Routing Algorithms and Routing in the Internet Network

Routing Algorithms and Routing in the Internet Network Layer 1

Interplay between routing and forwarding routing algorithm local forwarding table header value output link 0100 0101 0111 1001 3 2 2 1 value in arriving packet’s header 0111 1 3 2 Network Layer 2

Graph abstraction 5 2 u 2 1 Graph: G = (N, E) v x 3 w 3 1 5 z 1 y 2 N = set of routers = { u, v, w, x, y, z } E = set of links ={ (u, v), (u, x), (v, w), (x, y), (w, z), (y, z) } Remark: Graph abstraction is useful in other network contexts Example: P 2 P, where N is set of peers and E is set of TCP connections Network Layer 3

Graph abstraction: costs 5 2 u v 2 1 x • c(x, x’) = cost of link (x, x’) 3 w 3 1 5 z 1 y - e. g. , c(w, z) = 5 2 • cost could always be 1, or inversely related to bandwidth, or inversely related to congestion Cost of path (x 1, x 2, x 3, …, xp) = c(x 1, x 2) + c(x 2, x 3) + … + c(xp-1, xp) Question: What’s the least-cost path between u and z ? Routing algorithm: algorithm that finds least-cost path Network Layer 4

Routing Algorithm classification Global or decentralized information? Global: r all routers have complete topology, link cost info r “link state” algorithms Decentralized: r router knows physicallyconnected neighbors, link costs to neighbors r iterative process of computation, exchange of info with neighbors r “distance vector” algorithms Static or dynamic? Static: r routes change slowly over time Dynamic: r routes change more quickly m periodic update m in response to link cost changes Network Layer 5

A Link-State Routing Algorithm Dijkstra’s algorithm r net topology, link costs known to all nodes m accomplished via “link state broadcast” m all nodes have same info r computes least cost paths from one node (‘source”) to all other nodes m gives forwarding table for that node r iterative: after k iterations, know least cost path to k dest. ’s Notation: r c(x, y): link cost from node x to y; = ∞ if not direct neighbors r D(v): current value of cost of path from source to dest. v r p(v): predecessor node along path from source to v r N': set of nodes whose least cost path definitively known Network Layer 6

Dijsktra’s Algorithm 1 Initialization: 2 N' = {u} 3 for all nodes v 4 if v adjacent to u 5 then D(v) = c(u, v) 6 else D(v) = ∞ 7 8 Loop 9 find w not in N' such that D(w) is a minimum 10 add w to N' 11 update D(v) for all v adjacent to w and not in N' : 12 D(v) = min( D(v), D(w) + c(w, v) ) 13 /* new cost to v is either old cost to v or known 14 shortest path cost to w plus cost from w to v */ 15 until all nodes in N' Network Layer 7

Dijkstra’s algorithm: example Step 0 1 2 3 4 5 N' u ux uxyvwz D(v), p(v) D(w), p(w) 2, u 5, u 2, u 4, x 2, u 3, y D(x), p(x) 1, u D(y), p(y) ∞ 2, x D(z), p(z) ∞ ∞ 4, y 5 2 u v 2 1 x 3 w 3 1 5 z 1 y 2 Network Layer 8

Dijkstra’s algorithm, discussion Algorithm complexity: n nodes r each iteration: need to check all nodes, w, not in N r n(n+1)/2 comparisons: O(n 2) r more efficient implementations possible: O(nlogn) Oscillations possible: r e. g. , link cost = amount of carried traffic D 1 1 0 A 0 0 C e 1+e e initially B 1 2+e A 0 D 1+e 1 B 0 0 C … recompute routing 0 D 1 A 0 0 C 2+e B 1+e … recompute 2+e A 0 D 1+e 1 B e 0 C … recompute Network Layer 9

Distance Vector Algorithm (1) Bellman-Ford Equation (dynamic programming) Define dx(y) : = cost of least-cost path from x to y Then dx(y) = min {c(x, v) + dv(y) } where min is taken over all neighbors of x Network Layer 10

Bellman-Ford example (2) 5 2 u v 2 1 x 3 w 3 1 5 z 1 y Clearly, dv(z) = 5, dx(z) = 3, dw(z) = 3 2 B-F equation says: du(z) = min { c(u, v) + dv(z), c(u, x) + dx(z), c(u, w) + dw(z) } = min {2 + 5, 1 + 3, 5 + 3} = 4 Node that achieves minimum is next hop in shortest path ➜ forwarding table Network Layer 11

Distance Vector Algorithm (3) r Dx(y) = estimate of least cost from x to y r Distance vector: Dx = [Dx(y): y є N ] r Node x knows cost to each neighbor v: c(x, v) r Node x maintains Dx = [Dx(y): y є N ] r Node x also maintains its neighbors’ distance vectors m For each neighbor v, x maintains Dv = [Dv(y): y є N ] Network Layer 12

Distance vector algorithm (4) Basic idea: r Each node periodically sends its own distance vector estimate to neighbors r When node a node x receives new DV estimate from neighbor, it updates its own DV using B-F equation: Dx(y) ← minv{c(x, v) + Dv(y)} for each node y ∊ N r Under minor, natural conditions, the estimate Dx(y) converge the actual least cost dx(y) Network Layer 13

Distance Vector Algorithm (5) Iterative, asynchronous: each local iteration caused by: r local link cost change r DV update message from neighbor Distributed: r each node notifies neighbors only when its DV changes m neighbors then notify their neighbors if necessary Each node: wait for (change in local link cost of msg from neighbor) recompute estimates if DV to any dest has changed, notify neighbors Network Layer 14

Dx(y) = min{c(x, y) + Dy(y), c(x, z) + Dz(y)} = min{2+0 , 7+1} = 2 node x table cost to x y z x ∞∞ ∞ y ∞∞ ∞ z 71 0 from x 0 2 7 y 2 0 1 z 7 1 0 cost to x y z x 0 2 7 y 2 0 1 z 3 1 0 x 0 2 3 y 2 0 1 z 3 1 0 cost to x y z x 0 2 3 y 2 0 1 z 3 1 0 x 2 y 1 7 z cost to x y z from x ∞ ∞ ∞ y 2 0 1 z ∞∞ ∞ node z table cost to x y z x 0 2 3 y 2 0 1 z 7 1 0 cost to x y z from x 0 2 7 y ∞∞ ∞ z ∞∞ ∞ node y table cost to x y z Dx(z) = min{c(x, y) + Dy(z), c(x, z) + Dz(z)} = min{2+1 , 7+0} = 3 x 0 2 3 y 2 0 1 z 3 1 0 time Network Layer 15

Distance Vector: link cost changes Link cost changes: r node detects local link cost change r updates routing info, recalculates distance vector r if DV changes, notify neighbors “good news travels fast” 1 x 4 y 50 1 z At time t 0, y detects the link-cost change, updates its DV, and informs its neighbors. At time t 1, z receives the update from y and updates its table. It computes a new least cost to x and sends its neighbors its DV. At time t 2, y receives z’s update and updates its distance table. y’s least costs do not change and hence y does not send any message to z. Network Layer 16

Distance Vector: link cost changes Link cost changes: r good news travels fast r bad news travels slow - “count to infinity” problem! r 44 iterations before algorithm stabilizes: see text 60 x 4 y 50 1 z Poissoned reverse: r If Z routes through Y to get to X : m Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z) r will this completely solve count to infinity problem? Network Layer 17

Comparison of LS and DV algorithms Message complexity r LS: with n nodes, E links, O(n. E) msgs sent r DV: exchange between neighbors only m convergence time varies Speed of Convergence r LS: O(n 2) algorithm requires O(n. E) msgs m may have oscillations r DV: convergence time varies m may be routing loops m count-to-infinity problem Robustness: what happens if router malfunctions? LS: m m DV: m m node can advertise incorrect link cost each node computes only its own table DV node can advertise incorrect path cost each node’s table used by others • error propagate thru network Network Layer 18

Hierarchical Routing Our routing study thus far - idealization r all routers identical r network “flat” … not true in practice scale: with 200 million destinations: r can’t store all dest’s in routing tables! r routing table exchange would swamp links! administrative autonomy r internet = network of networks r each network admin may want to control routing in its own network Network Layer 19

Hierarchical Routing r aggregate routers into regions, “autonomous systems” (AS) r routers in same AS run same routing protocol m m Gateway router r Direct link to router in another AS “intra-AS” routing protocol routers in different AS can run different intra. AS routing protocol Network Layer 20

Interconnected ASes 3 c 3 a 3 b AS 3 1 a 2 a 1 c 1 d 1 b Intra-AS Routing algorithm 2 c AS 2 AS 1 Inter-AS Routing algorithm Forwarding table 2 b r Forwarding table is configured by both intraand inter-AS routing algorithm m m Intra-AS sets entries for internal dests Inter-AS & Intra-As sets entries for external dests Network Layer 21

Inter-AS tasks AS 1 needs: 1. to learn which dests are reachable through AS 2 and which through AS 3 2. to propagate this reachability info to all routers in AS 1 Job of inter-AS routing! r Suppose router in AS 1 receives datagram for which dest is outside of AS 1 m Router should forward packet towards on of the gateway routers, but which one? 3 c 3 a 3 b AS 3 1 a 2 a 1 c 1 d 1 b 2 c AS 2 2 b AS 1 Network Layer 22

Example: Setting forwarding table in router 1 d r Suppose AS 1 learns from the inter-AS protocol that subnet x is reachable from AS 3 (gateway 1 c) but not from AS 2. r Inter-AS protocol propagates reachability info to all internal routers. r Router 1 d determines from intra-AS routing info that its interface I is on the least cost path to 1 c. r Puts in forwarding table entry (x, I). Network Layer 23

Example: Choosing among multiple ASes r Now suppose AS 1 learns from the inter-AS protocol that subnet x is reachable from AS 3 and from AS 2. r To configure forwarding table, router 1 d must determine towards which gateway it should forward packets for dest x. r This is also the job on inter-AS routing protocol! r Hot potato routing: send packet towards closest of two routers. Learn from inter-AS protocol that subnet x is reachable via multiple gateways Use routing info from intra-AS protocol to determine costs of least-cost paths to each of the gateways Hot potato routing: Choose the gateway that has the smallest least cost Determine from forwarding table the interface I that leads to least-cost gateway. Enter (x, I) in forwarding table Network Layer 24

Intra-AS Routing r Also known as Interior Gateway Protocols (IGP) r Most common Intra-AS routing protocols: m RIP: Routing Information Protocol m OSPF: Open Shortest Path First m IGRP: Interior Gateway Routing Protocol (Cisco proprietary) Network Layer 25

RIP ( Routing Information Protocol) r Distance vector algorithm r Included in BSD-UNIX Distribution in 1982 r Distance metric: # of hops (max = 15 hops) u v A z C B D w x y destination hops u 1 v 2 w 2 x 3 y 3 z 2 Network Layer 26

RIP advertisements r Distance vectors: exchanged among neighbors every 30 sec via Response Message (also called advertisement) r Each advertisement: list of up to 25 destination nets within AS Network Layer 27

RIP: Example z w A x D B y C Destination Network w y z x …. Next Router Num. of hops to dest. …. . . A B B -- 2 2 7 1 Routing table in D Network Layer 28

RIP: Example Dest w x z …. Next C … w hops 4. . . A Advertisement from A to D z x Destination Network w y z x …. D B C y Next Router Num. of hops to dest. …. . . A B B A -- Routing table in D 2 2 7 5 1 Network Layer 29

RIP: Link Failure and Recovery If no advertisement heard after 180 sec --> neighbor/link declared dead m routes via neighbor invalidated m new advertisements sent to neighbors m neighbors in turn send out new advertisements (if tables changed) m link failure info quickly propagates to entire net m poison reverse used to prevent ping-pong loops (infinite distance = 16 hops) Network Layer 30

RIP Table processing r RIP routing tables managed by application-level process called route-d (daemon) r advertisements sent in UDP packets, periodically repeated routed Transprt (UDP) network (IP) link physical Transprt (UDP) forwarding table network (IP) link physical Network Layer 31

OSPF (Open Shortest Path First) r “open”: publicly available r Uses Link State algorithm m LS packet dissemination m Topology map at each node m Route computation using Dijkstra’s algorithm r OSPF advertisement carries one entry per neighbor router r Advertisements disseminated to entire AS (via flooding) m Carried in OSPF messages directly over IP (rather than TCP or UDP Network Layer 32

OSPF “advanced” features (not in RIP) r Security: all OSPF messages authenticated (to r r prevent malicious intrusion) Multiple same-cost paths allowed (only one path in RIP) For each link, multiple cost metrics for different TOS (e. g. , satellite link cost set “low” for best effort; high for real time) Integrated uni- and multicast support: m Multicast OSPF (MOSPF) uses same topology data base as OSPF Hierarchical OSPF in large domains. Network Layer 33

Hierarchical OSPF Network Layer 34

Hierarchical OSPF r Two-level hierarchy: local area, backbone. m Link-state advertisements only in area m each nodes has detailed area topology; only know direction (shortest path) to nets in other areas. r Area border routers: “summarize” distances to nets in own area, advertise to other Area Border routers. r Backbone routers: run OSPF routing limited to backbone. r Boundary routers: connect to other AS’s. Network Layer 35

Internet inter-AS routing: BGP r BGP (Border Gateway Protocol): the de facto standard r BGP provides each AS a means to: 1. 2. 3. Obtain subnet reachability information from neighboring ASs. Propagate the reachability information to all routers internal to the AS. Determine “good” routes to subnets based on reachability information and policy. r Allows a subnet to advertise its existence to rest of the Internet: “I am here” Network Layer 36

BGP basics r Pairs of routers (BGP peers) exchange routing info over semi- permanent TCP conctns: BGP sessions r Note that BGP sessions do not correspond to physical links. r When AS 2 advertises a prefix to AS 1, AS 2 is promising it will forward any datagrams destined to that prefix towards the prefix. m AS 2 can aggregate prefixes in its advertisement 3 c 3 a 3 b AS 3 1 a AS 1 2 a 1 c 1 d 1 b 2 c AS 2 2 b e. BGP session i. BGP session Network Layer 37

Distributing reachability info r With e. BGP session between 3 a and 1 c, AS 3 sends prefix reachability info to AS 1. r 1 c can then use i. BGP do distribute this new prefix reach info to all routers in AS 1 r 1 b can then re-advertise the new reach info to AS 2 over the 1 b-to-2 a e. BGP session r When router learns about a new prefix, it creates an entry for the prefix in its forwarding table. 3 c 3 a 3 b AS 3 1 a AS 1 2 a 1 c 1 d 1 b 2 c AS 2 2 b e. BGP session i. BGP session Network Layer 38

Path attributes & BGP routes r When advertising a prefix, advert includes BGP attributes. m prefix + attributes = “route” r Two important attributes: m AS-PATH: contains the ASs through which the advert for the prefix passed: AS 67 AS 17 m NEXT-HOP: Indicates the specific internal-AS router to next-hop AS. (There may be multiple links from current AS to next-hop-AS. ) r When gateway router receives route advert, uses import policy to accept/decline. Network Layer 39

BGP route selection r Router may learn about more than 1 route to some prefix. Router must select route. r Elimination rules: 1. 2. 3. 4. Local preference value attribute: policy decision Shortest AS-PATH Closest NEXT-HOP router: hot potato routing Additional criteria Network Layer 40

BGP messages r BGP messages exchanged using TCP. r BGP messages: m OPEN: opens TCP connection to peer and authenticates sender m UPDATE: advertises new path (or withdraws old) m KEEPALIVE keeps connection alive in absence of UPDATES; also ACKs OPEN request m NOTIFICATION: reports errors in previous msg; also used to close connection Network Layer 41

BGP routing policy r A, B, C are provider networks r X, W, Y are customer (of provider networks) r X is dual-homed: attached to two networks m. X does not want to route from B via X to C m. . so X will not advertise to B a route to C Network Layer 42

BGP routing policy (2) r A advertises to B the path AW r B advertises to X the path BAW r Should B advertise to C the path BAW? m No way! B gets no “revenue” for routing CBAW since neither W nor C are B’s customers m B wants to force C to route to w via A m B wants to route only to/from its customers! Network Layer 43

Why different Intra- and Inter-AS routing ? Policy: r Inter-AS: admin wants control over how its traffic routed, who routes through its net. r Intra-AS: single admin, so no policy decisions needed Scale: r hierarchical routing saves table size, reduced update traffic Performance: r Intra-AS: can focus on performance r Inter-AS: policy may dominate over performance Network Layer 44