Tutorial LS DV Routing

8/7/2019 Tutorial LS DV Routing

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Link-State and DistanceVector Routing Examples

CPSC 441

University of Calgary


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Link-State (LS) Routing AlgorithmDijkstras algorithm topology and link costs

known to all nodes

accomplished via linkstate broadcast

all nodes have same info

computes least cost paths

from one node (source) to allother nodes

gives forwarding table forthat node

iterative: after k iterations,know least cost path to kdestination nodes

Notation:

c(x,y): link cost from node xto y; set to if a and y are

not direct neighbors D(v): current value of cost of

path from source to dest. v

p(v): vs predecessor node

along path from source to v N': set of nodes whose least

cost path is definitivelyknown


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Dijsktras Algorithm1 Initialization (u = source node):2 N' = {u} /* path to self is all we know */3 for all nodes v

4 if v adjacent to u5 then D(v) = c(u,v) /* assign link cost to neighbour6 else D(v) =

7

8 Loop9 find w not in N' such that D(w) is a minimum10 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 known14 shortest path cost to w plus cost from w to v */15 until all nodes in N'


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Textbook Problem 4.21 x is source

6,x1,x3,xx0

D(z),p(z)D(y),p(y)D(w),p(w)D(v),p(v)D(u),p(u)D(t),p(t)D(s),p(s)NStep

w

t

s3 9

1

3

2

4

1

4

2

11

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61

y

x v

u

z

Initialization:- Store source node x in N- Assign link cost to neighbours (v,w,y)- Keep track of predecessor to destination node


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6,x2,w4,wxw1

6,x1,x3,xx0


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s3 9

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1

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y

x v

u

zNode and its minimum cost

are colour-coded in each

step

Loop step 1:- For all nodes not in N, find one that has minimum cost path (1)- Add this node (w) to N

- Update cost for all neighbours of added node that are not in Nrepeat until all nodes are in N


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7,txwvuyts6

7,t6,txwvuyt5

17,y5,u7,uxwvuy4

3,v5,u7,uxwvu3

3,v3,v11,vxwv2

6,x2,w4,wxw1

6,x1,x3,xx0


w

t

s3 9

1

3

2

4

1

4

2

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1y

x v

u

zNode and its minimum cost

are colour-coded in each

step


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Distance Vector Routing

Based on Bellman-Ford Equation

Define

dx(y) := cost of least-cost path from x to y

c(x,v) := cost of direct link from x to v Then, for all v that are neighbours of x

dx(y) = minv {c(x,v) + dv(y) }

yx

vc(x,v)

dx(y)

dv(y)


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Bellman-Ford Equation Example

u

yx

wv

z

2

21

3

1

1

2

53

5

Consider a path from uto zBy inspection, dv(z) = 5, dx(z) = 3, dw(z) = 3

du(z) = min { c(u,v) + dv(z),

c(u,x) + dx(z),c(u,w) + dw(z) }= min {2 + 5,

1 + 3,

5 + 3} = 4

Node that achieves minimum is nexthop in shortest path entry in forwarding table

B-F equation says:


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Distance Vector AlgorithmBasic idea:

Nodes keep vector (DV) ofleast costs to other nodes

These are estimates, Dx(y)

Each node periodically sendsits own DV to neighbors

When node xreceives DV fromneighbor, it keeps it andupdates its own DV using B-F:

Dx(y) minv{c(x,v) + Dv(y)}

for each node yN

Ideally, the estimate Dx(y)converges to the actual leastcostdx(y)

On each node:

waitfor (change in local linkcost or msg from neighbor)

recomputeestimates

if DV has changed, notifyneighbors


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117 1 0 time

x z12

7

y

x y z

x

yz

0 2 7

from

cost to

from

from

x y z

xyz

cost to

x y z

xy

z

cost to

2 0 1

node x table

node y table

node z table

Step 1: InitializationInitialize costs of direct links

Set to costs from neighbours


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x z12

7

y

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

x y z

x

yz

0 2 7

from

cost to

from

from

x y z

x

yz

0 23

from

cost to

x y z

xyz

cost to

x y z

xy

z

cost to

2 0 1

2 017 1 0

node x table

node y table

node z table

Step 2: Exchange DV and

iterate-In first iteration, node x savesneighbours DVs-Then, it checks path costs to

all nodes using received DVs

-E.g. new cost Dx(z) isobtained by adding costsmarked red


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x z12

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y

In similar fashion, algorithm proceeds until all nodes have updated tables

x y z

x

yz

0 2 7

from

cost to

from

from

x y z

xyz

0 2 3

from

cost tox y z

x

yz

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

xy

z

cost to

2 0 1

2 0 17 1 0

2 0 17 1 0

2 0 1

3 1 0

2 0 13 1 0

2 0 1

3 1 02 0 1

3 1 0

node x table

node y table

node z table


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Distance Vector: link cost changesLink cost changes:

node detects local link cost change

updates routing info, recalculatesdistance vector

if DV changes, notify neighbors

goodnewstravelsfast

x z14

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y1

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

At time t1, zreceives the update from yand updates its table.

It computes a new least cost to xand sends neighbors its DV.

At time t2, yreceives zs update and updates its distance table.

ys least costs do not change and hence ydoes notsend anymessage to z.


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Distance Vector: link cost changesLink cost changes:

bad news travels slow - count to infinityproblem!

When y detects cost change to 60, it willupdate its DV using the zs cost to x, whichis 5 (via y), to obtain an incorrect new costto x of 6, over the path yzyx that has

a loop 44 iterations before algorithm stabilizes,

while y and z exchange updates

Poisoned reverse:

If Z routes through Y to get to X : Z tells Y its (Zs) distance to X is infinite (so Y

wont route to X via Z)

Will this completely solve the problem?

x z

14

50

y60

Tutorial LS DV Routing

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