routing

1. routing CSE 4344

2. CSE 4344 network layer in context layer 1: physical (PHY) layer layer 2: datalink layer and MAC sublayer transmits frames (containing packets) between adjacent nodes, arbitrates access within collision domains layer 3: network layer routes packets between endpoints “end to end”, “source to destination”, “source to sink” transport layer cooperates with transport layer on node at other end to manage streams of traffic supporting app layer comms (layers above 1, 2, 3 differ by network protocol stack)

3. CSE 4344 challenges in internetworking heterogeneity many different kinds of networks: Ethernets, wireless, pt-to-pt links, switched rings, etc scale Internet doubled each year for the last 20 years which paths, thru millions/billions of nodes? efficient, loop-free unambiguous addressing of all these nodes?

4. CSE 4344 store-and-forward packet switching data network --- environment:

5. CSE 4344 store-and-forward packet switching routers perform store-and-forward receive packet, do checksum, [queue,] compute egress link, transmit over egress link routers are aware of each other on the network layer, but the transport layer is not aware of routers what is the transport layer aware of? a few generic system calls

6. CSE 4344 network services for transport layer ideals transport layer makes generic system calls to network transport layer otherwise ignorant of what goes on in network network shows tech-neutral face to transport layer whether connection-oriented or connectionless global network addresses

7. CSE 4344 network layer in a nutshell “datagram subnet”, “packet-switched network”, “statistically multiplexed network” Internet Protocol, ATM, others for each generic router: routing computations initialize & renew forwarding table forwarding table (“next hop” table): {(destination, egress line, <protocol specific>)} receive packet, [checksum,] [queue,] route toward sink next router does the same

8. CSE 4344 connectionless service routing within a packet-switching network (sink, next hop)

9. CSE 4344 routing algorithms the Optimality Principle shortest path routing flooding Distance Vector Routing (DVR) Link State Routing (LSR) hierarchical routing broadcast routing multicast routing routing for mobile hosts routing in ad hoc networks

10. CSE 4344 graph theory and the network layer like a horse and carriage set N of nodes, set E of edges edges are full duplex, arcs are simplex graph G = (N,E) N = (a,b,c,d) E = ((a,b), (a,c), (b,c), (b,c))

11. CSE 4344 graph theory walk: a sequence of adjacent nodes path: a walk with no node repeated cycle: walk (n1, n2, ..., nn), only n1 & nn the same connected graph unconnected graph components acyclic graph tree: acyclic connected graph cardinality(E) = cardinality(N) - 1

12. CSE 4344 subgraph subgraph G' = (N',E') G' is a graph, N' ⊆N, E' ⊆E let spanning tree T be a subgraph ofG where T is a tree and N' = N broadcast routing with tree: n transmits on all adjacent edges e ∈ E' other nodes relay on each non-ingress adjacent e ∈ E'  flood: n transmits on all adjacent edges, other nodes relay on each non-ingress adjacent e ∈ E

13. CSE 4344 flooding algorithms send packets everywhere, “flood” the network static algorithm receive flooding packet on one link transmit flooding packet out on all other links robust: if paths exist, flooding finds shortest benchmark for other routing algorithms

14. CSE 4344 challenges in flooding cycles/loops massive packet duplication how to make it stop? hop count field in flood packets hop count “too high”, discard packet Selective flooding (only in “right direction”) only forward “new” packets (higher seq#s) reverse path forwarding: only accept packets from source that arrive on the forwarding link to source

15. CSE 4344 uses for flooding downside: very high overhead good for: high risk environment, unreliable nodes battlefield, ad hoc networks distributed databases concurrent global update

16. CSE 4344 distributed spanning tree algorithms where do you start? stop? is it biased? not? minimum spanning tree (MST) algorithms fragment: a component of MST, a “subtree” generic MST: given a set of fragments, add a min weight edge to some fragment (no cycles) Prim-Dijkstra: some node is first fragment; add min weight adjacent edge Kruskal: all nodes are fragments; add min weight edge

17. CSE 4344 Prim-Dijkstra graph slides adapted from E. Modiano, MIT

18. CSE 4344 routing algorithms network layer routes from source to sink routing algorithm computation of output line per sink building lookup table: {(sink, output line)} forwarding: using lookup table ideal routing algorithms: simple, stable, fair, efficient cope well with changes in topology and load

19. CSE 4344 tuning the network layer min( hop count ) => less delay, bandwidth packet delay v. overall network tput/capacity fairness v. overall nwk capacity (optimality)

20. CSE 4344 optimality v. fairness Conflict between fairness and optimality. at max subnet throughput, path x → x’ is starved

21. CSE 4344 optimality principle IF node j is on an optimal path (OP), i→k, THEN an OP j→k is a subset of OP i→k the union of OPs for all nodes to a given sink is a sink tree routing algorithms seek to discover (or approximate) the sink trees of every sink in the subnet sink trees: max network capacity, min delay

22. CSE 4344 shortest path (least cost) routing ways to measure path goodness (or “cost”): hop length mean queuing delay (higher with higher loads) link latency/distance capacity actual hop cost is abstracted as “distance” routers choose shortest available path, whether explicitly, or implicitly

23. CSE 4344 static routing non-adaptive routes are computed in advance routes are optimal (global knowledge) routes do not change in response to topology and traffic pattern changes static routing used for: long-lasting topologies topologies with assigned PHY layer protection

24. CSE 4344 Dijkstra (1959) static algorithm for shortest path (optimal sink tree) G(N,E) set of nodes N; set of (edge, edge length) pairs E mark source node permanent, others temporary source becomes working node for each working node label each node adjacent to a permanent node as (predicate, distance to source) of all temps, choose temp with least distance to source mark temp permanent temp becomes next working node, until sink is reached worst case complexity of this algorithm? why?

25. CSE 4344 shortest path computation first 5 steps to compute the shortest path from A to D (arrows indicate working node) first working node (a) input to Dijkstra algorithm; (c) illustration for proof by contradiction Tanenbaum, Computer Networks, 2003, p. 354

26. CSE 4344 why is Dijkstra correct? in (c) above, E is now permanent could some AXYZE be shorter than ABE? if Z permanent, ZE already rejected if Z temp, and Z(dist to src) >= E(dist to src) then AXYZE is not shorter than ABE if Z temp, and Z(dist to src) < E(dist to src) then Z would be permanent before E why? {perms} = source REPEAT {perms} += closest temp UNTIL sink added

27. CSE 4344 a link to a scan of the hand-drawn image used in class to support the previous illustration of the Dijkstra proof has been placed on the class webpage, and leads to the following file. dijkstra-pf.pdf

28. CSE 4344 dynamic routing decisions made on-line reacts to changes in topology, traffic, delays dynamic routing algorithms distance vector link state

29. CSE 4344 distance vector routing aka: Routing Information Protocol (RIP), Bellman-Ford algorithm iterative, self-terminating, asynchronous, distributed nodes maintain adjacent link costs nodes exchange info, build forwarding tables estimated distance to each node forwarding table: {(node, line, distance)}

30. CSE 4344 Bellman-Ford equation dx(y): cost of least-cost path from x to y dx(y) = minv{ c(x,v) + dv(y) }, for all nodes y in N, for all neighbors v of x

31. CSE 4344 distance vector implementation data structures: cost vector: cost to each direct (adjacent) neighbor distance vector: estimated cost to each node in N distance vector of each direct neighbor algorithm: each node regularly sends DV to neighbors upon DV receipt, each node: saves neighbor’s DV updates own DV using Bellman-Ford equation if own DV changes, send it out to all neighbors

32. CSE 4344 distance vector routing example (a) subnet; (b) input for J from A, H, I, K; new routing table for J neighbor links J link delays

33. CSE 4344 distance vector routing fatal flaw A goes down; B believes C A comes up; B propagates fast convergence to shorter path count-to-infinity problem DVR: “where is it now?”

34. CSE 4344 link state routing best-known implementation: OSPF each router must: discover each neighbor (globally unique nwk ID) measure the delay or cost to each neighbor build packet: neighbor IDs, costs send packet to all other subnet routers compute shortest path to every other router

35. CSE 4344 link state routing implementation HELLO neighbor/address discovery ECHO delay/cost to reach neighbor queueing delay? realistic estimate of fully-loaded delay risk of oscillation

36. CSE 4344 building link state (update) packets update packet contents source ID sequence # TTL neighbor list: {(neighbor ID, delay)} when to send updates? triggered by state change on regular schedule (timer)

37. CSE 4344 link state packets subnet; (b) link state packets for subnet (note: these are symmetric links)

38. CSE 4344 reliable link state packet distribution source seq# in each update increment seq# each update higher seq# is more recent each router maintains seq# list for each other router: (router ID, seq#) for each update arriving from router X: if update seq# <= list seq# update packet is a duplicate, discard it if update seq# > list seq# copy new seq# to list forward update packet to remaining adjacent routers (flooding) update own routing table

39. CSE 4344 link state packet age each update packet includes age of packet TTL field: time to live TTL initialized to some reasonable value TTL “aged” by each router before relaying onward TTL periodically decremented (e.g., each second) when TTL reaches 0, packet is discarded prevents old info from wandering around forever

40. CSE 4344 link state update refinements update holding time wait to see if duplicate or fresher updates come in ACKs all update packets are ACKed

41. CSE 4344 where to relay, where to ACK packet buffer for router B (see prev. graph) each row indexes an update packet, ready for processing

42. CSE 4344 computing routes from link state updates global state info cooperative state distribution local computation routing computation aggregate link state info of all subnet routers shortest path or all-pairs-shortest-paths algorithm update local forwarding table

43. CSE 4344 DV versus LS Routing 1. each node gives info to all other nodes (only verified info) 2. link costs: delay, bandwidth, link reliability, distance, etc. 3. each node can contruct global topology from the info it receives from others 4. protocol convergence is fast 5. due to 3 & 4, routing loops do not occur 1. only neighbor-to-neighbor info exchange about what each has learned - low overhead 2. link costs: simple hop counts 3. nodes have no idea of global topology 4. protocol convergence is slow - count-to-infinity problem 5. due to 3 & 4, routing loops can occur

44. CSE 4344 hierarchical routing link state routing tax on subnet resources for n routers, averaging k neighbors memory footprint grows as kn bandwidth overhead grows as kn CPU cycles overhead grow as kn so, partition the overall subnet into much smaller, more manageable chunks (“regions”) delegate regional routing to the much smaller number of routers actually in that region

45. CSE 4344 the tradeoff with small regions, and limited connections into the next level of the hierarchy, routers gain much smaller, more manageable data structures the more levels, the longer the hop length of the average path for an N node subnet, (ln N) levels are optimal, with (e ln N) table entries per node

46. CSE 4344 hierarchical routing example

47. CSE 4344 broadcast routing: data to each host unicast to each host source sends N flows, one to each address flood still uses a lot of bandwidth multidestination routing packet has list of all sinks, parsed by each router sink tree routing each node must know current, global sink tree ... bullets in order of what?

48. CSE 4344 broadcast routing reverse path forwarding approximate sink tree forwarding for each broadcast routed packet received, a router checks which node sent the packet checks current forwarding table if packet comes in on the line going out to the source send copies out only on all other lines if packet comes in on any other line drop it no extra packet info, no state, self-terminating simple, easy, effective, efficient Radia Perlman

49. CSE 4344 reverse path forwarding example subnet; (b) sink tree; (c) tree built by reverse path forwarding sink tree: max 4 hops, 14 packets reverse path forwarding: max 5 hops, 24 packets ... ... depending on what?

50. CSE 4344 multicast routing sending identical flows to network subset what is the great virtue of multicast? senders to group use a discrete group address group management (using, e.g., IGMP) group creation, destruction dynamic membership local process discovers group out-of-band host learns group membership from local process routers learn group memberships from hosts routers tell other routers, maintain state registry of which groups are reachable through which routers (here is hierarchical addressing again)