network layer (contd.) routing

Network Layer (contd.)

Routing

source

application

transportnetwork

linkphysical

HtHn M

segment Ht

datagram

destination

application

transportnetwork

linkphysical

HtHnHl M

HtHn M

Ht M

M

networklink

physical

linkphysical

HtHnHl M

HtHn M

HtHn M

HtHnHl M

router

switch

Packet transfer in network

message M

Ht M

Hn

frame

Encapsulation

message

Network Layer 4-3

Network-Layer Functions

Forwarding: move packets from router’s input to router output

Image courtesy: http://www.nd.edu/~networks/Image%20Gallery/gallery_old.htm

Routing

application

transportnetworkdata linkphysical

application

transportnetworkdata linkphysical

1. Send data 2. Receive data??

??

??

Image courtesy: http://www.nd.edu/~networks/Image%20Gallery/gallery_old.htm

Goal: determine “good” paths(sequences of routers)

through network from source to dest.

Routing

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) }

Routing: Graph formulation

Graph abstraction for the routing problem:

graph nodes are routers graph edges are physical

links links have properties: delay,

capacity, $ cost, policy u

yx

wv

z2

2

13

1

1

2

53

5

Network Layer 4-6

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 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)

7

Key Desired Properties of a Routing Algorithm

Simplicity

Robustness

Optimalityfind good path

(for user/provider)

8

Routing Design Space

Routing has a large design space who decides routing?

• source routing: end hosts make decision• network routing: networks make decision

how many paths from source s to destination d?

• multi-path routing • single path routing

will routing adapt to network traffic demand?• adaptive routing• static routing

…

- Robustness- Optimality- Simplicity

9

Routing has a large design space who decides routing?

• source routing: end hosts make decisionnetwork routing: networks/routers make decision

- Based on information available from the network how many paths from source s to destination

d?• multi-path routing • single path routing

will routing adapt to network traffic demand?• adaptive routing• static routing

…

- Robustness- Optimality- Simplicity

Routing Design Space: examplenetwork routing

Network Layer 4-10

Routing Algorithm design based on available information

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 neighbors iterative process of computation, exchange

of info with neighbors “distance vector” algorithms

u

yx

wv

z2

21

3

1

12

53

5

Network Layer 4-11

Link state (LS) routing algorithm

Network Layer 4-12

Link-State Routing Algorithm

Network topology, link costs known to all nodes accomplished via “link state broadcast” all nodes have same info

Problem

Given a topology, link costs, and a source-destination (S-D) pair, determine a route from S to D so that the route has the minimum cost (i.e., is the shortest).

Solution: Dijkstra’s shortest-path algorithm

u

yx

wv

z2

21

3

1

12

53

5

Network Layer 4-13

A Link-State Routing Algorithm: Dijkstra’s Algorithm

Parameters: c(x,y): link cost from node x to y; = ∞ 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 N': set of nodes whose least cost path definitively

known

Network Layer 4-14

Dijkstra’s algorithm: example

u

yx

wv

z2

2

13

1

1

2

53

5

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

Shortest paths:u x: 1,uu v: 2,uu y: 2,xu w: 3,yu z: 4,y

Network Layer 4-15

Dijkstra’s algorithm: example (2)

u

yx

wv

z

Resulting shortest-path tree from u:

vx

y

w

z

(u,v)(u,x)

(u,x)

(u,x)

(u,x)

destination link

Resulting forwarding table in u:

Shortest paths:u x: 1,uu v: 2,uu y: 2,xu w: 3,yu z: 4,y

Network Layer 4-16

Dijkstra’s Algorithm

1 Initialization: 2 N' = {u} 3 for all nodes v 4 if v adjacent to 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 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'

Network Layer 4-17

Let’s solve this example!

Determine shortest paths from R1 to all other nodes with corresponding predecessor nodes!

Network Layer 4-18

Distance Vector routing algorithm

Distance Vector Routing

Practically entire network topology (each link state) may not be known accurately Only the information to a direct neighbor may be known

Distance-vector routing algorithm operates by Each router trusting its direct neighbors Each router maintain a table (vector) estimating

• the best known distance to each destination• which line to use to get there

Tables (vectors) are updated by exchanging information with the direct neighbors

At node i, the basic update rule

where - di denotes the distance

estimation from i to the destination,

- N(i) is set of neighbors of node i, and

- dij is the distance of the direct link from i to j

- dj denotes the distance estimation feedback from j to i

Based on Bellman-Ford algorithm

Distance Vector Routing: Basic Idea

)(min )( jijiNji ddd

i

jid

jdijd

destination

Network Layer 4-21

Distance Vector Algorithm

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

recompute estimates

if DV to any dest has

changed, notify neighbors

Each node:

neighbors then notify their neighbors and so on…

Iterative & Distributed

Network Layer 4-22

x y z

xyz

0 2 7

∞ ∞ ∞∞ ∞ ∞

from

cost tofr

om

from

x y z

xyz

∞ ∞

∞ ∞ ∞

cost to

x y z

xyz

∞ ∞ ∞7 1 0

cost to

2 0 1

∞ ∞ ∞

time

x z12

7

y

node x table

node y table

node z table

∞

Initially:

D-V Algorithm example

Network Layer 4-23

x y z

xyz

0 2 7

∞ ∞ ∞∞ ∞ ∞

from

cost to

from

from

x y z

xyz

0

from

cost to

x y z

xyz

∞ ∞

∞ ∞ ∞

cost to

x y z

xyz

∞ ∞ ∞7 1 0

cost to

∞2 0 1

∞ ∞ ∞

2 0 17 1 0

time

x z12

7

y

node x table

node y table

node z table

Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)} = min{2+0 , 7+1} = 2

Dx(z) = min{c(x,y) + Dy(z), c(x,z) + Dz(z)} = min{2+1 , 7+0} = 3

32

Network Layer 4-24

x y z

xyz

0 2 7

∞ ∞ ∞∞ ∞ ∞

from

cost to

from

from

x y z

xyz

0 2 3

from

cost to

x y z

xyz

∞ ∞

∞ ∞ ∞

cost tox y z

xyz

0 2 7

from

cost to

x y z

xyz

0 2 7

from

cost to

x y z

xyz

∞ ∞ ∞7 1 0

cost to

∞2 0 1

∞ ∞ ∞

2 0 17 1 0

2 0 17 1 0

2 0 13 1 0

time

x z12

7

y

node x table

node y table

node z table

Network Layer 4-25

x y z

xyz

0 2 7

∞ ∞ ∞∞ ∞ ∞

from

cost to

from

from

x y z

xyz

0 2 3

from

cost tox y z

xyz

0 2 3

from

cost to

x y z

xyz

∞ ∞

∞ ∞ ∞

cost tox y z

xyz

0 2 7

from

cost to

x y z

xyz

0 2 3

from

cost to

x y z

xyz

0 2 3

from

cost tox y z

xyz

0 2 7

from

cost to

x y z

xyz

∞ ∞ ∞7 1 0

cost to

∞2 0 1

∞ ∞ ∞

2 0 17 1 0

2 0 17 1 0

2 0 13 1 0

2 0 13 1 0

2 0 1

3 1 0

2 0 1

3 1 0

time

x z12

7

y

node x table

node y table

node z table

Network Layer 4-26

Distance Vector: link cost changes

Link cost changes: node detects local link cost

change updates routing info, recalculates

distance vector if DV changes, notify neighbors

“goodnews travelsfast”

x z14

50

y1

At time t0, y detects the link-cost change, updates its DV, and informs its neighbors.

At time t1, z receives the update from y and updates its table. It computes a new least cost to x and sends its neighbors its DV.

At time t2, y receives z’s update and updates its distance table. y’s least costs do not change and hence y does not send any message to z.

Distance-Vector Algorithms: Link cost changes Bad news propagate slowly

This is called the counting-to-infinity problem

Distances to A

A goes down or line between

A and B is down

Solution: Split Horizon Hack

Actual distance to a destination is not reported on the line on which packets to that destination are sent.

Instead these distances are reported as “infinity: Poisoned reverse”

Will this completely solve count-to-infinity problem?

B

D

A

C C tells D the truthabout its distance toA, but lies to B andsays the distance isinfinity.

A topology where split horizon fails

Suppose that D becomes unreachable from C.

A and B are reportinginfinite distances to C, butthey are reporting distancesof length 2 to each other.

A and B will count to infinity.

Network Layer 4-30

Comparison of LS and DV algorithms

Message complexity LS: with n nodes, E links,

O(nE) msgs sent DV: exchange between

neighbors only convergence time varies

Speed of Convergence LS: O(n2) algorithm requires

O(nE) msgs may have oscillations

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