week13 lec1

Chapter 4 Network Layer

Computer Networking: A Top Down Approach 4th edition. Jim Kurose, Keith RossAddison-Wesley, July 2007.

Routing Protocols• Define how routers exchange network

information– What type of information– The format of information exchange– When to exchange– Which router to exchange information with

• Examples– Routing Information Protocol (RIP)– Enhanced Interior Gateway Routing Protocol

(EIGRP)– CISCO Proprietary

– Open Shortest Path First (OSPF)– Border Gateway Protocol (BGP)

Routing AlgorithmsGiven a set of routers a routing algorithm finds a “Good” path from source router to destination router

Least cost path

A graph is used to formulate routing problems

A Graph G=(N,E) is a Set of N nodes and a collection E of edgesNodes in the graph represent RoutersEdges represent physical links

1

23

0111

packet’s header

routing algorithm

local forwarding tableheader value output link

0100010101111001

3221

u

yx

wv

z2

2

13

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

Graph Abstraction: costs

u

yx

wv

z2

2

13

1

1

2

53

5 • c(x,x’) = cost of link (x,x’)

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

• Cost can be• Physical length of the link• Delay etc.

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

Routing Algorithm ClassificationGlobal Routing

Algorithm

Computes least cost path using complete global knowledge about the network.

Takes connectivity between all nodes and all link costs as input.

All routers have complete topology, link cost information

Also called “Link State” Algorithms

Used by Open Shortest Path First Protocol (OSPF)

Decentralized Routing Algorithm

No node has complete information about the cost of all links.

In the beginning knowledge of its own directly attached links.

Computes least cost path by an iterative process of calculation and exchange of information.

Also called Distance Vector (DV) Algorithm

Used by Routing Information Protocol (RIP)

Link-State Routing Algorithm Network topology and

link costs are known to all nodes Each node broadcast

link state packets to all other nodes in the network

Each link state packet contains the identities and cost of its attached links

Dijkstra’s Algorithm Computes least cost

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

Iterative: After k iterations, least cost paths to k destinations are known

Notation: D(v): Current value of least

cost path from source to destination (v).

p(v): Predecessor node along path from source to v

N': Subset of nodes whose least cost path is definitively known

Dijkstra’s Algorithm: Example

Step012345

N'u

uxuxy

uxyvuxyvw

uxyvwz

D(v),p(v)2,u2,u2,u

D(w),p(w)5,u4,x3,y3,y

D(x),p(x)1,u

D(y),p(y)∞

2,x

D(z),p(z)∞ ∞

4,y4,y4,y

u

yx

wv

z2

2

13

1

1

2

53

5

x

v

y

wz

(u,x)

(u,v)

(u,x)

(u,x)(u,x)

destination link

Resulting forwarding table in u:

Dijkstra’s Algorithm

1 Initialization: 2 N' = {u} 3 for all nodes v 4 if v is a neighbor of 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 each neighbor v of 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'

u

yx

wv

z2

2

13

1

1

2

53

5

Dijkstra’s Algorithm-Example

Find the shortest path from S to all nodes using Dijkstra’s Algorithm?

Solution

Step N’D(x), p(x) D(t),p(t) D(u),p(u) D(v),p(v) D(w),p(w) D(y),p(y) D(z),p(z)

0 s ∞ 1,s 4,s ∞ ∞ ∞ ∞

1 st ∞ 3,t 5,t ∞ 8,t 6,t

2 stu ∞ 5,t 6,u 8,t 6,t

3 stuv 8,v 6,u 6,v 6,t

4 stuvy 8,v 6,u 6,t

5 stuvyz 8,v 6,u

6 stuvyzw 8,v

7 stuvyzwx