1. Hierarchical Routing: 1.Leonard Kleinrock and Farouk Kamoun: Hierarchical routing for large networks: Performance evaluation and optimization, Computer Networks, Vol. 1(3):155-174,, Jan. 1977. 2.PNNI Routing, Private Network-Network Interface Specification Version 1.0, ATM Forum, March 1996. 3.Paul Tsuychia, The Landmark Hierarchy: A new hierarchy for routing in very large networks, ACM Sigcomm, p. 35-42, 1988.

2. Leonard Kleinrock and Farouk Kamoun: Hierarchical routing for large networks Performance evaluation and optimization Computer Networks, Vol. 1(3), Jan 1977, pp. 155-174 (uses slides prepared by Boris Drazic)

3. Routing in the 1970s Computer networks are new and have a small number of nodes ARPANET is predecessor of Internet Uses concepts of: – routing table (RT) – Distributed routing protocols ARPANET 1969

4. Routing in the 1970s Computer networks are new and have a small number of nodes ARPANET is predecessor of Internet Uses concepts of: – routing table (RT) – Distributed routing protocols ARPANET 1971

5. Routing in the 1970s Computer networks are new and have a small number of nodes ARPANET is predecessor of Internet Uses concepts of: – routing table (RT) – Distributed routing protocols One routing table for each “node” of the network ARPANET 1980

6. Number of Internet Hosts Source: Internet Systems Consortium (www.isc.org)

7. Active BGP Entries (FIB) Source: http://www.cidr-report.org/

8. Example of Routing Table (1) DestinationNext-hop bb cc db eb fb gb hb ib Routing table for node a

9. Hierarchical Routing Schemes Goal: Reduce the size of routing tables (RT) Approach: Keep complete routing information about nodes that are “close” and less information about nodes that are “far away” – One RT entry for every destination that is “close” – One RT entry for every set of destinations that is “far away” Forwarding has two parts: 1.Forward the message “close” to the destination 2.Forward the message to the destination

10. Example of RT (2) DestinationNext-hop bb cc 2b 3b Routing table for node a “close” destinations “far away” destinations `

11. m-level Hierarchical Clustering Create a hierarchy with m levels by: – Each node is a 0 th level cluster – Group nodes into 1 st level clusters – Group 1 st level clusters into 2 nd level clusters – …

12. ` 3 rd level cluster 2 nd level cluster 1 st level cluster 0 th level cluster

13. Tree representation in 3-level hierarchy

14. ` 3 rd level cluster 2 nd level cluster 1 st level cluster 0 th level cluster

15. RT in 3-level Hierarchical Clustering DestinationNext-hop 1.1.1self 1.1.2 1.1.3 1.1.41.1.2 1.1self 1.21.1.2 1.31.1.2 1self 21.1.2 31.1.3 nodes in same cluster ` clusters in same supercluster superclusters 0 th level cluster entries 1 st level cluster entries 2 nd level cluster entries

16. Example: Source: 1.1.1 Destination: 3.2.2

17. What is the optimal clustering in a network with N nodes? Proposition 1: Given the number of levels m, if each cluster has the same number of lower level clusters, the minimum routing table lengths is. Proposition 2: The global optimal clustering is achieved for m=ln(N), when each cluster has e lower level clusters, and the minimum table length is l=e ln(N).

18. Minimum Relative Table Length RT size decreases fast for m < ln(N) Minima for: m = ln(N)

19. Hierarchical Routing increases path length Shortest path: 4 hopsWith hierarchical routing: 5 hops Example: Source: a Destination: i

20. Increased Path Length Assumption 1: Every cluster has the same number of sub-clusters and for every pair of nodes in a cluster a path exists between them in that cluster Assumption 2: The diameter of any k th level cluster is less or equal to some quantity d k h c is average path length with clustering h is average path length without clustering

21. Increased Path Length Proposition 10: Under Assumptions 1 and 2

22. Limiting Performance Assumption 3: Any cluster contains the shortest path between any pair of nodes that belong to that cluster Proposition 11: Under Assumptions 1-3, for an m-level optimal clustering hierarchy where the diameter of any cluster is bounded by a power law function of the number of nodes in that cluster:

23. Increased Path Length Define as the increase in path length produced by introducing clustering Observe E, which is a bound on D Presented results for a network where Assumptions 1-3 hold

24. Decrease in RT Length for a Given Maximum Increase in Path Length Interpret “E” as the tolerated “stretch” factor

25. Conclusion In very large networks, hierarchical routing schemes achieve great reduction of routing table size with only a small increase in path lengths between nodes, when compared to non-hierarchical routing schemes

26. Hierarchical Routing Application: ATM Networks In the 1990s, the ATM Forum adopted a routing scheme which is based on hierarchical routing

27. ATM Connection Acronyms VC - virtual channel, synonymous with “ circuit ” or “ connection ” VPC - virtual path connection VCC - virtual channel connection PVC - permanent virtual circuit PVP - permanent virtual path SVC - switched virtual circuit SVP - switched virtual path SPVC - switched/signaled/soft permanent virtual circuit PMP - point-to-multipoint

28. Traditional Network Infrastructure Company A Company B Telephone network Data network Residential user x Video network

29. The B-ISDN vision (from mid 1980s!) Company A Company B Residential user x Broadband Integrated Services Network (B-ISDN)

30. ATM’s Key Concepts ATM uses Virtual-Circuit Packet Switching – ATM can reserve capacity for a virtual circuit. This is useful for voice and video, which require a minimum level of service – Overhead for setting up a connection is expensive if data transmission is short (e.g., web browsing) ATM packets are small and have a fixed sized – Packets in ATM are called cells – Small packets are good for voice and video transmissions Header (5 byte) Data (48 byte) Cell is 53 byte long

31. Virtual Paths and Virtual Circuits Virtual Path Connections Virtual Channel Connection VPI identifies virtual path (8 or 12 bits) VCI identifies virtual channel in a virtual path (16 bits) Link

32. VPI/VCI assignment at ATM switches 1/24 7/24 3/24 1/40 3/24 2/17

33. PNNI UNI: User-to-Network Interface NNI: Network-to-Network Interface PNNI: Suite of protocols for topology discovery and routing of an ATM network

34. PNNI Routing Goal of PNNI Routing: Establish a switching path from sender to receiver PNNI characteristics: – Link State Routing – Source Routing – Hierarchical Routing – Crankback Routing protocol information is sent on VPI/VCI=0/18

35. Link State Routing Algorithm B.2.2 B.2.1 B.2.3 B.1.1B.1.2 B.3.2 B.3.1 PNNI uses link state routing: – Each node floods route messages on its links to all nodes in the network – Each node has complete topology information Source routing: PNNI computes route at the first switch QoS: Route messages also contain QoS information on links Hierarchy: PNNI deals with complex networks by using a hierarchy

36. PNNI Routing Hierarchy Routing hierarchy is defined recursively: – Neighbor nodes build Peer Groups by comparing their address prefixes (nodes with longest prefix match are in the same peer group) – Each group behaves like a Logical Group Node (LGN) in the next level peer group A.1.2 A.1.1 A.2.2 A.2.1 A.2.3 B.2.2 B.2.1 B.2.3 B.1.1B.1.2 B.3.2 B.3.1 C.1.2 C.1.1 A.1 A.2 B.2 B.1 B.3 C.1 A C B

37. Building the PNNI Routing Hierarchy A.1.2 A.1.1 A.2.2 A.2.1 A.2.3 B.2.2 B.2.1 B.2.3 B.1.1B.1.2 B.3.2 B.3.1 C.1.2 C.1.1 Each switch is initialized with a 20-byte ATM address

38. PNNI Routing Hierarchy Nodes with common prefix A.1, A.2, B.2, B.2, B.3, C.1 each form a logical group node A.1.2 A.1.1 A.2.2 A.2.1 A.2.3 B.2.2 B.2.1 B.2.3 B.1.1B.1.2 B.3.2 B.3.1 C.1.2 C.1.1 A.1 A.2 B.2 B.3 C.1 B.1

39. PNNI Routing Hierarchy Nodes with common prefix A, B, C each form a logical group node at the next level A.1.2 A.1.1 A.2.2 A.2.1 A.2.3 B.2.2 B.2.1 B.2.3 B.1.1B.1.2 B.3.2 B.3.1 C.1.2 C.1.1 A.1 A.2 B.2 B.3 C.1 B.1 A C B

40. Resulting Hierarchy Within each peer group, nodes or LGNs elect a peer group leader (PGL), which represents the peer group at the next level A.1.2 A.1.1 A.2.2 A.2.1 A.2.3 B.2.2 B.2.1 B.2.3 B.1.1B.1.2 B.3.2 B.3.1 C.1.2 C.1.1 A.1 A.2 B.2 B.1 B.3 C.1 A C B

41. Complete Hierarchy A.1A.2 B.2 B.1 B.3 C.1 A C B

42. Routing Messages Hierarchy A.1A.2 B.2 B.1 B.3 C.1 A C B Routing messages are called PNNI Topology State Packets (PTSP) 1.Nodes within each peer group exchange PTSP 2.Group Leader relays routing information from higher level topology to lower layer

43. Resulting Hierarchy Node B.2.3 ’ s view of the network topology Node can now run source routing C B.1 B.2.2 B.2.1 B.2.3 B.2 C B B.3 A

44. Source routing in the hierarchy At A.1.1 : Route = [ (A.1.1, A.1.2), (A.1, A.2), (A, B)] At A.1.2 : Route = [ (A.1, A.2), (A, B)] At A.2.1 : Route = [ (A.2.1, A.2.2, A.2.3), (A.1, A.2), (A, B)] At A.2.2 : Route = [ (A.2.1, A.2.2, A.2.3), (A.1, A.2), (A, B)] At A.2.3 : Route = [ (A, B)] At B.1: Route= [ (B.1, B.3), (A, B) ] At B.3: Route= [ ] A.1.2 A.1.1 A.2.1 A.2.2 A.2.3 B.2 B.1 B.3 A.1 A.2 A B desti- nation source

45. Crankback and Alternate routing At A.1.1 : Route = [ (A.1.1, A.1.2), (A.1, A.2), (A, B)] At A.1.2 : Route = [ (A.1, A.2), (A, B)] At A.2.1 : Route = [ (A.2.1, A.2.2, A.2.3), (A.1, A.2), (A, B)] At A.2.2 : Route = [ crankback: (A.2.1, A.2.2, A.2.3), (A.1, A.2), (A, B)] At A.2.1 : Route = [ (A.2.1, A.2.3), (A.1, A.2), (A, B)] At A.2.3 : Route = [ (A, B)] and so on A.1.2 A.1.1 A.2.1 A.2.2 A.2.3 B.2 B.1 B.3 A.1 A.2 A B desti- nation source QoS cannot be satisfied

46. Paul Tsuychia: The Landmark Hierarchy: A new hierarchy for routing in very large networks ACM Sigcomm 1988, p. 35-42

47. Drawback of Hierarchical Routing 1.2.1 1.2.2

48. Enter “Landmarks” Landmarks can be seen from far away! Landmark router: Normal router can see a landmark router from several hops away  Information about landmark routers is disseminated to normal routers

49. Landmark router Router 1 is landmark router with radius 2 – Routers up to 2 hops away have routing entries for Router 1  Router 1 can be seen from 2 hops away

50. Hierarchy of Landmarks Every router is a level-0 landmark with a small radius Some level-0 landmarks are level-1 landmarks 1.Radius of level-1 landmark is greater than that of level-0; 2.Each level-0 landmark LM 0 [id] can reach at least one level-1 landmark in r 0 [id] hops Some level-1 landmarks are level-2 landmarks 1.Radius of level-2 landmark is greater than that of level-1; 2.Each level-1 landmark LM 1 [id] can reach at least one level-11 landmark in r 1 [id] hops …… A small number of routers are level-H landmarks (“global landmarks”) 1.Every router “can see” all level-H landmarks Notation: i : level number (0 is lowest level, H is highest level) LM i : landmark at level-i LM i [id]: specific landmark at level i with identifier id r i [id]: Radius of LM i [id]

51. Forwarding in Landmark Hierarchy Destination: LM 0 [a] Source forwards packet towards LM 2 [c] Once the packet is within reach of r 1 [b], packet is sent towards LM 1 [c] Once the packet is within reach of r 0 [a], packet is sent towards LM 0 [a] r 2 [c] r 1 [b] r 0 [a] Source LM 0 [a] LM 1 [b] LM 2 [c]

52. Routing Table Each router keeps a table of the next hop on the shortest path to each landmark for which it has routing entries: – Each router has entries … for every LM 0 [id] within a radius of r 0 [id], … every LM1[id] within a radius of r1[id], … and so on. This ensure that a router – has full knowledge of all routers within immediate vicinity (i.e., the LM 0 routers) – has knowledge of a portion of the network routers further away – Has full local information, and increasingly less information further away in all directions Note the difference to pure hierarchical routing

53. Addressing In a pure hierarchy: The address of a router is a reflection of the area(s) at each hierarchical level in which the router resides e.g., telephone number +1-416-946-3403 In a Landmark hierarchy: The address of a router is a reflection of the Landmark(s) at each hierarchical level which the router is near. Landmark Address is a series of Landmark identifiers LM H [id H ].LM H-1 [ID H-1 ]...LM 0 [id 0 ] such that: 1.The landmark represented by each address component must be within radius of the landmark in the next lower address component 2.Nodes may have multiple address (since more than one level-n landmark may be within radius of a level-n-1 landmark)

54. Forwarding Path: Source  LM0[a] Address of LM0[a]: LM 2 [c].LM 1 [b].LM 0 [a] 1.At source: – has entry for LM 2 [c] – forwards towards LM 2 [c] 2.At first router within r 1 [b]: – has entry for LM 1 [b] – forwards towards LM 1 [b] 3.At first router within r 0 [a]: – has entry for LM 0 [a] – forwards towards LM 0 [a ] r 2 [c] r 1 [b] r 0 [a] Source LM 0 [a] LM 1 [b] LM 2 [c]

55. Forwarding 1.Routing path in landmark routing are longer than shortest path 2.Path do not necessarily traverse the landmarks given in a landmark address r 2 [c] r 1 [b] r 0 [a] Source LM 0 [a] LM 1 [b] LM 2 [c]

56. Example: d.i.k All routers are LM 0 (r 0 =2) Diamonds: LM 1 (r 1 =4) Large circles: LM 2 (r 2 =8)

57. Example: All routers are LM 0 (r 0 =2) Diamonds: LM 1 (r 1 =4) Large circles: LM 2 (r 2 =8) LandmarkLevelNext Hop LM 2 [d]2f LM 1 [i]1k LM 0 [e]0f LM 0 [k]0k LM 0 [f]0f Routing table of g:

58. Example: Source: g Destination: t Address of t: d.n.t LandmarkLevelNext Hop LM 2 [d]2f LM 1 [i]1k LM 0 [e]0f LM 0 [k]0k LM 0 [f]0f Routing table of g:

59. Dynamic Algorithms Several algorithms are needed: – Assign landmarks and determine radii – Discover landmarks and establish path to landmarks – Needs to use distance vector, and not link state (Why?) – Modification to distance vector: radius limits advertisements – Bind identifiers (id’s) to addresses – Addresses of a router can change

60. Performance Evaluated by simulation Performance metrics: – Average routing table size: R – Stretch: Ratio of paths length of landmark or hierarchical routing ( ) to shortest path ( )

61. Simulations Compared simulation of pure hierarchy with landmark hierarchy 200 routers Different settings Comment: Method of comparison questionable

62. Landmark routing r i : radius of level-i landmark d i : distance to nearest level-i landmark

63. Summary Landmark hierarchy has similar performance as pure hierarchical routing Easier to configure (claimed): – Not very sensitive to placement of landmarks – More sensitive to failures