Shortest-Path RoutingReading: Sections 4.2 and 4.3.4COS 461: Computer NetworksSpring 2006 (MW 1:30-2:50 in Friend 109)

Jennifer RexfordTeaching Assistant: Mike Wawrzoniak http://www.cs.princeton.edu/courses/archive/spring06/cos461/

Goals of Todays LecturePath selection

Minimum-hop and shortest-path routingDijkstra and Bellman-Ford algorithmsTopology change

Using beacons to detect topology changesPropagating topology or path informationRouting protocols

Link state: Open Shortest Path FirstDistance vector: Routing Information Protocol

What is Routing?A famous quotation from RFC 791

A name indicates what we seek.An address indicates where it is.A route indicates how we get there. -- Jon Postel

Forwarding vs. RoutingForwarding: data plane

Directing a data packet to an outgoing linkIndividual router using a forwarding tableRouting: control plane

Computing paths the packets will followRouters talking amongst themselvesIndividual router creating a forwarding table

Why Does Routing Matter?End-to-end performance

Quality of the path affects user performancePropagation delay, throughput, and packet lossUse of network resources

Balance of the traffic over the routers and linksAvoiding congestion by directing traffic to lightly-loaded linksTransient disruptions during changes

Failures, maintenance, and load balancingLimiting packet loss and delay during changes

Shortest-Path RoutingPath-selection model

Destination-basedLoad-insensitive (e.g., static link weights)Minimum hop count or sum of link weights 3221141453

Shortest-Path Problem Given: network topology with link costs

c(x,y): link cost from node x to node yInfinity if x and y are not direct neighborsCompute: least-cost paths to all nodes

From a given source u to all other nodesp(v): predecessor node along path from source to v3221141453uvp(v)

Dijkstras Shortest-Path AlgorithmIterative algorithm

After k iterations, know least-cost path to k nodesS: nodes whose least-cost path definitively known

Initially, S = {u} where u is the source nodeAdd one node to S in each iterationD(v): current cost of path from source to node v

Initially, D(v) = c(u,v) for all nodes v adjacent to u and D(v) = for all other nodes vContinually update D(v) as shorter paths are learned

Dijsktras Algorithm1 Initialization: 2 S = {u} 3 for all nodes v 4 if v adjacent to u {5 D(v) = c(u,v) 6 else D(v) = 7 8 Loop 9 find w not in S with the smallest D(w)10 add w to S 11 update D(v) for all v adjacent to w and not in S: 12 D(v) = min{D(v), D(w) + c(w,v)} 13 until all nodes in S

Dijkstras Algorithm Example

Dijkstras Algorithm Example

Shortest-Path TreeShortest-path tree from u

Forwarding table at u

link

Link-State RoutingEach router keeps track of its incident links

Whether the link is up or downThe cost on the linkEach router broadcasts the link state

To give every router a complete view of the graphEach router runs Dijkstras algorithm

To compute the shortest paths and construct the forwarding tableExample protocols

Open Shortest Path First (OSPF)Intermediate System Intermediate System (IS-IS)

Detecting Topology ChangesBeaconing

Periodic hello messages in both directionsDetect a failure after a few missed hellos

Performance trade-offs

Detection speedOverhead on link bandwidth and CPULikelihood of false detectionhello

Broadcasting the Link StateFlooding

Node sends link-state information out its linksAnd then the next node sends out all of its links except the one where the information arrivedXACBD(a)XACBD(b)XACBD(c)XACBD(d)

Broadcasting the Link StateReliable flooding

Ensure all nodes receive link-state information and that they use the latest versionChallenges

Packet lossOut-of-order arrivalSolutions

Acknowledgments and retransmissionsSequence numbersTime-to-live for each packet

When to Initiate FloodingTopology change

Link or node failureLink or node recoveryConfiguration change

Link cost changePeriodically

Refresh the link-state informationTypically (say) 30 minutesCorrects for possible corruption of the data

ConvergenceGetting consistent routing information to all nodes

E.g., all nodes having the same link-state databaseConsistent forwarding after convergence

All nodes have the same link-state databaseAll nodes forward packets on shortest pathsThe next router on the path forwards to the next hop3221141453

Transient DisruptionsDetection delay

A node does not detect a failed link immediately and forwards data packets into a blackholeDepends on timeout for detecting lost hellos3221141453

Transient DisruptionsInconsistent link-state database

Some routers know about failure before othersThe shortest paths are no longer consistentCan cause transient forwarding loops3221141453322114143

Convergence DelaySources of convergence delay

Detection latencyFlooding of link-state informationShortest-path computationCreating the forwarding tablePerformance during convergence period

Lost packets due to blackholes and TTL expiryLooping packets consuming resourcesOut-of-order packets reaching the destinationVery bad for VoIP, online gaming, and video

Reducing Convergence DelayFaster detection

Smaller hello timersLink-layer technologies that can detect failuresFaster flooding

Flooding immediatelySending link-state packets with high-priorityFaster computation

Faster processors on the routersIncremental Dijkstra algorithmFaster forwarding-table update

Data structures supporting incremental updates

Scaling Link-State RoutingOverhead of link-state routing

Flooding link-state packets throughout the networkRunning Dijkstras shortest-path algorithmIntroducing hierarchy through areas

Area 0Area 1Area 4areaborderrouter

Bellman-Ford AlgorithmDefine distances at each node x

dx(y) = cost of least-cost path from x to yUpdate distances based on neighbors

dx(y) = min {c(x,v) + dv(y)} over all neighbors v3221141453uvwxyzstdu(z) = min{c(u,v) + dv(z), c(u,w) + dw(z)}

Distance Vector Algorithm c(x,v) = cost for direct link from x to v

Node x maintains costs of direct links c(x,v)Dx(y) = estimate of least cost from x to y

Node x maintains distance vector Dx = [Dx(y): y N ]Node x maintains its neighbors distance vectors

For each neighbor v, x maintains Dv = [Dv(y): y N ]Each node v periodically sends Dv to its neighbors

And neighbors update their own distance vectorsDx(y) minv{c(x,v) + Dv(y)} for each node y NOver time, the distance vector Dx converges

Distance Vector AlgorithmIterative, asynchronous: each local iteration caused by: Local link cost change Distance vector update message from neighbor

Distributed:Each node notifies neighbors only when its DV changesNeighbors then notify their neighbors if necessary

Each node:

Distance Vector Example: Step 0AEFCDB23641113Optimum 1-hop paths

Table for ADstCstHopA0AB4BCDE2EF6F

Table for BDstCstHopA4AB0BCD3DEF1F

Table for CDstCstHopABC0CD1DEF1F

Table for DDstCstHopAB3BC1CD0DEF

Table for EDstCstHopA2ABCDE0EF3F

Table for FDstCstHopA6AB1BC1CDE3EF0F

Distance Vector Example: Step 2Optimum 2-hop pathsAEFCDB23641113

Table for ADstCstHopA0AB4BC7FD7BE2EF5E

Table for BDstCstHopA4AB0BC2FD3DE4FF1F

Table for CDstCstHopA7FB2FC0CD1DE4FF1F

Table for DDstCstHopA7BB3BC1CD0DEF2C

Table for EDstCstHopA2AB4FC4FDE0EF3F

Table for FDstCstHopA5BB1BC1CD2CE3EF0F

Distance Vector Example: Step 3Optimum 3-hop pathsAEFCDB23641113

Table for ADstCstHopA0AB4BC6ED7BE2EF5E

Table for BDstCstHopA4AB0BC2FD3DE4FF1F

Table for CDstCstHopA6FB2FC0CD1DE4FF1F

Table for DDstCstHopA7BB3BC1CD0DE5CF2C

Table for EDstCstHopA2AB4FC4FD5FE0EF3F

Table for FDstCstHopA5BB1BC1CD2CE3EF0F

Distance Vector: Link Cost ChangesLink cost changes:Node detects local link cost change Updates the distance table If cost change in least cost path, notify neighbors

algorithmterminatesgoodnews travelsfast

Distance Vector: Link Cost ChangesLink cost changes:Good news travels fast Bad news travels slow - count to infinity problem!

algorithmcontinueson!

Distance Vector: Poison ReverseIf Z routes through Y to get to X :Z tells Y its (Zs) distance to X is infinite (so Y wont route to X via Z)Still, can have problems when more than 2 routers are involved

algorithmterminates

Routing Information Protocol (RIP)Distance vector protocol

Nodes send distance vectors every 30 seconds or, when an update causes a change in routingLink costs in RIP

All links have cost 1Valid distances of 1 through 15 with 16 representing infinitySmall infinity smaller counting to infinity problemRIP is limited to fairly small networks

E.g., used in the Princeton campus network

Comparison of LS and DV algorithmsMessage complexityLS: with n nodes, E links, O(nE) messages sent DV: exchange between neighbors only

Convergence time variesSpeed of ConvergenceLS: O(n2) algorithm requires O(nE) messagesDV: convergence time varies

May be routing loopsCount-to-infinity problemRobustness: what happens if router malfunctions?LS: Node can advertise incorrect link costEach node computes only its own tableDV:DV node can advertise incorrect path costEach nodes table used by others (error propagates)

ConclusionsRouting is a distributed algorithm

React to changes in the topologyCompute the shortest pathsTwo main shortest-path algorithms

Dijkstra link-state routing (e.g., OSPF and IS-IS)Bellman-Ford distance vector routing (e.g., RIP)Convergence process

Changing from one topology to anotherTransient periods of inconsistency across routersNext time: policy-based path-vector routing

Reading: Section 4.3.3