alternate path to Omega for the selected node.

Doing so, we have isolated two paths:

• one along its own shortest path that is contained within its own Dependent Set and that leads to the owner Safe Node of this set.
• and one via the selected neighbor, along its own shortest path within the selected neighbor's Dependent Set and that leads to the owner Safe Node of that other set.

Because the two sets are different and have no intersection, these paths are non-congruent. And because the two non-congruent paths lead to two different Safe Nodes, this node is Safe.

It might happen that:

• the selected node's parent is already a Safe Node, in which case the selected node is the Edge AN on its shortest path side.
• It might also happen that the selected neighbor is already a Safe Node, in which case selected node is the Edge AN on its alternate side.

If both conditions are met for a same AN, then that AN forms a collapsed ARC by itself.

5.4. Bending An ARC

Now we form an ARC as follows:

• A height is attributed to this ARC that must be strictly more than that of the ARCs it terminates into, if any. The order in which the ARCs are built may be used in some cases.
• The ARC terminates in the two Safe Nodes that are the owners of the two DSets. The normal behaviour is to make a Edge Link the link to the Safe Node.
• If the Safe Node at one end forms a collapsed ARC by itself, it may be absorbed in the ARC in order to build a multi-edged ARC.
• If one of the two Safe Nodes pertains in a ARC or a Comb construct that is higher than the other end, then this ARC may be merged at the Safe Node with its original ARC, in order to form a Comb construct whereby this ARC is a Buttressing ARC of the Comb. The resulting Comb conserves the height on the original ARC or Comb that it extends.
• The ARC is built by adjoining the two non-congruent paths that we isolated for the selected node.
• The selected node is the node farthest from Omega in the resulting ARC, so we make it the Cursor.
• The link between the selected node and the selected neighbor would not have been used in a classical reverse SPF tree. Here, we have determined that this link is in fact critical to connect 2 zones of the network (the DSets) that can act as a back up for one another in case of the failure of their respective single points of failure (the Safe Nodes).
• Because the ARC can be used in both directions, each AN along the ARC has two non-congruent paths to the Safe Nodes that the ARC terminates into. So it is a Safe Node. We create individual DSets for each AN and we move the AN to its own DSet.

5.5. Orienting Links

For each ARC Node along the ARC:

• any link (there can be zero for a collapsed ARC, one for an Edge AN or two of them for a Intermediate AN) between this AN and a next AN along this ARC is made an Intermediate Link, that is, reversible. The normal direction, away from the Cursor, preserves the shortest path.
• If this AN is an Edge AN for this ARC, than all links off this node that terminate in a Safe Node are made Edge Links, that is, outgoing but not reversible.
• All the other links left undertermined.

The nodes left in the Dependent Sets but the owner Safe Node are still not Safe. They are moved back to the original Set of Nodes to enable forming additional ARCs which might depend on this ARC in the ARC Set.

5.6. Looping or recursing

We are done processing the particular node we had picked in the original Set of Nodes. If the Set of Nodes as it stands now is not empty, we continue from Section 5.2.

If the Set of Nodes went empty, we are done with this pass and we consider the Dependent Sets that we have put together. In a biconnected graph, there should be one set per node and one node per set, denoting that every node is a Safe Node.

If some portion of the graph is monoconnected, then each monoconnected portion forms the Dependent Set of the Safe Node that is its single point of failure. In order to be maximally redundant, we need to form the ARCs again, within the Dependent Set.

To do so, we remove the Safe Node from the Dependent set and make it Omega. We make the resulting DSet our Set of Nodes and run the algorithm again.

This may recurse a number of times if the graph has monoconnected zones within others.

6. Forwarding Along An ARC Set

Under normal conditions, the traffic flows away from the Cursor of the current ARC and cascades into the next ARC on that side of the Cursor, with the Height of the current ARC decreasing monotonically from ARC to ARC till Omega is reached.

The same goes for a generic Comb construct. When Buttressing ARCs are applied on a main ARC or other Buttressing ARCs, the final construct assumes the shape of a tree. The tree may be walked in different manners but the shortest path requires to start going down the current ARC or Buttressing ARC to its Edge.

In case of Label forwarding, the same recursivity is applied and a multiple ARC label path is constructed. Each ARC has is own set of label path per Omega, each ARC Set label path being merged into the lower ARC label set, thus at the interconnection point. At minimum, ARC label path should be built from the Cursor toward each edge, but this would require label path recompilation upon Cursor move, the proposed approach is then to build for the normal flow to an Omega one pair of label path from edge to edge.

As this label construct maps the ARC topology with local significant label, the Label Distribution Protocol (LDP) could be reused to announce label association to neighbors on the ARC.

Upon a breakage inside an ARC, until a corrective action takes place, some traffic will be lost. The corrective action might be either operated at the control plane or the data plane, if immediate action and near-zero packet loss is required.

6.1. Control Plane Recovery

Upon a first breakage in an ARC, the Cursor is moved to the breakage point, either a node or a link, so that traffic flows away from the Cursor again.

Upon a second breakage within a same ARC, a segment of the ARC is now isolated. Both breakage points become sinks till an additional corrective action, such as modifying the ARC Set, takes place. All incoming links in the isolated segment are blocked , causing the traffic to exit at the other end of the incoming ARCs.

Blocking an Edge Link in the incoming ARC may create an isolated segment in the incoming ARC as well if it is a second breakage there too, or if both edges of the incoming ARC tterminate in the broken segment. In that case the process recurses and the broken zone can be determined as the collection of the isolated segments.

If a segment of an ARC is getting isolated by a dual failure but that ARC segment has incoming Edges then the ARC can be reversed. This reversal is done by reversing of all the incoming Edges, which become outgoing. The segment that was isolated now benefits from multiple exits in a loop free fashion. This process might in turn isolate a segment of an ARC that was incoming and the process recurses and some links flap. If a real exit exits the process will stabilize, but a count to infinity must be put in place to avoid a permanent flapping when a whole ARC Subset is physically isolated. One may consider that this process is in fact the classical link reversal technique, as applied to the DAG of ARCs.

6.2. Data Plane Recovery

Upon a breakage inside an ARC, it is possible in the data plane to reverse the direction of -to turn- a given packet once along the ARC so the packets exits over the other Edge Link. But in order to avoid loops, it is undesirable to reverse the direction of a given packet a second time.

Note that once a given packet leaves an ARC to enter the next, it is free to bounce again in the next ARC. In other Words, the domain that is impacted by a turn is limited to the current ARC itself; the ARC forms the event horizon wherein the notion that a turn happened may cause a loop.

So a local strategy must be put in place inside an ARC to allow a given packet to bounce once upon a breakage, and get dropped upon a second breakage.

In the case of IP packet forwarding, a packet can be tagged when it bounces inside an ARC, or when it passes the Cursor, for instance by reserving a TOS bit for that purpose. When the packet bounces, the bit is set and when the packet leaves the ARC, the bit is reset and may be used again in the next ARC. In the generic case of a Comb, a strategy must be put in place to walk the structure and drop a packet that tries all the Edges. it attempts to pass the Cursor twice in a same direction, meaning that more than a full walk was already accomplished.

In the case of MPLS forwarding, the same result can be achieved with either 3 or 4 Labels Switched Paths (LSPs) along the ARC.

3-Labels method:

In this case we lay a primary LSP from the cursoo to the Edge in each direction, and a backup LSP Edge to Edge in each direction. So a node along the way has three labels, one primary and two backup, one in each direction. Should the primary path fail, the packet can be placed along the backup LSP in the other direction. We'll note that this method contrains the location of the Cursor. Should the Cursor move, The primary LSPs have to be recomputed, at a minimum between the old and the new location of the Cursor where the direction is reversed.

4-Labels method:

In this case we have two primary and two backup LSPs Edge to Edge in each direction. The labels are independent of the location of the Cursor, so the Cursor can be moved in control plane with no impact on labels.

7. Manageability

This specification describes a generic model. Protocols and management will come later

8. IANA Considerations

This specification does not require IANA action.

9. Security Considerations

This specification is not found to introduce new security threat.

10. Acknowledgements

The authors wishes to thank Dirk Anteunis, Stewart Bryant, IJsbrand Wijnands, George Swallow, Eric Osborne, Clarence Filsfils and Eric Levy-Abegnoli for their participation and continuous support to the work presented here.

11. References

11.1. Normative References

[RFC2119]	Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC6291]	Andersson, L., van Helvoort, H., Bonica, R., Romascanu, D. and S. Mansfield, "Guidelines for the Use of the "OAM" Acronym in the IETF", BCP 161, RFC 6291, June 2011.

11.2. Informative References

[I-D.thubert-rtgwg-arc-bicast]	Thubert, P. and I. Wijnands, "Applying Available Routing Constructs to bicasting", Internet-Draft draft-thubert-rtgwg-arc-bicast-01, October 2013.
[RFC5921]	Bocci, M., Bryant, S., Frost, D., Levrau, L. and L. Berger, "A Framework for MPLS in Transport Networks", RFC 5921, July 2010.

Authors' Addresses