Lecture 7 Overview

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Lecture 7 Overview
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Two Key Network-Layer Functions

• forwarding move packets from routers input to
  appropriate router output
• routing determine route taken by packets from
  source to dest.
• routing algorithms
• Analogy
• routing process of planning trip from source to
  destination
• forwarding process of getting through single
  interchange

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routing and forwarding
value in arriving packets header
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Connection setup

• 3rd important function in some architectures
• ATM, frame relay, X.25
• before datagrams flow, two end hosts and
  intervening routers establish virtual connection
• routers get involved
• network vs transport layer connection service
• network between two hosts
• may also involve intervening routers in case of
  VCs
• transport between two processes

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Network layer service models
Guarantees ?
Network Architecture Internet ATM ATM ATM ATM
Service Model best effort BR VBR ABR UBR
Congestion feedback no (inferred via
loss) no congestion no congestion yes no
Bandwidth none constant rate guaranteed rate gua
ranteed minimum none
Loss no yes yes no no
Order no yes yes yes yes
Timing no yes yes no no
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Virtual Circuit Implementation

• A Virtual Circuit consists of
• path from source to destination
• VC numbers
• one number for each link along path
• entries in forwarding tables in routers along
  path
• Each packet carries VC identifier
• VC number can be changed on each link
• Every router on source-dest path maintains
  state for each passing connection

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Forwarding table
VC number
22
32
12
3
1
2
interface number
Forwarding table in northwest router
Routers maintain connection state information!
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Virtual circuits signaling protocols

• used to setup, maintain teardown VC
• used in ATM, frame-relay, X.25
• not used in todays Internet

6. Receive data
5. Data flow begins
4. Call connected
3. Accept call
1. Initiate call
2. incoming call
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Datagram networks

• 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 src-dst pair may take
  different paths

1. Send data
2. Receive data
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Forwarding table
4 billion possible entries
Destination Address Range
Link
Interface 11001000 00010111 00010000
00000000
through
0 11001000
00010111 00010111 11111111 11001000
00010111 00011000 00000000
through
1
11001000 00010111 00011000 11111111
11001000 00010111 00011001 00000000
through

2 11001000 00010111 00011111 11111111
otherwise

3
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Longest prefix matching
Prefix Match
Link Interface
11001000 00010111 00010
0 11001000 00010111
00011000 1
11001000 00010111 00011
2
otherwise
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Examples
Interface 0
DA 11001000 00010111 00010110 10100001
DA 11001000 00010111 00011000 10101010
Interface 1
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Datagram or VC network why?

• Internet (datagram)
• data exchange among computers
• elastic service, no strict timing requirement
• smart end systems (computers)
• can adapt, perform control, error recovery
• simple inside network, complexity at edge
• many link types
• different characteristics
• uniform service difficult

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Datagram or VC network why?

• ATM (VC)
• evolved from telephony
• human conversation
• strict timing, reliability requirements
• need for guaranteed service
• dumb end systems
• telephones
• complexity inside network

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Lecture 8Routing Algorithms

• CPE 401 / 601
• Computer Network Systems

slides are modified from Dave Hollinger
slides are modified from J. Kurose K. Ross
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Graph abstraction
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 is useful in other network
contexts Example P2P, where N is set of peers
and E is set of TCP connections
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Graph abstraction costs

• 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 Whats the least-cost path between u
and z ?
Routing algorithm algorithm that finds
least-cost path
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Routing Algorithm classification

• Global or decentralized information?
• Global link state algorithms
• all routers have complete topology,
• link cost info
• Decentralized distance vector algorithms
• router knows physically-connected neighbors
• link costs to neighbors
• iterative process of computation,
• exchange of info with neighbors

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Routing Algorithm classification

• Static or dynamic?
• Static
• routes change slowly over time
• Dynamic
• routes change more quickly
• periodic update
• in response to link cost changes

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Dijkstras Algorithm
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Dijkstras algorithm

• A Link-State Routing Algorithm
• Topology, link costs known to all nodes
• accomplished via link state broadcast
• all nodes have same info
• Compute least cost paths from source node to all
  other nodes
• produces forwarding table for that node
• Iterative
• after k iterations, know least cost path to k
  dests

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Dijkstras Algorithm

• Notation
• c(x,y) link cost from node x to y
• 8 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
• N' set of nodes whose least cost path
  definitively known

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Dijsktras 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) 8
• 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

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Dijkstras algorithm example
D(v),p(v) 2,u 2,u 2,u
D(x),p(x) 1,u
Step 0 1 2 3 4 5
D(w),p(w) 5,u 4,x 3,y 3,y
D(y),p(y) 8 2,x
N' u ux uxy uxyv uxyvw uxyvwz
D(z),p(z) 8 8 4,y 4,y 4,y
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Dijkstras algorithm example
Resulting shortest-path tree from u
Resulting forwarding table in u
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Dijkstras algorithm, discussion

• Algorithm complexity
• n nodes
• each iteration need to check all nodes, w, not
  in N
• n(n1)/2 comparisons O(n2)
• more efficient implementations possible O(nlogn)

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Dijkstras algorithm, discussion

• Oscillations possible
• e.g., link cost amount of carried traffic

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Distance Vector Algorithm
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Distance Vector Algorithm

• Bellman-Ford Equation
• dynamic programming
• Define
• dx(y) cost of least-cost path from x to y
• Then
• dx (y) minv c(x,v) dv(y)
• where min is taken over all neighbors v of x

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Bellman-Ford example
Clearly, dv(z) 5, dx(z) 3, dw(z) 3
B-F equation says
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 next hop in
shortest path ? forwarding table
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Distance Vector Algorithm

• Dx (y) estimate of least cost from x to y
• Node x knows cost to each neighbor v c(x,v)
• Node x maintains distance vector
• Dx Dx (y) y ? N
• Node x also maintains its neighbors distance
  vectors
• For each neighbor v, x maintains Dv Dv(y) y ?
  N

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Distance vector algorithm

• Basic idea
• From time-to-time, each node sends its own
  distance vector estimate to neighbors
• Asynchronous
• When a node x receives new DV estimate from
  neighbor, it updates its own DV using B-F
• Under minor, natural conditions, the estimate
  Dx(y) converge to the actual least cost dx(y)

Dx(y) ? minvc(x,v) Dv(y) for each node y ?
N
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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

Each node
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Dx(z) minc(x,y) Dy(z), c(x,z)
Dz(z) min21 , 70 3
Dx(y) minc(x,y) Dy(y), c(x,z) Dz(y)
min20 , 71 2
node x table
cost to
x y z
x
0
3
2
y
from
2 0 1
z
7 1 0
node y table
cost to
x y z
x
8
8
8 2 0 1
y
from
z
8
8
8
node z table
cost to
x y z
x
8 8 8
y
from
8
8
8
z
7
1
0
time
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Dx(z) minc(x,y) Dy(z), c(x,z)
Dz(z) min21 , 70 3
Dx(y) minc(x,y) Dy(y), c(x,z) Dz(y)
min20 , 71 2
node x table
cost to
cost to
x y z
x y z
x
0 2 3
x
0 2 3
y
from
2 0 1
y
from
2 0 1
z
7 1 0
z
3 1 0
node y table
cost to
cost to
cost to
x y z
x y z
x y z
x
8
8
x
0 2 7
x
0 2 3
8 2 0 1
y
y
from
y
2 0 1
from
from
2 0 1
z
z
8
8
8
z
7 1 0
3 1 0
node z table
cost to
cost to
cost to
x y z
x y z
x y z
x
0 2 3
x
0 2 7
x
8 8 8
y
y
2 0 1
from
from
y
2 0 1
from
8
8
8
z
z
z
3 1 0
3 1 0
7
1
0
time
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Link cost changes

• Link cost changes
• node detects local link cost change
• updates routing info, recalculates distance
  vector
• if DV changes, notify neighbors

At time t0, y detects the link-cost change,
updates its DV, and informs its neighbors.
good news travels fast
At time t1, z receives the update from y and
updates its table. It computes a new least cost
to x and sends its neighbors its DV.
At time t2, y receives zs update and updates its
distance table. ys least costs do not change
and hence y does not send any message to z.
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Link cost changes

• Link cost changes
• good news travels fast
• bad news travels slow
• count to infinity problem!
• 44 iterations before algorithm stabilizes
• 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 count to infinity
  problem?

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LS vs DV

• Message complexity
• LS with n nodes, E links, O(nE) msgs sent
• DV exchange between neighbors only
• 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

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LS vs DV

• 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 nodes table used by others
• error propagate thru network