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Link State and Distance Vector Routing

EECS 489 Computer Networkshttp://www.eecs.umich.edu/~zmao/eecs489

Z. Morley MaoTuesday Sept 21, 2004

Acknowledgement: Some slides adapted from Kurose&Ross and Katz&Stoica

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IP Header

§ Vers: IP versions§ HL: Header length (in 32-

bits)§ Type: Type of service§ Length: size of datagram

(header + data; in bytes) § Identification: fragment ID§ Fragment offset: offset of

current fragment (x 8 bytes)§ TTL: number of network

hops§ Protocol: protocol type (e.g.,

TCP, UDP)§ Source IP addresses§ Destination IP address

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What is Routing?

Routing is the core function of a networkIt ensures that

• information accepted for transfer • at a source node • is delivered to the correct• set of destination nodes, • at reasonable levels of performance.

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Internet Routing

§ Internet organized as a two level hierarchy§ First level – autonomous systems (AS’s)

- AS – region of network under a single administrative domain

§ AS’s run an intra-domain routing protocols- Distance Vector, e.g., Routing Information Protocol (RIP)- Link State, e.g., Open Shortest Path First (OSPF)

§ Between AS’s runs inter-domain routing protocols, e.g., Border Gateway Routing (BGP)- De facto standard today, BGP-4

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Example

AS-1

AS-2

AS-3

Interior router

BGP router

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Intra-domain Routing Protocols

§ Based on unreliable datagram delivery§ Distance vector

- Routing Information Protocol (RIP), based on Bellman-Ford- Each neighbor periodically exchange reachability information

to its neighbors- Minimal communication overhead, but it takes long to

converge, i.e., in proportion to the maximum path length

§ Link state- Open Shortest Path First (OSPF), based on Dijkstra- Each network periodically floods immediate reachability

information to other routers- Fast convergence, but high communication and computation

overhead

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Routing

§ Goal: determine a “good” path through the network from source to destination

- Good means usually the shortest path

§ Network modeled as a graph- Routers à nodes- Link àedges

• Edge cost: delay, congestion level,…

A

ED

CB

F

22

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1

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5

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1

23

0111

value in arrivingpacket’s header

routing algorithm

local forwarding tableheader value output link

0100010101111001

3221

Interplay between routing and forwarding

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u

yx

wv

z2

21

3

1

1

2

53

5

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

21

3

1

1

2

53

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 Algorithm classification

Global or decentralized information?

Global:§ all routers have complete

topology, link cost info§ “link state” algorithmsDecentralized:§ router knows physically-

connected neighbors, link costs to neighbors

§ iterative process of computation, exchange of info with neighbors

§ “distance vector” algorithms

Static or dynamic?Static:§ routes change slowly over

timeDynamic:§ routes change more quickly

- periodic update- in response to link cost

changes

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Outline

Ø Link State§ Distance Vector

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A Link State Routing Algorithm

Dijkstra’s algorithm§ Net topology, link costs known

to all nodes- Accomplished via “link

state flooding” - All nodes have same info

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

§ Iterative: after k iterations, know least cost paths to k closest destinations

Notations§ 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 destination v

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

§ S: set of nodes whose least cost path definitively known

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Link State Flooding Example

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5

4

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Link State Flooding Example

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Link State Flooding Example

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Link State Flooding Example

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Dijsktra’s Algorithm

1 Initialization:2 S = {A};3 for all nodes v4 if v adjacent to A5 then D(v) = c(A,v); 6 else D(v) = ;7 8 Loop9 find w not in S such that D(w) is a minimum; 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) );

// new cost to v is either old cost to v or known// shortest path cost to w plus cost from w to v

13 until all nodes in S;

∞

Notations

§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 destination v

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

next to v

§S: set of nodes whose least cost path definitively known

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Example: Dijkstra’s Algorithm

Step012345

start SA

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

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

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

D(E),p(E) D(F),p(F)

A

ED

CB

F

22

13

1

1

2

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∞ ∞

1 Initialization:2 S = {A};3 for all nodes v4 if v adjacent to A5 then D(v) = c(A,v); 6 else D(v) = ;…

∞

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Example: Dijkstra’s Algorithm

Step012345

start SA

AD

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

D(C),p(C)5,A4,D

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

D(E),p(E)

2,D

D(F),p(F)

A

ED

CB

F

22

13

1

1

2

53

5

∞ ∞∞

…8 Loop9 find w not in S s.t. D(w) is a minimum; 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;

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Example: Dijkstra’s Algorithm

Step012345

start SA

ADADE

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

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

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

D(E),p(E)

2,D

D(F),p(F)

4,E

∞ ∞∞

A

ED

CB

F

22

13

1

1

2

53

5…8 Loop9 find w not in S s.t. D(w) is a minimum; 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;

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Example: Dijkstra’s Algorithm

Step012345

start SA

ADADE

ADEB

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

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

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

D(E),p(E)

2,D

D(F),p(F)

4,E

∞ ∞∞

A

ED

CB

F

22

13

1

1

2

53

5…8 Loop9 find w not in S s.t. D(w) is a minimum; 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;

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Example: Dijkstra’s Algorithm

Step012345

start SA

ADADE

ADEBADEBC

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

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

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

D(E),p(E)

2,D

D(F),p(F)

4,E

∞ ∞∞

A

ED

CB

F

22

13

1

1

2

53

5…8 Loop9 find w not in S s.t. D(w) is a minimum; 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;

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Example: Dijkstra’s Algorithm

Step012345

start SA

ADADE

ADEBADEBC

ADEBCF

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

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

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

D(E),p(E)

2,D

D(F),p(F)

4,E

∞ ∞∞

A

ED

CB

F

22

13

1

1

2

53

5…8 Loop9 find w not in S s.t. D(w) is a minimum; 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;

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Complexity

§ Assume a network consisting of n nodes- Each iteration: need to check all nodes, w, not in S- n*(n+1)/2 comparisons: O(n2)- More efficient implementations possible: O(n*log(n))

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Oscillations

§ Assume link cost = amount of carried traffic

A

D

C

B1 1+e

e0

e

1 1

0 0

initially

A

D

C

B2+e 0

001+e 1

… recomputerouting

A

D

C

B0 2+e

1+e10 0

… recompute

A

D

C

B2+e 0

e01+e 1

… recompute

§ How can you avoid oscillations?

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Outline

§ Link StateØ Distance Vector

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Distance Vector Routing Algorithm

§ Iterative: continues until no nodes exchange info§ Asynchronous: nodes need not exchange info/iterate in lock

steps§ Distributed: each node communicates only with directly-

attached neighbors§ Each router maintains

- Row for each possible destination- Column for each directly-attached neighbor to node- Entry in row Y and column Z of node X è best known distance from X

to Y, via Z as next hop (remember this !)

§ Note: for simplicity in this lecture examples we show only the shortest distances to each destination

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Distance Vector Routing

§ Each local iteration caused by: - Local link cost change - Message from neighbor: its least cost

path change from neighbor to destination

§ Each node notifies neighbors onlywhen its least cost path to any destination changes- Neighbors then notify their neighbors if

necessary

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

recompute distance table

if least cost path to any desthas changed, notifyneighbors

Each node:

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Distance Vector Algorithm (cont’d)

1 Initialization:2 for all neighbors V do3 if V adjacent to A4 D(A, V) = c(A,V); 5 else• D(A, V) = 8; • loop:8 wait (until A sees a link cost change to neighbor V9 or until A receives update from neighbor V) 10 if (D(A,V) changes by d) 11 for all destinations Y through V do12 D(A,Y) = D(A,Y) + d13 else if (update D(V, Y) received from V)

/* shortest path from V to some Y has changed */14 D(A,Y) = D(A,V) + D(V, Y);15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever

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Example: Distance Vector Algorithm

A C12

7

B D3

1-8D

C7C

B2B

NextHopCostDest.

Node A

D3D

C1C

A2A

NextHopCostDest.

Node B

D1D

B1B

A7A

NextHopCostDest.

Node C

C1C

B3B

-8A

NextHopCostDest.

Node D1 Initialization:2 for all neighbors V do3 if V adjacent to A4 D(A, V) = c(A,V); 5 else6 D(A, V) = 8; …

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C8D

C7C

B2B

NextHopCostDest.

Node A

Example: 1st Iteration (C à A)

A C12

7

B D3

1D3D

C1C

A2A

NextHopCostDest.

Node B

D1D

B1B

A7A

NextHopCostDest.

Node C

C1C

B3B

-8A

NextHopCostDest.

Node D

D(A, D) = D(A, C) + D(C,D) = 7 + 1 = 8

(D(C,A), D(C,B), D(C,D))

7 loop:…

13 else if (update D(V, Y) received from V) 14 D(A,Y) = D(A,V) + D(V, Y);15 if (there is a new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever

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B5D

B3C

B2B

NextHopCostDest.

Node A

Example: 1st Iteration (BàA, CàA)

A C12

7

B D3

1D3D

C1C

A2A

NextHopCostDest.

Node B

D1D

B1B

A7A

NextHopCostDest.

Node C

C1C

B3B

-8A

NextHopCostDest.

Node D

D(A,D) = D(A,B) + D(B,D) = 2 + 3 = 5 D(A,C) = D(A,B) + D(B,C) = 2 + 1 = 3

7 loop:…

13 else if (update D(V, Y) received from V) 14 D(A,Y) = min(D(A,V), D(A,V) + D(V, Y))15 if (there is a new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever

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Example: End of 1st Iteration

A C12

7

B D3

1B5D

B3C

B2B

NextHopCostDest.

Node A

C2D

C1C

A2A

NextHopCostDest.

Node B

D1D

B1B

B3A

NextHopCostDest.

Node C

C1C

C2B

B5A

NextHopCostDest.

Node D7 loop:

…13 else if (update D(V, Y) received from V) 14 D(A,Y) = D(A,V) + D(V, Y);15 if (there is a new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever

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Example: End of 2nd Iteration

A C12

7

B D3

1B4D

B3C

B2B

NextHopCostDest.

Node A

C2D

C1C

A2A

NextHopCostDest.

Node B

D1D

B1B

B3A

NextHopCostDest.

Node C

C1C

C2B

C4A

NextHopCostDest.

Node D7 loop:

…13 else if (update D(V, Y) received from V) 14 D(A,Y) = D(A,V) + D(V, Y);15 if (there is a new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever

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Example: End of 3rd Iteration

A C12

7

B D3

1B4D

B3C

B2B

NextHopCostDest.

Node A

C2D

C1C

A2A

NextHopCostDest.

Node B

D1D

B1B

B3A

NextHopCostDest.

Node C

C1C

C2B

C4A

NextHopCostDest.

Node D

Nothing changes à algorithm terminates

7 loop:…

13 else if (update D(V, Y) received from V) 14 D(A,Y) = D(A,V) + D(V, Y);15 if (there is a new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever

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Distance Vector: Link Cost Changes

A C14

50

B1

“goodnews travelsfast”

B1C

A4A

NCDNode B

B1B

B5A

NCDNode C

B1C

A1A

NCD

B1B

B5A

NCD

B1C

A1A

NCD

B1B

B2A

NCD

B1C

A1A

NCD

B1B

B2A

NCD

Link cost changes heretime

7 loop:8 wait (until A sees a link cost change to neighbor V9 or until A receives update from neighbor V) 10 if (D(A,V) changes by d) 11 for all destinations Y through V do12 D(A,Y) = D(A,Y) + d13 else if (update D(V, Y) received from V) 14 D(A,Y) = D(A,V) + D(V, Y);15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever

Algorithm terminates

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Distance Vector: Count to Infinity Problem

A C14

50

B60

“badnews travelsslowly”

B1C

A4A

NCDNode B

B1B

B5A

NCDNode C

B1C

C6A

NCD

B1B

B5A

NCD

B1C

C6A

NCD

B1B

B7A

NCD

B1C

C8A

NCD

B1B

B2A

NCD

Link cost changes here; recall that B also maintains shortest distance to A through C, which is 6. Thus D(B, A) becomes 6 !

time

7 loop:8 wait (until A sees a link cost change to neighbor V9 or until A receives update from neighbor V) 10 if (D(A,V) changes by d) 11 for all destinations Y through V do12 D(A,Y) = D(A,Y) + d ;13 else if (update D(V, Y) received from V) 14 D(A,Y) = D(A,V) + D(V, Y);15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever

…

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Distance Vector: Poisoned Reverse

A C14

50

B60§ If C routes through B to get to A:

- C tells B its (C’s) distance to A is infinite (so B won’t route to A via C)

- Will this completely solve count to infinity problem?

B1C

A4A

NCDNode B

B1B

B5A

NCDNode C

B1C

A60A

NCD

B1B

B5A

NCD

B1B

A50A

NCD

Link cost changes here; B updates D(B, A) = 60 as C has advertised D(C, A) = 8

time

B1C

A60A

NCD

B1B

A50A

NCD

B1C

C51A

NCD

B1B

A50A

NCD

B1C

C51A

NCD

Algorithm terminates

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Look at this example

§ Initially, both A and B have a distance 2 to D, C has a distance 1

§ Assume CD goes down§ Using split horizon, A and

B tell C that they cannot get to D

§ C concludes D is unreachable, reports to A and B

§ A hears that B has a path of length 2 to D

§ B concludes it can get to D via A in 3 hops

§ A and B set their distance to D to 4

§ Count to infinity????

A B

C

D

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Link State vs. Distance Vector

Per node message complexity§ LS: O(n*e) messages; n –

number of nodes; e – number of edges

§ DV: O(d) messages; where d is node’s degree

Complexity§ LS: O(n2) with O(n*e)

messages§ DV: convergence time varies

- may be routing loops- count-to-infinity problem

Robustness: what happens if router malfunctions?

§ LS: - 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 through network