announcement r project 2 due next week! r homework 3 available soon, will put it online r recitation...
Post on 22-Dec-2015
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Announcement
Project 2 due next week! Homework 3 available soon, will put it
online Recitation tomorrow on Minet and project
2
Outline
Introduction and Network Service Models
Routing Principles Link State Algorithm Distance Vector Algorithm
Network layer functions
transport packet from sending to receiving hosts
network layer protocols in every host, router
three important functions: path determination: route
taken by packets from source to dest. Routing algorithms
forwarding: move packets from router’s input to appropriate router output
call setup: some network architectures require router call setup along path before data flows
networkdata linkphysical
networkdata linkphysical
networkdata linkphysical
networkdata linkphysical
networkdata linkphysical
networkdata linkphysical
networkdata linkphysical
networkdata linkphysical
application
transportnetworkdata linkphysical
application
transportnetworkdata linkphysical
Virtual circuits
call setup, teardown for each call before data can flow
each packet carries VC identifier (not destination host ID)
every router on source-dest path maintains “state” for each passing connection
“source-to-dest path behaves much like telephone circuit” performance-wise network actions along source-to-dest path
Virtual circuits: signaling protocols
used to setup, maintain teardown VC used in ATM, frame-relay, X.25 not used in today’s Internet
application
transportnetworkdata linkphysical
application
transportnetworkdata linkphysical
1. Initiate call 2. incoming call
3. Accept call4. Call connected5. Data flow begins 6. Receive data
Datagram networks: the Internet model no call setup at network layer routers: no state about end-to-end connections
no network-level concept of “connection”
packets forwarded using destination host address packets between same source-dest pair may take
different paths
application
transportnetworkdata linkphysical
application
transportnetworkdata linkphysical
1. Send data 2. Receive data
Datagram or VC network: why?
Internet data exchange among
computers “elastic” service, no
strict timing req. “smart” end systems
(computers) can adapt, perform
control, error recovery simple inside network,
complexity at “edge” many link types
different characteristics uniform service difficult
ATM evolved from telephony human conversation:
strict timing, reliability requirements
“dumb” end systems telephones complexity inside
network
Outline
Introduction and Network Service Models
Routing Principles Link State Algorithm Distance Vector Algorithm
Router Architecture Overview
Two key router functions: run routing algorithms/protocol (RIP, OSPF, BGP) forwarding datagrams from incoming to outgoing link
u
yx
wv
z2
2
13
1
1
2
53
5
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) }
Graph abstraction
Remark: Graph abstraction is useful in other network contexts
Example: P2P, where N is set of peers and E is set of TCP connections
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)
Question: What’s the least-cost path between u and z ?
Routing algorithm: algorithm that finds least-cost path
Routing Algorithm classification
Global or decentralized information?
Global: all routers have complete
topology, link cost info “link state” algorithmsDecentralized: router knows physically-
connected neighbors, link costs to neighbors
iterative process of computation, exchange of info with neighbors
“distance vector” algorithms
Static or dynamic?Static: routes change slowly
over timeDynamic: routes change more
quickly periodic update in response to link
cost changes
A Link-State Routing Algorithm
Dijkstra’s algorithm net topology, link costs
known to all nodes accomplished via “link
state broadcast” all nodes have same
info computes least cost paths
from one node (‘source”) to all other nodes gives routing table for
that node iterative: after k iterations,
know least cost path to k dest.’s
Notation: c(i,j): link cost from node
i to j. cost infinite 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, that is next v
N: set of nodes whose least cost path definitively known
Dijsktra’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'
Dijkstra’s algorithm: example
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
u
yx
wv
z2
2
13
1
1
2
53
5
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:
Dijkstra’s algorithm, discussionAlgorithm complexity: n nodes each iteration: need to check all nodes, w, not in N n*(n+1)/2 comparisons: O(n^2) more efficient implementations possible: O(nlogn)
Oscillations possible: e.g., link cost = amount of carried traffic
A
D
C
B1 1+e
e0
e
1 1
0 0
initially
A
D
C
B2+e 0
001+e1
… recomputerouting
A
D
C
B0 2+e
1+e10 0
… recompute
A
D
C
B2+e 0
e01+e1
… recompute
Distance Vector Algorithm
Bellman-Ford Equation (dynamic programming)
Definedx(y) := cost of least-cost path from x to y
Then
dx(y) = min {c(x,v) + dv(y) }
where min is taken over all neighbors v of x
v
Bellman-Ford example
u
yx
wv
z2
2
13
1
1
2
53
5Clearly, 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 ➜ forwarding table
B-F equation says:
Distance Vector Algorithm
Dx(y) = estimate of least cost from x to y
Distance vector: Dx = [Dx(y): y є N ] Node x knows cost to each neighbor v:
c(x,v) Node x maintains Dx = [Dx(y): y є N ] Node x also maintains its neighbors’
distance vectors For each neighbor v, x maintains
Dv = [Dv(y): y є N ]
Distance vector algorithm
Basic idea: Each node periodically sends its own distance
vector estimate to neighbors When a node x receives new DV estimate from
neighbor, it updates its own DV using B-F equation:
Dx(y) ← minv{c(x,v) + Dv(y)} for each node y ∊ N
Under minor, natural conditions, the estimate Dx(y) converge to the actual least cost dx(y)
Distance Vector Algorithm
Iterative, asynchronous: each local iteration caused by:
local link cost change DV update message from
neighbor
Distributed: each node notifies
neighbors only when its DV changes neighbors then notify
their neighbors if necessary
wait for (change in local link cost of msg from neighbor)
recompute estimates
if DV to any dest has
changed, notify neighbors
Each node:
x y z
xyz
0 2 7
∞ ∞ ∞∞ ∞ ∞
from
cost to
from
from
x y z
xyz
∞ ∞
∞ ∞ ∞
cost to
x y z
xyz
∞ ∞ ∞7 1 0
cost to
∞2 0 1
∞ ∞ ∞
x y z
xyz
0 2 3
from
cost to
x y z
xyz
0 2 3
from
cost to
x y z
xyz
0 2 3
from
cost to
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
Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)} = min{2+0 , 7+1} = 2
x y z
xyz
0 2 3
from
cost to
x y z
xyz
0 2 7
from
cost to
x y z
xyz
0 2 7
from
cost to
2 0 17 1 0
2 0 17 1 0
2 0 13 1 0
Dx(z) = min{c(x,y) + Dy(z), c(x,z) + Dz(z)} = min{2+1 , 7+0} = 3
Distance Vector: link cost changes
Link cost changes: node detects local link cost
change updates distance table (line 15) if cost change in least cost path,
notify neighbors (lines 23,24)
X Z14
50
Y1
algorithmterminates“good
news travelsfast”
Distance Vector: link cost changes
Link cost changes: good news travels fast bad news travels slow -
“count to infinity” problem! X Z14
50
Y60
algorithmcontinues
on!
Distance Vector: poisoned reverse
If Z routes through Y to get to X : Z tells Y its (Z’s) distance to X is infinite (so
Y won’t route to X via Z) will this completely solve count to infinity
problem? X Z
14
50
Y60
algorithmterminates
Comparison of LS and DV algorithms
Message complexity LS: with n nodes, E links,
O(nE) msgs sent each 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 thru
network
Distance Table: example
A
E D
CB7
8
1
2
1
2
D ()
A
B
C
D
A
1
7
6
4
B
14
8
9
11
D
5
5
4
2
Ecost to destination via
dest
inat
ion
D (C,D)E
c(E,D) + min {D (C,w)}D
w== 2+2 = 4
D (A,D)E
c(E,D) + min {D (A,w)}D
w== 2+3 = 5
D (A,B)E
c(E,B) + min {D (A,w)}B
w== 8+6 = 14
loop!
loop!
Distance table gives routing table
D ()
A
B
C
D
A
1
7
6
4
B
14
8
9
11
D
5
5
4
2
Ecost to destination via
dest
inat
ion
A
B
C
D
A,1
D,5
D,4
D,2
Outgoing link to use, cost
dest
inat
ion
Distance table Routing table
Distance Vector Algorithm:
1 Initialization: 2 for all adjacent nodes v: 3 D (*,v) = infinity /* the * operator means "for all rows" */ 4 D (v,v) = c(X,v) 5 for all destinations, y 6 send min D (y,w) to each neighbor /* w over all X's neighbors */
XX
Xw
At all nodes, X:
Distance Vector Algorithm (cont.):8 loop 9 wait (until I see a link cost change to neighbor V 10 or until I receive update from neighbor V) 11 12 if (c(X,V) changes by d) 13 /* change cost to all dest's via neighbor v by d */ 14 /* note: d could be positive or negative */ 15 for all destinations y: D (y,V) = D (y,V) + d 16 17 else if (update received from V wrt destination Y) 18 /* shortest path from V to some Y has changed */ 19 /* V has sent a new value for its min DV(Y,w) */ 20 /* call this received new value is "newval" */ 21 for the single destination y: D (Y,V) = c(X,V) + newval 22 23 if we have a new min D (Y,w)for any destination Y 24 send new value of min D (Y,w) to all neighbors 25 26 forever
w
XX
XX
X
w
w