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Week 6Routing Concepts

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Network Layer Functionstransport packet from sending to receiving hosts network layer protocols in every host, router

path determination: route taken by packets from source to dest. Routing algorithmsswitching: move packets from router’s input to appropriate router outputcall setup: some network architectures require router call setup along path before data flows

networkdata linkphysical

networkdata linkphysical

networkdata linkphysical

networkdata linkphysical

networkdata linkphysical

networkdata linkphysical

networkdata linkphysical

networkdata linkphysical

application

transportnetworkdata linkphysical

application

transportnetworkdata linkphysical

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1

23

0111

value in arrivingpacket’s header

routing algorithm

local forwarding tableheader value output link

0100010101111001

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Interplay between routing and forwarding

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u

yx

wv

z2

2

13

1

1

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Graph: G = (N,E)

N = set of routers = { u, v, w, x, y, z }

E = set of links ={ (u,v), (u,x), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) }

Graph abstraction

Remark: Graph abstraction is useful in other network contexts

Example: P2P, where N is set of peers and E is set of TCP connections

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Graph abstraction: costs

u

yx

wv

z2

2

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1

1

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5 • c(x,x’) = cost of link (x,x’)

- e.g., c(w,z) = 5

• cost could always be 1, or inversely related to bandwidth,or inversely related to congestion

Cost of path (x1, x2, x3,…, xp) = c(x1,x2) + c(x2,x3) + … + c(xp-1,xp)

Question: What’s the least-cost path between u and z ?

Routing algorithm: algorithm that finds least-cost path

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Routing

Graph abstraction for routing algorithms:graph nodes are routersgraph edges are physical links

• link cost: delay, $ cost, or congestion level

Goal: determine “good” path

(sequence of routers) thru network from source to

dest.

Routing protocol

A

ED

CB

F

2

2

13

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“good” path:• typically means

minimum cost path• other definitions possible

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Routing Algorithm Classification

Global or decentralized information?

Global:all routers have complete topology, link cost info“link state” algorithms

Decentralized: router knows physically-connected neighbors, link costs to neighborsiterative process of computation, exchange of info with neighbors“distance vector” algorithms

Static or dynamic?Static:

routes change slowly over time

Dynamic: routes change more quickly

• periodic update• in response to link cost

changes

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Distance Vector Routing Algorithm (Old Arpanet Routing or Bellman-Ford)

iterative:continues until no nodes exchange info.self-terminating: no “signal” to stop

asynchronous:nodes need not exchange info/iterate in lock step!

distributed:each node communicates only with directly-attached neighbors

Distance Table data structure each node has its ownrow for each possible destinationcolumn for each directly-attached neighbor to nodeexample: in node X, for dest. Y via neighbor Z:

D (Y,Z)X

distance from X toY, via Z as next hop

c(X,Z) + min {D (Y,w)}Z

w

=

=

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Distance Table: Example

A

E D

CB7

8

1

2

1

2

D ()

A

B

C

D

A

1

7

6

4

B

14

8

9

11

D

5

5

4

2

Ecost to destination via

dest

inat

ion

D (C,D)E

c(E,D) + min {D (C,w)}D

w== 2+2 = 4

D (A,D)E

c(E,D) + min {D (A,w)}D

w== 2+3 = 5

D (A,B)E

c(E,B) + min {D (A,w)}B

w== 8+6 = 14

loop!

loop!

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Distance table gives routing table

D ()

A

B

C

D

A

1

7

6

4

B

14

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Ecost to destination via

dest

inat

ion

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A,1

D,5

D,4

D,4

Outgoing link to use, cost

dest

inat

ion

Distance table Routing table

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Distance Vector Routing: Overview

Iterative, asynchronous: each local iteration caused by: local link cost change message from neighbor: its least cost path change from neighbor

Distributed:each node notifies neighbors only when its least cost path to any destination changes

• neighbors then notify their neighbors if necessary

wait for (change in local link cost or message from neighbor)

Recompute distance table

if least cost path to any dest has changed, notify neighbors

Each node:

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Distance Vector Algorithm

1 Initialization: 2 for all adjacent nodes v: 3 D (*,v) = infty /* the * operator means "for all rows" */ 4 D (v,v) = c(X,v) 5 for all destinations, y 6 send min D (y,w) to each neighbor /* w over all X's neighbors */

XX

Xw

At all nodes, X:

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Distance Vector Algorithm (cont.):8 loop 9 wait (until I see a link cost change to neighbor V 10 or until I receive update from neighbor V) 11 12 if (c(X,V) changes by d) 13 /* change cost to all dest's via neighbor v by d */ 14 /* note: d could be positive or negative */ 15 for all destinations y: D (y,V) = D (y,V) + d 16 17 else if (update received from V wrt destination Y) 18 /* shortest path from V to some Y has changed */ 19 /* V has sent a new value for its min DV(Y,w) */ 20 /* call this received new value is "newval" */ 21 for the single destination y: D (Y,V) = c(X,V) + newval 22 23 if we have a new min w D X (Y,w) for any destination Y 24 send new value of min w D X (Y,w) to all neighbors 25 26 forever

w

XX

X

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Distance Vector Algorithm: example

X Z12

7

Y

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Distance Vector Algorithm: example

X Z12

7

Y

D (Y,Z)X

c(X,Z) + min {D (Y,w)}w=

= 7+1 = 8

Z

D (Z,Y)X

c(X,Y) + min {D (Z,w)}w=

= 2+1 = 3

Y

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Distance Vector: link cost changes

Link cost changes:node detects local link cost change updates distance table (line 15)if cost change in least cost path, notify neighbors (lines 23,24)

X Z14

50

Y1

algorithmterminates“good

news travelsfast”

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Distance Vector: link cost changes

Link cost changes:good news travels fast bad news travels slow - “count to infinity” problem! X Z

14

50

Y60

algorithmcontinues

on!

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What to do -- Split Horizon

If router R forwards traffic for destination D thru neighbor N, then R reports to N that R’s distance to D is infinity.Because R is routing traffic for D thru N, R’s real distance to N cannot simply matter to N.Works in the previous case but does not work in some casesExample

R2

R1

R3

D

The count-to-infinity problem still exists

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Distance Vector: Poison Reverse

If Z routes through Y to get to X :Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z)will this completely solve count to infinity problem?

X Z14

50

Y60

algorithmterminates

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Link State Routing

Each router is responsible for meeting its neighbours and learning their namesEach router constructs a packet known as link state packet, or LSP, which contains a list of names of and cost to each of its neighbours

• A router generates an LSP periodically as well as when R discovers that

it has a new neighbour the cost of a link to a neighbour has changed a link to a neighbour has gone down

The LSP is somehow transmitted (this is the most complex and critical piece) to all other routers and each router stores the most recently generated LSP from each other routerEach router armed now with a complete map of the topology, computes routes to each destination.

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Disseminating the LSP to all Routers

A simple scheme for routing that does not depend having any routing info is flooding, in which each packet received is transmitted to each neighbour except the one from which the packet is received. Also let the packet have a hop count.A better and simple LSP distribution scheme is as follows:

• If an LSP is received from neighbour N with source S and if the LSP is identical to the one from S that is stored, then ignore the received LSP (it is a duplicate)

• If the received LSP is not identical to the one from S currently stored or no LSP from S is stored, store the received LSP and transmit it to all neighbours

• The problem is that router cannot assume that the LSP most recently received from S is the one most recently generated.

• Use sequence number/age schemes

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Sequence number/age Schemes

A sequence number is a counterEach router S keeps track of the sequence number it used the last time it generated an LSP; when S needs to generate a new LSP, it uses the next sequence numberWhen router R receives an LSP from from S, router R compares sequence number of the received LSP with the one from S stored in memory and assumes that the the one with the higher sequence number is the more recently generated.Problem 1. Sequence number field is of finite size

• Wrap around, count as 0,1,…,n-1,n,0,1,…• How would you compare two sequence numbers a and b

in this framework?

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Sequence number/age schemes

a

n-1n 0 1

< a

> a

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Sequence number/age schemes

What happens if router S goes down and forgets the sequence number it was using? If it starts at 0 again, will its LSPs be believed by the network, or will they look older than the LSPs that S had issued before?To solve this problem, a second field, known as the age of the LSP is added to each LSP packet.It starts at some value and is decremented by routers as it is held in memory.When an LSP’s age reaches 0, the LSP can be considered too old, and an LSP with a nonzero age is accepted as newer regardless of its sequence number.LSP distribution scheme intelligently uses age and sequence number for dissemination of LSPs; used in IS-IS, OSPF, and PNNI.

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A Link-State Routing Algorithm

Dijkstra’s algorithmnet topology, link costs known to all nodes

• accomplished via “link state broadcast”

• all nodes have same info

computes least cost paths from one node (‘source”) to all other nodes

• gives routing table for that node

iterative: after k iterations, know least cost path to k dest.’s

Notation:c(i,j): link cost from node i to j. cost infinite if not direct neighbors

D(v): current value of cost of path from source to dest. v

p(v): predecessor node along path from source to v, that is next v

N: set of nodes whose least cost path definitively known

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Dijsktra’s Algorithm -- Shortest Path

1 Initialization: 2 N = {A} 3 for all nodes v 4 if v adjacent to A 5 then D(v) = c(A,v) 6 else D(v) = infty 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

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Dijkstra’s algorithm: example

Step012345

start NA

ADADE

ADEBADEBC

ADEBCF

D(B),p(B)2,A2,A2,A

D(C),p(C)5,A4,D3,E3,E

D(D),p(D)1,A

D(E),p(E)infinity

2,D

D(F),p(F)infinityinfinity

4,E4,E4,E

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Dijsktra’s Algorithm -- Widest Path

1 Initialization: 2 N = {A} 3 for all nodes v 4 if v adjacent to A 5 then D(v) = b(A,v) /* b(A,v) is the available bandwidth*/6 else D(v) = 0 7 8 Loop 9 find w not in N such that D(w) is a maximum 10 add w to N 11 update D(v) for all v adjacent to w and not in N: 12 D(v) = max[ D(v), min(D(w),b(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

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Dijkstra’s algorithm -- Widest Path

Step012345

start NA

ACACF

ACFBACFBD

ACFBDE

D(B),p(B)2,A3,C3,C

D(C),p(C)5,A

D(D),p(D)

1,A3,C3,C3,C

D(E),p(E)0

1,C2,F2,F2,F

D(F),p(F)0

5,C

A

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Dijkstra’s algorithm, Discussion

Algorithm complexity: n nodeseach iteration: need to check all nodes, w, not in Nn*(n+1)/2 comparisons: O(n^2)more efficient implementations possible: O(n logn)

Oscillations possible:e.g., link cost = amount of carried traffic

A

D

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B1 1+e

e0

e

1 1

0 0

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B2+e 0

001+e1

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B0 2+e

1+e10 0

A

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B2+e 0

e01+e1

initially… recompute

routing… recompute … recompute

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Comparison of LS and DV algorithmsMessage complexity and memory

LS: with n nodes, E links, O(nE) messages sent each, larger tablesDV: exchange between neighbors only

• convergence time varies, smaller distance tables

Speed of ConvergenceLS: O(n^2) algorithm requires O(nE) messages

• may have oscillationsDV: convergence time varies

• may have routing loops• count-to-infinity problem

link state routing converges more quickly than distance vector

• a router cannot pass routing information on until it has computed its distance vector

• looping

Robustness: what happens if router malfunctions?

LS: • node can advertise

incorrect link cost• each node computes only

its own table

DV:• DV node can advertise

incorrect path cost• each node’s table used by

others error propagate thru

network

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Link Costs

Whether link costs are fixed or they vary with the utilization of the link?Proponents of variable costs:

• traffic is routed more optimally• having costs assigned by network management requires

additional configuration

Proponents of fixed link costs:• routing info needs to be generated only if the link goes

down or recovers• if link costs change frequently, the network is often in an

unconverged state, not making good routing decisions• stability

There are recent studies that find link costs in the networks so as to maximize the total traffic through the network (traffic matrix should be known)

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Load Splitting

If costs are equal then traffic can be split amongst equal-cost paths; splitting otherwise may lead to routing loopsApplicable to both LS and DVHowever, this annoys the transport layer

• Out of order packets• Transport layer requires a uniform service for RTT and

MTU calculations

Flow-level splitting• Packets of the same flow would follow the same path• The router, if it has two equal cost paths, can do a hash

of (source IP, dest. IP, source port, dest. port) to select which path the packet should take

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Hierarchical Routing

scale: with 200 million destinations:can’t store all dest’s in routing tables!

routing table exchange would swamp links!

administrative autonomyinternet = network of networkseach network admin may want to control routing in its own network

Our routing study thus far - idealization all routers identicalnetwork “flat”

… not true in practice

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Hierarchical Routing

aggregate routers into regions, “autonomous systems” (AS)routers in same AS run same routing protocol

• “intra-AS” routing protocol

• routers in different AS can run different intra-AS routing protocol

Gateway routerDirect link to router in another AS

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3b

1d

3a

1c2aAS3

AS1

AS21a

2c2b

1b

Intra-ASRouting algorithm

Inter-ASRouting algorithm

Forwardingtable

3c

Interconnected ASes

Forwarding table is configured by both intra- and inter-AS routing algorithm

• Intra-AS sets entries for internal dests

• Inter-AS & Intra-As sets entries for external dests

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3b

1d

3a

1c2aAS3

AS1

AS21a

2c2b

1b

3c

Inter-AS tasks

Suppose router in AS1 receives datagram for which dest is outside of AS1

• Router should forward packet towards on of the gateway routers, but which one?

AS1 needs:1. to learn which dests are

reachable through AS2 and which through AS3

2. to propagate this reachability info to all routers in AS1

Job of inter-AS routing!

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Example: Setting forwarding table in router 1d

Suppose AS1 learns from the inter-AS protocol that subnet x is reachable from AS3 (gateway 1c) but not from AS2.Inter-AS protocol propagates reachability info to all internal routers.Router 1d determines from intra-AS routing info that its interface I is on the least cost path to 1c.Puts in forwarding table entry (x,I).

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Learn from inter-AS protocol that subnet x is reachable via multiple gateways

Use routing infofrom intra-AS

protocol to determine

costs of least-cost paths to each

of the gateways

Hot potato routing:Choose the

gatewaythat has the

smallest least cost

Determine fromforwarding table the interface I that leads

to least-cost gateway. Enter (x,I) in

forwarding table

Example: Choosing among multiple ASes

Now suppose AS1 learns from the inter-AS protocol that subnet x is reachable from AS3 and from AS2.To configure forwarding table, router 1d must determine towards which gateway it should forward packets for dest x. This is also the job on inter-AS routing protocol!Hot potato routing: send packet towards closest of two routers.

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Intra-AS Routing

Also known as Interior Gateway Protocols (IGP)Most common Intra-AS routing protocols:

• RIP: Routing Information Protocol

• OSPF: Open Shortest Path First

• IGRP: Interior Gateway Routing Protocol (Cisco proprietary)