Chapter 4 Distance Vector Problems, and Link-State Routing

Chapter 4Distance Vector Problems, and

Link-State Routing

Professor Rick HanUniversity of Colorado at Boulder

[email protected]

Prof. Rick Han, University of Colorado at Boulder

Announcements• Handing back HW #1, TA OH, solutions

online later today• Homework #2 available on Web site, due

Feb. 26• Last week’s lectures are now on Web site• Midterm for the week of March 12• Next, Distance vector problems, and link-

state routing, …


Recap of Previous Lecture• Distributed Bellman-Ford = Distance Vector• Bellman-Ford Equation

• D(i,j) = min {d(i,k) + D(k,j)} for all i<>j k neighbors

• Bellman-Ford Algorithm [Ford & Fulkerson]• D(i,j)[h+1] = min {d(i,k) + D(k,j)[h]} for all i<>j,

h=0,1, … k neighbors

• Distributed Bellman-Ford Algorithm• Physically distribute the calculation of D(i,j)[h] to

router i only, and • Exchange the results of your D(i,j)[h] with

neighboring routers at each iteration h


RIP is simple1. At each step, exchange distance vectors with

each neighbor2. Update distance table with new distance

vector, adding one (all link costs are one)3. Calculate minimum hop path to each

destination by looking at minimum in the row

A

C

BA aB bC c A a

B bC c

Dest A B CA a++ --- a++B b++ --- b++C c++ --- c++

Distance table at BVia Port/Link


Link Failure Causes “Bouncing” Effect

A

25

1

1

B

C

BC 2

1

dest cost

XBB

via

AC 1

1

dest cost

CA

via

AB 1

2

dest cost

BB

via


B Notices A-B Link Failure

A

25 1

B

C

B notices failure, resets cost via A toinfinity in distance table (not shown), &knows cost via C is 26

BC 2

1

dest cost

BB

via

AC 1

26

dest cost

CC

via

AB 1

2

dest cost

BB

via


C Sends Dist. Vector to B

A

25 1

B

C

BC 2

1

dest cost

BB

via

AC 1

3

dest cost

CC

via

AB 1

2

dest cost

BB

via

C sends routing update to B


B Updates Distance to A

A

25 1

B

C

Packet sent from Cto A bounces between C and B

until TTL=0!

BC 2

1

dest cost

BB

via

AC 1

3

dest cost

CC

via

AB 1

2

dest cost

BB

via


B Sends Dist. Vector to C

A

25 1

B

C

C adds one to B’sadvertised distanceto A. (Why does C

overrideits storeddistance of 2to A with 4,larger value?)

BC 2

1

dest cost

BB

via

AC 1

3

dest cost

CC

via

AB 1

4

dest cost

BB

via



A

25 1

B

C

B adds one to C’sadvertised distanceto A. (overrides

its storeddistance of 3to A with 5,larger value)

BC 2

1

dest cost

BB

via

AC 1

5

dest cost

CC

via

AB 1

4

dest cost

BB

via


Link Failure: Bad News Travels Slowly

A

25 1

B

C

After 20+ exchanges,routing tables looklike this:

BC 25

26

dest cost

CC

via

AC 1

25

dest cost

CC

via

AB 1

24

dest cost

BB

viaAssume A has advertisedits link cost of 25 to C during B<->C exchanges.C stores this cost in its distancetable (not shown)


Bad News Travels Slowly (2)

A

25 1

B

C

C increments B’supdate by 1, andchooses 25 via Ato A, instead of 26

Via B to A

BC 25

26

dest cost

CC

via

AC 1

25

dest cost

CC

via

AB 1

25

dest cost

BA

via


Bad News Travels Slowly (3)

A

25 1

B

C

After 25 B-Cexchanges, finallyconverge tostable routing

BC 25

26

dest cost

CC

via

AC 1

26

dest cost

CC

via

AB 1

25

dest cost

BA

via


Link Failure Causes “Counting to Infinity” Effect

A

25

1

1

B

C

BC 2

1

dest cost

XBB

via

AC 1

1

dest cost

CA

via

AB 1

2

dest cost

BB

via



A

25 1

B

C

B notices failure,resets cost to 26

BC 2

1

dest cost

BB

via

AC 1

26

dest cost

CC

via

AB 1

2

dest cost

BB

via



A

25 1

B

C

BC 2

1

dest cost

BB

via

AC 1

3

dest cost

CC

via

AB 1

2

dest cost

BB

via

C sendsrouting update to B


A-C Link Fails

A

1

B

C

C detects link to A has failed,but no change in C’srouting table (why?)

AC 1

3

dest cost

CC

via

AB 1

2

dest cost

BB

via


Now, B and C Count to Infinity

A

1

B

C

AC 1

3

dest cost

CC

via

AB 1

4

dest cost

BB

via


B and C Count to Infinity (2)

A

1

B

C

AC 1

5

dest cost

CC

via

AB 1

4

dest cost

BB

via


Some “Solutions”• Split horizon

– C does not advertise route to B when it sends its distance vector

• Poisoned reverse– C advertises route to B with infinite

distance in its distance vector• Works for two node loops

– Does not work for loops with more nodes



A

25 1

B

C

B notices failure,resets cost to 26

BC 2

1

dest cost

BB

via

AC 1

26

dest cost

CC

via

AB 1

2

dest cost

BB

via


Split Horizon

A

25 1

B

C

BC 2

1

dest cost

BB

via

AC 1

26

dest cost

CC

via

AB 1

2

dest cost

BB

via

C sends routing updateto B

B 1

dest cost

No need to send destA via B, since B shouldalready know this


Split Horizon With Poisoned Reverse

A

25 1

B

C

BC 2

1

dest cost

BB

via

AC 1

~

dest cost

C--

via

AB 1

2

dest cost

BB

via

C sends routingupdate to B

AB 1

~

dest cost

If lowest cost path is viaB, then when updating Bsend infinite cost


Example Where Split Horizon Fails

1

11

1

A

• When link breaks, C marks D as unreachable and reports that to A and B

• Suppose A learns it first– A now thinks best path to D

is through B– A reports D unreachable to

B and a route of cost=3 to C• C thinks D is reachable

through A at cost 4 and reports that to B

• B reports a cost 5 to A who reports new cost to C

• etc...

X

B

C

D


Alternative Shortest Path Calc.• Compute a shortest path tree

• Observation: • shortest path to nodes further from the root must

go through a branch of the shortest path tree closer to the root

• Strategy: expand outwards, calculating the shortest path tree from the root (B)

4

36

21

9

1

1D

A

FE

B

C


Dijkstra’s Shortest Path Algorithm

• Let N = set of nodes in graph• l(i,j) = link cost between i,j (= infinity if not

neighbors)• SPT = set of nodes in shortest path tree thus

far• S = source node• C(n) = cost of path from

S to node n4

36

21

9

1

1D

A

FE

B

C


Dijkstra’s Shortest Path Algorithm (2)

• Initialize shortest path tree SPT = {S}• For each n not in SPT, C(n) = l(s,n)• While (SPT<>N)

• SPT = SPT U {w} such that C(w) is minimum for all w in (N-SPT)

• For each n in (N-SPT)• C(n) = MIN (C(n), C(w) + l(w,n))

4

36

21

9

1

1D

A

FE

B

C



• Initialize shortest path tree SPT = {B}• For each n not in SPT, C(n) = l(s,n)

• C(E) = 1, C(A) = 3, C(C) = 4, C(others) = infinity• Add closest node to the tree: SPT = SPT U

{E} since C(E) is minimum for all w not in SPT.• No shorter path to E can ever be found via some

other roundabout path.

4

36

21

9

1

1D

A

FE

B

C

• Shortest path tree SPT = {B, E}



• Recalculate C(n) = MIN (C(n), C(E) + l(E,n)) for all nodes n not yet in SPT• C(A) = MIN( C(A)=3, 1 + 1) = MIN(3,2) = 2• C(D) = MIN( infinity, 1 + 1) = 2• C(F) = MIN( infinity, 1 + 2) = 3• C(C ) = MIN( 4, 1 + infinity) = 4

4

36

21

9

1

1D

A

FE

B

C

• Each new node in tree, could create a lower cost path, so redo costs



• Loop again, select node with the lowest cost path:• C(A) = 2, C(D) = 2, C(F) = 3, C(C ) = 4• SPT = SPT U {A} = {B, E, A}• No shorter path can be found from B to A,

regardless of any new nodes added to tree

4

36

21

9

1

1D

A

FE

B

C

• Recalc: C(n) = MIN (C(n), C(A) + l(A,n)) for all n not yet in SPT• C(D) = MIN(2, 2+inf) =

2• C(F) = 3, C(C) = 4



• Continue to loop, adding lowest cost node at each step and updating costs

• SPT crawls outward• Remember to store the links in SPT as they

are added (each node’s predecessor is stored)

• Each node has to store the entire topology, or database of link costs

4

36

21

9

1

1D

A

FE

B

C


Link-State Routing = Reliable Flooding + Dijkstra SPT

• Start condition– Each node assumed to know state of links to its

neighbors• Step 1

– Each node broadcasts its state to all other nodes– Reliable flooding mechanism

• Step 2– Each node locally computes shortest paths to all

other nodes from global state– Dijkstra’s shortest path tree (SPT) algorithm


Link State Packets (LSPs)• Periodically, each node creates a

link state packet containing:– Node ID– List of neighbors and link cost– Sequence number

• Needed to avoid stale information from flood

– Time to live (TTL)– Node outputs LSP on all its links


Reliable Flooding of LSPs• When node J receives LSP from node K

– If LSP is the most recent LSP from K that J has seen so far, J saves it in database and forwards a copy on all links except link LSP was received on

– Otherwise, discard LSP• How to tell more recent

– Use sequence numbers– Same method as sliding window protocols


OSPF – Open Shortest Path First

• A particular realization of link-state routing, used for intra-domain routing in the Internet

• Additional support for:– Authentication of routing updates– Support for broadcast networks– Different cost metrics

• Periodic and event-triggered flooding of LSP routing updates, like RIP

Chapter 4 Distance Vector Problems, and Link-State Routing

Documents

distance vector problems

new distance vector

boulderb updates distance

neighborupdate distance

exchange distance vectors

boulderlink failure

boulderbad news travels

c stores