network routing dv

8/3/2019 Network Routing DV

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Network and Network Routing

October 28 2009

1



Networ overview

2



dest.

Network layer in every host,

Basic functions:

Data lane: forwardin

move packets fromrouter’s input port to

Control plane: ath

determination and call setup

determine route taken by

3

destination



routing and callsetup

4



guaranteed bandwidth?

- loss-free delivery?

in-order deliver ?

Interaction between users and network

signaling: congestion feedback/resource reservation

efficiency

5

scalability



Guarantees ?

Architecture Model Bandwidth Loss Order Timing feedback

n erne

ATM

es e or

CBR

none

constant

no

yes

no

yes

no

yes

no n errevia loss/delay)no

ATM VBR rateguaranteedrate

yes yes yes congestionnocon estion

ATM

ATM

ABR

UBR

guaranteed

minimumnone

no

no

yes

es

no

no

yes

Internet model being extended: Intserv, Diffserv

6

ATM: Asynchronous Transfer Mode; CBR: Constant Bit Rate; V: Variable; A: available; U: User



:

Network layer functions:

Transport layerRouting protocols•path selection•e.g., RIP, OSPF, BGP

Control protocols•error reportinge.g. ICMP

Control protocols- router “signaling”e.g. RSVP

Networklayer

forwarding. .,

•addressing conventions

•packet format•packet handling conventions

Link layer

7

physical layer



Networ overview

Control lane: routin overview

8



Routin

Goal: determine “good” paths

(sequences of routers) thru

Gra h abstraction for the

.

routing problem:

graph nodes are routers

ra h ed es are h sicalCB

2 53

links links have properties: delay, ED

21

3 12

9

capac y, cos , po cy



Optimality

(for user/provider)

Sim licit

10



- Robustness- Optimality

- mp c y

Assume eac in as a atency unction e x :

latency of link e when x amount of trafficgoes t roug e, e.g., prop. + 1/( –x), where prop. is link

propagation delay and the link capacity

Objective: min e xe • le(xe)l(x) = x

s ttotal demand = 1

11

l(x) = 1



- Robustness- Optimality - mp c y

ou ng as a arge es gn space

who decides routing? • ource rou ng en o ma e ec on• network routing: networks make decision

h h i i

• multi-path routing• single path routing

wi routing a apt to networ tra ic eman

• adaptive routing•

…

12



Routing Design Space:


- , , - mp c y


who decides routing? ource rou ng en o ma e ec on• network routing: networks make decision

h h i imulti-path routing• single path routing

wi routing a apt to networ tra ic eman

adaptive routing•

…

13



, ,

:(selfish routing)

14

Braess’s paradox



For a networ wit inear atency unctions

total latency of user (selfish) routing foriven traffic demand

≤ 4/3

total latenc o network o ti al routinfor the traffic demand

15



For any networ wit continuous, non-

decreasing latency functions

total latency of user (selfish) routing

or given tra ic eman

≤

tota atency o networ optima routingfor twice traffic demand

16




Routing Design Space:

- mp c y


who decides routing? • ource rou ng en o ma e ec onnetwork routing: networks make decision

- (applications such as overlay and p2p are trying to bypass it)

how many paths from source s to destination d?• multi-path routing

s ng e pa rou ng w sma amoun o mu pa

will routing adapt to network traffic demand?•static routing (mostly static; adjust in larger timescale)

…

17



network links, the path from a source

protocol is a shortest path among all

t e stat c n costs may e a uste n a

longer time scale: this is called traffic

19



Networ overview

Control lane: routin overview Distance vector protocols

20



Distance Vector Routin

, ,protocols

-algorithm (BFA)

,destination separately



Distance Vector Routin : Basic Idea

At node i the basic u date rule

min d d d

estination

- di denotes the distance

estimation from i to thedestination,

- N(i) is set of neighbors of

jid

ijd no e , an

- dij is the distance of i jd

22

assume positive



Networ overview


23



-CB7 1

Nodes update in rounds:

A

E D810 2

there is a global clock;

at the beginning of each round, each node sendsits estimate to all of its neighbors;

at the end of the round, updates its estimation

))((min)1( )( hd d hd jiji N ji ?)0(d

E

24

CD



Networ overview


- SBF/

25



CB7 1

A

E D810 2

Initia ization time 0 :

desti0

otherwisei

26



CB71

A

E D810 2

Consider D as destination; d(t) is a vector consisting of

A B C E D

es ma on o eac no e a roun

d(0) 0

d 1

d(2) 12 3 2 2 0

d(3) 10 3 2 2 0

d(4) 10 3 2 2 0

27

Observation: d(0) d(1) d(2) d(3) d(4) =d*

))((min)1( )( hd d hd jijiNji



))(()( )( jiji N ji

Consi er two con igurations t an ’ t

If d(t) d’(t) i.e., each node has a hi her estimate in one

scenario (d) than in another scenario (d’),

then d(t+1) d’(t+1) i.e. each node has a hi her esti ate in d than in d’

after one round of synchronous update.

28




))(()( )( jiji N ji

:shortest path from i to the destination

≤

a e ca e r v a y rue

a u e rue or ,i.e., Li(h)= di(h), Li(h-1)= di(h-1), …

29




))(()( )( jiji N ji

≤ + :

)1(h L )))((min),(min( h Ld h L minmin hd d hd

1min hd hd

since di(h)≤di(h-1)

)())1((min))((min)1( )()( hd hd d hd d hd i jiji N j jiji N ji

30

)1()1( hd h L ii

B ll E i



Bellman E uation

Bellman equations (BE):

)(min )( jiji N ji d d d

where dD = 0.

- SBF/ solves the equations in a

distributed wa- Does the equation have a unique

31

o u on .e., e or e a one

)(min )( jijiNji ddd




Assume anot er so ution , we wi s ow t at

d = d*case 1: we show d d*

,paths as follows: for each i, pick a j which

,

23

1Dest.A

7

8 210

32

11E D22

)(min )( jijiNji ddd




Case 2: we s ow ≤

assume we run SBF with two initiali i :

one is d ,

-> monotonicit and conver ence of SBF/ im lthat d ≤ d*

33



Networ overview


- SBF/- SBF/-1

34

SBF at another CB 1



SBF at another CB7 1

a o gura o - A

E D

810

2

Initialization (time 0):

desti0

otherwise1i

35

CB 1



CB 1

A

E D

810

2

Consider D as destination

A B C E D

d(0) -1 -1 -1 -1 0d(1) 6 0 0 2 0

d(3) 8 2 2 2 0

d(4) 9 3 3 2 0

d(5) 10 3 3 2 0

d(6) 10 3 3 2 0

36

Observation: d(0) d(1) d(2) d(3) d(4) d(5) = d(6) = d*

Bellman Equation and ))((min)1( )( hd d hd jiji N ji



q -

-1 i i

At equilibrium, SBF/-1 satisfies the set of equations

called Bellman e uations BE


where dD = 0.

Another solution is shortest path solution d*

thus SBF/-1 converges to shortest path

-

37

Problems of running synchronous BF?



Networ overview


asynchronous Bellman-Ford (ABF)

38



-

No notion o g o a iterations

each node updates at its own paceAsynchronously each node i computes

usin last received value di from nei hbor .m n )( jiji N ji

its neighbor i:

packets (no worry for out of order)



-

In genera , no es are using i erent an

possibly inconsistent estimates

j d j

i j

CB 1



CB 1

A

810

2Below is just one step! The protocol repeats forever!

2distance tables

from neighborscomputation E’s

distance distance

table E sends

A

Eta e

to its neighbors

10 15

0 7

A: 10

B

B: 87 0 B: 817 8

C C: 4 1 2 D: 4 9 4

D D: 2 0 D: 2 2

E: 010 8 2



-

ABF wi eventua y converge to t e s ortest

path links can go down and come up – but if topology isstabilized after some time t, ABF will eventuallyconverge o e s or es pa

t e networ s connecte , t en

converges in finite amount of time, ifcon t ons are met



T ere are too many i erent “runs” o ABF,

so need to use monotonicity

i :

• SBF/; call the sequence U()• SBF/-1; call the sequence L()



j

i

where can distance estimate from node j appear?



distance estimates

:

dj

- d j: currentdistance estimate

di j di j at node j- di j: last d j that

- di

j: those d

jthat

to neighbor i



Consi er t e time w en t e topo ogy isstabilized as time 0

i

at time 0 on all corresponding elements ofstates L j (0) ≤ d j ≤ U j (0) for all d j state at node j

≤ i ≤

L j (0) ≤ update messages di j ≤ U j (0)



j

after at least oneup ate at no e j:d j falls between dj

j j j

did

i j di j

j :

eventually all di j thatare on y oun e y

L j (0) and U j (0) are

L j(1) and U j(1)



-

communicates its routing table to-

Iterative: continues periodically or

when link changes, e.g. detects a linkfailureAsynchronous: nodes need not

Convergence in finite steps,

network is connected



-

Goo news propagate ast



-

This is called the counting-to-infinity

problemQuestion: why does counting-to-infinity happen?



Backup Slides

51

Using Virtual Circuit to Implement



e wor erv ces

n or er o prov e some unc ona es, anetwork may choose virtual circuit, e.g., Virtual

Private Network VPN

52

Using Datagram to Implement the



os as c e wor erv ce

A datagram network generally provides simpleservices: the forwarding of packets from src to

dest. We will focus on datagram networks which provide

best effort service

53

the multimedia networking part of the course

network routing dv

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