Transcript routing principles & algorithms

Announcement #1
 Did you all receive homework #1 and #2?
 Homework #3 will be available online during
the day
 Midterm
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Announcement #2
 CS395/495 Advanced Networking
 “Let’s bring down the Internet together!”
 Classes
 Analyzing some classical and novel networking
papers
• You read the paper and provide a review before the
class
• Two teams give opposite presentation in-favor and
against the paper (20 minutes each)
• Two teams argue about the paper (20 minutes)
• The whole class discusses the paper (20 minutes)
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CS395/495 Advanced Networking
 Projects
I will provide you with initial suggestions
 You are free to come up with your own idea for
the project
 We will submit the best paper to a conference

 Goals
 To help you learn how to do networking (or more
broadly systems) research
 To help you learn how to argue and convey your
ideas
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Network Layer
 Introduction
 Virtual circuit and datagram networks
 Routing algorithms
 Link state
 Distance vector
 Hierarchical routing
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Network layer
 transport segment from




sending to receiving host
on sending side
encapsulates segments
into datagrams
on rcving side, delivers
segments to transport
layer
network layer protocols
in every host, router
Router examines header
fields in all IP datagrams
passing through it
application
transport
network
data link
physical
network
data link
physical
network
data link
physical
network
data link
physical
network
data link
physical
network
data link
physical
network
data link
physical
network
data link
physical
network
data link
physical
application
transport
network
data link
physical
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Key Network-Layer Functions
 forwarding: move
packets from router’s
input to appropriate
router output
 routing: determine
route taken by
packets from source
to dest.

analogy:
 routing: process of
planning trip from
source to dest
 forwarding: process
of getting through
single interchange
Routing algorithms
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Interplay between routing and forwarding
routing algorithm
local forwarding table
header value output link
0100
0101
0111
1001
3
2
2
1
value in arriving
packet’s header
0111
1
3 2
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Network Layer
 Introduction
 Virtual circuit and datagram networks
 Routing algorithms
 Link state
 Distance vector
 Hierarchical routing
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Network layer connection and
connection-less service
 Datagram network provides network-layer
connectionless service
 VC network provides network-layer
connection service
 Analogous to the transport-layer services,
but:
Service: host-to-host
 No choice: network provides one or the other
 Implementation: in the core

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Virtual circuits
“source-to-dest path behaves much like telephone
circuit”


performance-wise
network actions along source-to-dest path
 call setup, teardown for each call before data can flow
 each packet carries VC identifier (not destination host
address)
 every router on source-dest path maintains “state” for
each passing connection
 link, router resources (bandwidth, buffers) may be
allocated to VC
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VC implementation
A VC consists of:
1.
2.
3.
Path from source to destination
VC numbers, one number for each link along
path
Entries in forwarding tables in routers along
path
 Packet belonging to VC carries a VC
number.
 VC number must be changed on each link.

New VC number comes from forwarding table
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Forwarding table
VC number
22
12
1
Forwarding table in
northwest router:
Incoming interface
1
2
3
1
…
2
32
3
interface
number
Incoming VC #
12
63
7
97
…
Outgoing interface
3
1
2
3
…
Outgoing VC #
22
18
17
87
…
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 today’s Internet
application
transport 5. Data flow begins
network 4. Call connected
data link 1. Initiate call
physical
6. Receive data application
3. Accept call
2. incoming call
transport
network
data link
physical
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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 source-dest pair may take
different paths
application
transport
network
data link 1. Send data
physical
application
transport
network
2. Receive data
data link
physical
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Datagram vs. VC
 Which of the above introduces larger
signaling load?

VC
• each time a new connection arrives – a new VC has to
be set
• Each time a connection is closed – the state has to be
changed in each router along the path

Datagram
• No changes in routing tables are made because of
flow arrivals/departures
• Changes are made on much longer time-scales (e.g.,
hours, days)
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Forwarding table
Destination Address Range
4 billion
possible entries
Link Interface
11001000 00010111 00010000 00000000
through
11001000 00010111 00010111 11111111
0
11001000 00010111 00011000 00000000
through
11001000 00010111 00011000 11111111
1
11001000 00010111 00011001 00000000
through
11001000 00010111 00011111 11111111
2
otherwise
3
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Longest prefix matching
Prefix Match
11001000 00010111 00010
11001000 00010111 00011000
11001000 00010111 00011
otherwise
Link Interface
0
1
2
3
Examples
DA: 11001000 00010111 00010110 10100001
Which interface?
DA: 11001000 00010111 00011000 10101010
Which interface?
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Datagram or VC network: why?
Internet
 data exchange among
ATM
 evolved from telephony
computers
 human conversation:
 “elastic” service, no strict
 strict timing, reliability
timing req.
requirements
 “smart” end systems
 need for guaranteed
(computers)
service
 can adapt, perform
 “dumb” end systems
control, error recovery
 telephones
 simple inside network,
 complexity inside
complexity at “edge”
network
 many link types
 different characteristics
 uniform service difficult
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Network Layer
 Introduction
 Virtual circuit and datagram networks
 Routing algorithms
 Link state
 Distance vector
 Hierarchical routing
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Interplay between routing and
forwarding
routing algorithm
local forwarding table
header value output link
0100
0101
0111
1001
3
2
2
1
value in arriving
packet’s header
0111
1
3 2
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Graph abstraction
5
2
u
2
1
Graph: G = (N,E)
v
x
3
w
3
1
5
1
y
z
2
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) }
Remark: 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
5
2
u
v
2
1
x
• c(x,x’) = cost of link (x,x’)
3
w
3
1
5
1
y
2
- e.g., c(w,z) = 5
z
• 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
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Routing Algorithm classification
Global or decentralized
information?
Global:
 all routers have complete
topology, link cost info
 “link state” algorithms
Decentralized:
 router knows physicallyconnected 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 time
Dynamic:
 routes change more
quickly
 periodic update
 in response to link
cost changes
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Network Layer
 Introduction
 Virtual circuit and datagram networks
 Routing algorithms
 Link state
 Distance vector
 Hierarchical routing
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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 forwarding table
for that node
 iterative: after k
iterations, know least cost
path to k dest.’s
Notation:
 c(x,y): link cost from node
x to y; = ∞ 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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Dijsktra’s Algorithm
1 Initialization:
2 N' = {u}
3 for all nodes v
4
if v adjacent to u
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then D(v) = c(u,v)
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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' :
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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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Dijkstra’s algorithm: example
Step
0
1
2
3
4
5
N'
u
ux
uxy
uxyv
uxyvw
uxyvwz
D(v),p(v) D(w),p(w)
2,u
5,u
2,u
4,x
2,u
3,y
3,y
D(x),p(x)
1,u
D(y),p(y)
∞
2,x
D(z),p(z)
∞
∞
4,y
4,y
4,y
5
2
u
v
2
1
x
3
w
3
1
5
1
y
z
2
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Dijkstra’s algorithm, discussion
Algorithm complexity: n nodes
 each iteration: need to check all nodes, w, not in N
 n(n-1)/2 comparisons: O(n2)
 more efficient implementations possible: O(nlogn)
Oscillations possible:
 e.g., link cost = amount of carried traffic
D
1
1
0
A
0 0
C
e
1+e
B
e
initially
2+e
D
0
1
A
1+e 1
C
0
B
0
… recompute
routing
0
D
1
A
0 0
2+e
B
C 1+e
… recompute
2+e
D
0
A
1+e 1
C
0
B
e
… recompute
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