network routing dv
TRANSCRIPT
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Network and Network Routing
October 28 2009
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Networ overview
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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
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destination
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routing and callsetup
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guaranteed bandwidth?
- loss-free delivery?
in-order deliver ?
Interaction between users and network
signaling: congestion feedback/resource reservation
efficiency
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scalability
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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
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ATM: Asynchronous Transfer Mode; CBR: Constant Bit Rate; V: Variable; A: available; U: User
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:
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
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physical layer
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Networ overview
Control lane: routin overview
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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
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links links have properties: delay, ED
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3 12
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capac y, cos , po cy
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Optimality
(for user/provider)
Sim licit
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- 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
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l(x) = 1
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- 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•
…
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Routing Design Space:
- 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 imulti-path routing• single path routing
wi routing a apt to networ tra ic eman
adaptive routing•
…
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, ,
:(selfish routing)
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Braess’s paradox
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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
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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
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- Robustness- Optimality
Routing Design Space:
- mp c y
ou ng as a arge es gn space
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)
…
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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
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Networ overview
Control lane: routin overview Distance vector protocols
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Distance Vector Routin
, ,protocols
-algorithm (BFA)
,destination separately
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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
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assume positive
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Networ overview
Control lane: routin overview Distance vector protocols
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-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
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CD
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Networ overview
Control lane: routin overview Distance vector protocols
- SBF/
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CB7 1
A
E D810 2
Initia ization time 0 :
desti0
otherwisei
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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
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Observation: d(0) d(1) d(2) d(3) d(4) =d*
))((min)1( )( hd d hd jijiNji
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))(()( )( 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.
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))((min)1( )( hd d hd jijiNji
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))(()( )( 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), …
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))((min)1( )( hd d hd jijiNji
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))(()( )( 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
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)1()1( hd h L ii
B ll E i
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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
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o u on .e., e or e a one
)(min )( jijiNji ddd
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)(min )( jiji N ji d d d
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
,
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1Dest.A
7
8 210
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11E D22
)(min )( jijiNji ddd
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)(min )( jiji N ji d d d
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*
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Networ overview
Control lane: routin overview Distance vector protocols
- SBF/- SBF/-1
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SBF at another CB 1
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SBF at another CB7 1
a o gura o - A
E D
810
2
Initialization (time 0):
desti0
otherwise1i
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CB 1
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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
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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
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q -
-1 i i
At equilibrium, SBF/-1 satisfies the set of equations
called Bellman e uations BE
)(min )( jiji N ji d d d
where dD = 0.
Another solution is shortest path solution d*
thus SBF/-1 converges to shortest path
-
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Problems of running synchronous BF?
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Networ overview
Control lane: routin overview Distance vector protocols
asynchronous Bellman-Ford (ABF)
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-
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)
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-
In genera , no es are using i erent an
possibly inconsistent estimates
j d j
i j
CB 1
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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
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-
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
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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()
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j
i
where can distance estimate from node j appear?
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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
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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)
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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)
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-
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
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Goo news propagate ast
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This is called the counting-to-infinity
problemQuestion: why does counting-to-infinity happen?
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Backup Slides
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Using Virtual Circuit to Implement
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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
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Using Datagram to Implement the
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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
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the multimedia networking part of the course