ee 122: intra-domain routing - university of california ...ee122/fa02/notes/lecture10x4.pdf · 21...

1

EE 122: Intra-domain routing

Ion StoicaSeptember 30, 2002

(* this presentation is based on the on-line slides of J. Kurose & K. Rose)

isto [email protected] 2

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., RIP- Link State, e.g., OSPF

� Between AS’s runs inter-domain routing protocols, e.g., Border Gateway Routing (BGP)

- De facto standard today, BGP-4


Example

AS-1

AS-2

AS-3

Interior router

BGP router


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 Protocol (OSPF), based on Dijkstra- Each network periodically floods immediate reachability

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

overhead

2


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 �

nodes- Link

�edges

• Edge cost: delay, congestion level,…

A

ED

CB

F

2

2

13

1

1

2

53

5


A Link State Routing Algorithm

Dijkstra’s algorithm� Net topology, link costs known

to all nodes- Accomplished via “link state

broadcast” - All nodes have same info

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

� Iterative: after k iterations, know least cost path 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


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) );13 // new cost to v is either old cost to v or known14 // shortest path cost to w plus cost from w to v15 until all nodes in S;

∞


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

2

2

13

1

1

2

53

5

∞ ∞

3



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

2

2

13

1

1

2

53

5

∞ ∞∞



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

2

2

13

1

1

2

53

5



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

2

2

13

1

1

2

53

5



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

2

2

13

1

1

2

53

5

4



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

2

2

13

1

1

2

53

5


Dijkstra’s Algorithm: Discussion

� Algorithm complexity: n nodes- Each iteration: need to check all nodes, w, not in S- n*(n+1)/2 comparisons: O(n**2)- More efficient implementations possible: O(n*log(n))

� Oscillation possible- E.g., 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


Distance Vector Routing Algorithm

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

step!� Distributed: each node communicates only with directly-

attached neighbors� Routing (distance) table data structure – 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 � distance from X to Y, via Z as

next hop

)},({min),(),( wZDZXcZYD Zw

X +=isto [email protected] 16

Example: Distance (Routing) Table

A

E D

CB6

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

i na

tion

D (C,D)E

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

= 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!

5


Routing Table �

Forwarding Table

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

i na

tion

A

B

C

D

A,1

D,5

D,4

D,2

Outgoing link to use, cost

dest

i na

tion

Distance (routing) table Forwarding table


Distance Vector Routing: Overview

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

path change from neighbor� 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 of msg from neighbor)

recompute distance table

if least cost path to any dest has changed, notifyneighbors

Each node:


Distance Vector Algorithm

1 Initialization: 2 for all adjacent nodes v: 3 D (*,v) = /* 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:

∞


Distance Vector Algorithm (cont’d)8 loop9 wait (until I see a link cost change to neighbor V 10 or until I receive update from neighbor V) 11 12 i f (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 D (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 i f we have a new min D (Y,w) for any destination Y 24 send new value of min D (Y,w) to all neighbors 25 26 forever

w

XX

XX

X

ww

V

6


Example: Distance Vector Algorithm

X Z12

7

Y



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



X Z12

7

Y



X Z12

7

Y

7


Distance Vector: Link Cost Changes

X Z14

50

Y1

algorithmterminates“good

news travelsfast”

� 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)


Distance Vector: Link Cost Changes

X Z14

50

Y60

algorithmcontinues

on!

� Link cost changes- Good news travels fast - Bad news travels slow - “count

to infinity” problem!


Distance Vector: Poisoned Reverse

X Z14

50

Y60

algorithmterminates

� 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?


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(n**2) 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:

- DV node can advertise incorrect path cost

- each node’s table used by others; error propagate through network

ee 122: intra-domain routing - university of california ...ee122/fa02/notes/lecture10x4.pdf · 21...

Documents