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Chapter 7
Packet-Switching
Networks
7.1 Network Services and Internal Network
Operation
7.2 Packet Network Topology
7.3 Datagrams and Virtual Circuits
7.4 Routing in Packet Networks
7.5 Shortest Path Routing
ATM Networks
Traffic Management
Chapter 7
Packet-Switching
Networks
7.1 Network Services and
Internal Network Operation
Network Layer
Network layer is the most complex layer
Requires the coordinated actions of multiple,
geographically distributed network elements
(switches & routers)
Must be able to deal with very large scales
Billions of users (people & communicating devices)
Biggest Challenges
Addressing: where should information be directed to?
Routing: what path should be used to get information there?
Packet Switching
t0 t1
Network
Transfer of information as payload in data packets
Packets undergo random delays & possible loss
Different applications impose differing requirements
on the transfer of information
Network Service
Messages
Messages
Transport Segments Transport
layer layer
Network Network
service service
Network Network Network Network
layer layer layer layer
Data link Data link Data link Data link End
End layer layer layer layer
system
system
Physical Physical Physical Physical β
α layer
layer layer layer
Network layer can offer a variety of services to transport layer
Connection-oriented service or connectionless service
Best-effort or delay/loss guarantees
Network Service vs. Operation
Network Service Internal Network Operation
Connectionless Connectionless
Datagram Transfer IP
Connection-Oriented Connection-Oriented
Reliable and possibly Telephone connection
constant bit rate transfer ATM
Various combinations are possible
Connection-oriented service over connectionless operation
Connectionless service over connection-oriented operation
Context & requirements determine what makes sense
Complexity at the Edge or in the Core?
C
12 3 21
End system End system
α β
4 3 21 12 3 21
Medium
12 3 21 123 4
2
A B 1
Network
1 Physical layer entity 3 Network layer entity
Data link layer entity 3 Network layer entity
2 4 Transport layer entity
End-to-End Argument for System Design
An end-to-end function is best implemented at a
higher level than at a lower level
End-to-end service requires all intermediate components to
work properly
Higher-level better positioned to ensure correct operation
Example: stream transfer service
Establishing an explicit connection for each stream across
network requires all network elements (NEs) to be aware of
connection; All NEs have to be involved in re-
establishment of connections in case of network fault
In connectionless network operation, NEs do not deal with
each explicit connection and hence are much simpler in
design
Network Layer Functions
Essential
Routing: mechanisms for determining the set of
best paths for routing packets requires the
collaboration of network elements
Forwarding: transfer of packets from NE inputs to
outputs
Priority & Scheduling: determining order of packet
transmission in each NE
Optional: congestion control, segmentation &
reassembly, security
Chapter 7
Packet-Switching
Networks
7.2 Packet Network Topology
End-to-End Packet Network
Packet networks are very different than telephone
networks
Individual packet streams are highly bursty
Statistical multiplexing is used to concentrate streams
User demand can undergo dramatic change
Peer-to-peer applications stimulated huge growth in traffic
volumes
Internet structure highly decentralized
Paths traversed by packets can go through many networks
controlled by different organizations
No single entity responsible for end-to-end service
Access Multiplexing
Access
MUX
To
packet
network
Packet traffic from users multiplexed at access to
network into aggregated streams
DSL traffic multiplexed at DSL Access Mux (DSLAM)
Cable modem traffic multiplexed at Cable Modem
Termination System
Oversubscription
Access Multiplexer
r N subscribers connected @ c bps to mux
r Each subscriber active with avg trans rate r = r/c of time
Mux has C=nc bps to network
•••
•••
nc Oversubscription ratio: N/n
r
Find n so that at most 1% overflow probability
Nr Nc
Feasible oversubscription rate increases with size N
N r/c n N/n
10 0.01 1 10 10 extremely lightly loaded users
10 0.05 3 3.3 10 very lightly loaded user
10 0.1 4 2.5 10 lightly loaded users
20 0.1 6 3.3 20 lightly loaded users
40 0.1 9 4.4 40 lightly loaded users
100 0.1 18 5.5 100 lightly loaded users
Home LANs
WiFi
Ethernet Home
Router
To
packet
network
Home Router
LAN Access using Ethernet or WiFi (IEEE 802.11)
Private IP addresses in Home (192.168.0.x) using Network
Address Translation (NAT)
Single global IP address from ISP issued using Dynamic
Host Configuration Protocol (DHCP)
LAN Concentration
Switch
/ Router
LAN hubs and switches in the access network also
aggregate packet streams that flows into switches
and routers
Servers have
Campus Network redundant
connectivity to
backbone
Organization
To Internet or Servers
wide area
network
s s
Gateway
Backbone
R R
R
S
S S
Departmental R R
Server R
s
s
s
High-speed
Only outgoing
campus
packets leave s s s s
backbone net s s
LAN through
connects dept
router
routers
Connecting to Internet Service Provider
Internet service provider
Border routers
Campus
Border routers
Network
Inter-domain level
Autonomous
System (AS) or
domain
Intra-domain level
s
LAN network administered
s s
by single organization
Internet Backbone
National Service Provider A
National Service Provider B
NAP
NAP
National Service Provider C Private
peering
Network Access Point (NAP): set up during original
commercialization of Internet to facilitate exchange of traffic
Private Peering Points: two-party inter-ISP agreements to
exchange traffic
Key Role of Routing
How to get packets from here to there?
Decentralized nature of Internet makes
routing a major challenge
Interior gateway protocols (IGPs) are used to
determine routes within a domain
Exterior gateway protocols (EGPs) are used to
determine routes across domains
Routes must be consistent & produce stable flows
POSTECH 캠퍼스 네트워크망 구성도 수정일 : 2005/10/03
남기숙사 #1
남기숙사 #2
Catalyst 3550 낙원아파트 #2
공학1동 남기숙사 #3
Catalyst 2950G
공학2동 낙원아파트 #2 남기숙사 #4
Catalyst 2950G 남기숙사 #5
Catalyst 3550
낙원아파트 #3
남기숙사 #6
Catalyst 2950G
공학3동
남기숙사 #7
Catalyst 3550 낙원아파트 #4
Catalyst 2950G 남기숙사 #8
공학4동 낙원아파트 #5
남기숙사 #9
Catalyst 3550 Catalyst 2950G
낙원아파트 #6 남기숙사 #10
공학5동
Catalyst 2950G 남기숙사 #41
Catalyst 3550
남기숙사 #12
정보통신연구소 Catalyst 3550G
Catalyst 6506 남기숙사 #13
Catalyst 3550
남기숙사 #14
Catalyst 6513
LG전자연구동 Catalyst 6513 남기숙사 #15
Catalyst 3550
남기숙사 #416
환경공학동 남기숙사 #17
본부동/동편
Catalyst 3550
Campus Core Switch 남기숙사 #18
Catalyst 3550 남기숙사 #19
본부동/서편 남기숙사 #20
Catalyst 3550
여기숙사 #1
인문사회학동
Catalyst 3550 여기숙사 #2
학생회관
여기숙사 #3
Catalyst 3550
철강대학원 대학원APT #1
Catalyst 3550 대학원APT #2
Catalyst 6509
산과원1동 대학원APT #3
Catalyst 2916MXL 대학원APT #4
산과원2동
기숙사 P/P
Catalyst 2916MXL
Catalyst 5500
1 P/P 지곡회관
Catalyst 2924CXL Catalyst 3560
교수아파트 #4
산과원3동
교수아파트 #5
무은재기념관
교수아파트 #6
Catalyst 6509 Catalyst 3550
학술정보관
Catalyst 3550 Catalyst 3550 Catalyst 3550 Catalyst 3550 Catalyst 3550 교수아파트 #7
생명공학연구센터
Catalyst 5500 Catalyst 5500 교수아파트 #8
4 P/P 가속기연구소 교수아파트 #9
Catalyst 2916 Catalyst 6509 Catalyst 2924CXL Catalyst 2924CXL Catalyst 2924CXL
기계실험동 화공실험동 산공실험동 화학관 생명과학관 공작동 풍동동 2 P/P 체육관
POSTECH 인터넷전용회선 망 구성도 수정일 : 2005/08/01
KREONET KORNET BORANET
LX (Singlemode)
RS 38000 RS 3000 SX (Multimode)
계획중
침입방지시스템-IPS
2.5G LX MSPP Switch FDF (NXG IPS2000) FDF
(ONS 15454))
1G LX 1G LX
QoS 장비
(Packetshape QoS 장비
r 8500) 1G SX 1G SX (Packetshaper
8500)
Internet 전용 Router 1G LX 1G LX Internet 전용 Router
(Cisco 7513) (Cisco 7401ASR)
Thin Server
100M Tx
(Linux)
Giga TAP Station
(Monitoring Port)
1G SX 1G SX
Campus Core Switch
(Catalyst 6513) 1G SX
1G SX 1G SX
100M Tx
4G LX
Server Farm Switch
(Catalyst 3550)
1G LX
Building Switch
1G LX 1G LX
(Catalyst 3550T)
공학1동 공학5동 무은재기념관 기계실험동 생명공학연구센터
Chapter 7
Packet-Switching
Networks
Datagrams and Virtual Circuits
The Switching Function
Dynamic interconnection of inputs to outputs
Enables dynamic sharing of transmission resource
Two fundamental approaches:
Connectionless
Connection-oriented: Call setup control, Connection control
Backbone Network
Switch
Access Network
Packet Switching Network
Packet switching network
User Transfers packets
between users
Transmission
line Transmission lines +
packet switches
Network (routers)
Packet
switch Origin in message
switching
Two modes of operation:
Connectionless
Virtual Circuit
Message Switching
Message switching
invented for telegraphy
Message Message Entire messages
Message multiplexed onto shared
Source
lines, stored & forwarded
Message Headers for source &
destination addresses
Routing at message
Switches Destination
switches
Connectionless
Message Switching Delay
Source T
t
Switch 1
t
Switch 2
t
t
Destination
Delay
Minimum delay = 3 + 3T
Additional queueing delays possible at each link
Packet Switching - Datagram
Messages broken into
smaller units (packets)
Source & destination
Packet 1
addresses in packet header
Packet 1
Connectionless, packets
Packet 2
routed independently
(datagram)
Packets may arrive out of Packet 2
order
Packet 2
Lower delay than message
switching, suitable for
interactive traffic
Packet Switching Delay
Assume three packets corresponding to one message
traverse same path
t
1 2 3
t
1 2 3
t
1 2 3
t
Delay
Minimum Delay = 3τ + 5(T/3) (single path assumed)
Additional queueing delays possible at each link
Packet pipelining enables message to arrive sooner
Delay for k-Packet Message over L Hops
Source
t
1 2 3
Switch 1
t
1 2 3
Switch 2
t
1 2 3
t
Destination
3 hops L hops
3 + 2(T/3) first bit received L + (L-1)P first bit received
3 + 3(T/3) first bit released L + LP first bit released
3 + 5 (T/3) last bit released L + LP + (k-1)P last bit released
where T = k P
Routing Tables in Datagram Networks
Destination Output
Route determined by table
address port
lookup
0785 7 Routing decision involves
finding next hop in route to
1345
given destination
12
Routing table has an entry
1566 6 for each destination
specifying output port that
leads to next hop
Size of table becomes
2458 12
impractical for very large
number of destinations
Example: Internet Routing
Internet protocol uses datagram packet
switching across networks
Networks are treated as data links
Hosts have two-part IP address:
Network address + Host address
Routers do table lookup on network address
This reduces size of routing table
In addition, network addresses are assigned so
that they can also be aggregated
Packet Switching – Virtual Circuit
Packet Packet
Packet
Packet
Virtual circuit
Call setup phase sets up pointers in fixed path along network
All packets for a connection follow the same path
Abbreviated header identifies connection on each link
Packets queue for transmission
Variable bit rates possible, negotiated during call set-up
Delays variable, cannot be less than circuit switching
Connection Setup
Connect Connect Connect
request request request
SW SW … SW
1 2 n
Connect Connect Connect
confirm confirm confirm
Signaling messages propagate as route is selected
Signaling messages identify connection and setup tables
in switches
Typically a connection is identified by a local tag, Virtual
Circuit Identifier (VCI)
Each switch only needs to know how to relate an
incoming tag in one input to an outgoing tag in the
corresponding output
Once tables are setup, packets can flow along path
Connection Setup Delay
t
Connect
request
1 2 3
CC
t
Release
CR 1 2 3
CC
t
Connect
CR 1 2 3
confirm
t
Connection setup delay is incurred before any
packet can be transferred
Delay is acceptable for sustained transfer of large
number of packets
This delay may be unacceptably high if only a few
packets are being transferred
Virtual Circuit Forwarding Tables
Input Output Output
VCI port VCI
Each input port of packet switch
12 13 44
has a forwarding table
Lookup entry for VCI of
15 15 23
incoming packet
Determine output port (next hop)
27 13 16 and insert VCI for next link
Very high speeds are possible
Table can also include priority
58 7
or other information about how
34
packet should be treated
Cut-Through Switching
A modified form of virtual-circuit switching
Can be used when retransmissions are not used in the
underlying data link control
Perform error checking on header only, so packet can be
forwarded as soon as header is received & processed
Assumes that all lines are available to transmit the packet
immediately
Desirable for applications such as VoIP, streaming which
has a delay requirement but can tolerate some errors
Appropriate when the transmission is virtually error free,
e.g., optical fiber transmission
Cut-Through Switching
Source
t
1 2 3
Switch 1
t
1 2 3
Switch 2
t
1 2 3
t
Destination
Minimum delay = 3 + T
Delays reduced with cut-through switching
Example: ATM Networks
All information mapped into short fixed-length
packets called cells
Connections set up across network
Virtual circuits established across networks
Tables setup at ATM switches
Several types of network services offered
Constant bit rate (CBR) connections
Variable bit rate (VBR) connections
Chapter 7
Packet-Switching
Networks
Datagrams and Virtual Circuits
Structure of a Packet Switch
Packet Switch: Intersection where
Traffic Flows Meet
•••
1 1
•••
2 2
•••
N N
Inputs contain multiplexed flows from access muxs &
other packet switches
Flows demultiplexed at input, routed and/or forwarded
to output ports
Packets buffered, prioritized, and multiplexed on output
lines
Generic Packet Switch
Ingress Line Cards
Controller Header processing
Demultiplexing
Routing in large switches
Controller
1 Line card Line card 1 Routing in small switches
2 2 Signalling & resource
Interconnection
Line card Line card
3 3
allocation
fabric
Line card Line card
Interconnection Fabric
Transfer packets between
…
…
…
…
line cards
N Line card Line card N Egress Line Cards
Scheduling & priority
Input ports Output ports Multiplexing
Data path
Control path (a)
Line Cards
Transceiver Framer
Network Backplane
processor transceivers
Transceiver Framer
Interconnection
To To To
fabric
physical switch
ports fabric
other
line
cards
Folded View
1 circuit board is ingress/egress line card
Physical layer processing
Data link layer processing
Network header processing
Physical layer across fabric + framing
Shared Memory Packet Switch
Ingress Output
Processing Buffering
Connection
Control
1 1
Queue
2 Control 2
3 3
Shared
…
…
Memory
N N
Small switches can be built by reading/writing into shared memory
Crossbar Switches
(a) Input buffering (b) Output buffering
Inputs Inputs
1 3 1
2 83 2
3 3
…
…
N N
… …
1 2 3 N 1 2 3 N
Outputs Outputs
Large switches built from crossbar & multistage space switches
Requires centralized controller/scheduler (who sends to whom
when)
Can buffer at input, output, or both (performance vs complexity)
Self-Routing Switches
Inputs Outputs
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
Stage 1 Stage 2 Stage 3
Self-routing switches do not require controller
Output port number determines route
101 → (1) lower port, (2) upper port, (3) lower port
Chapter 7
Packet-Switching
Networks
Routing in Packet Networks
Routing in Packet Networks
1 3
6
4
2 Node
5
(switch or router)
Three possible (loopfree) routes from 1 to 6:
1-3-6, 1-4-5-6, 1-2-5-6
Which is “best”?
Min delay? Min hop? Max bandwidth? Min cost?
Max reliability?
Creating the Routing Tables
Need information on state of links
Link up/down; congested; delay or other metrics
Need to distribute link state information using a
routing protocol
What information is exchanged? How often?
Exchange with neighbors – how?
Need to compute routes based on information
Single metric; multiple metrics
Single route; alternate routes
Routing Algorithm Requirements
Responsiveness to changes
Topology or bandwidth changes, congestion
Rapid convergence of routers to consistent set of routes
Freedom from persistent loops
Optimality
Resource utilization, path length
Robustness
Continues working under high load, congestion, faults,
equipment failures, incorrect implementations
Simplicity
Efficient software implementation, reasonable processing
load
Routing in Virtual-Circuit Packet Networks
2
1 7 8
1 3 B
A 3
5 1 6 5
4
2
VCI
Host 4
3 5 Switch or router
2
C 5
6
2 D
Route determined during connection setup
Tables in switches implement forwarding that
realizes selected route
Routing Tables in VC Packet Networks
Node 3
Incoming Outgoing
Node 1 Node VCI Node VCI Node 6
Incoming Outgoing 1 2 6 7 Incoming Outgoing
Node VCI Node VCI 1 3 4 4 Node VCI Node VCI
A 1 3 2 4 2 6 1 3 7 B 8
A 5 3 3 6 7 1 2 3 1 B 5
3 2 A 1 6 1 4 2 B 5 3 1
3 3 A 5 4 4 1 3 B 8 3 7
Node 4
Incoming Outgoing
Node VCI Node VCI
Node 2 2 3 3 2
Node 5
3 4 5 5
Incoming Outgoing 3 2 2 3 Incoming Outgoing
Node VCI Node VCI 5 5 3 4 Node VCI Node VCI
C 6 4 3 4 5 D 2
4 3 C 6 D 2 4 5
Example: VCI from A to D
From A & VCI 5 → 3 & VCI 3 → 4 & VCI 4
→ 5 & VCI 5 → D & VCI 2
Routing Tables in Datagram
Packet Networks
Node 3
Node 1 Destination Next node Node 6
Destination Next node 1 1 Destination Next node
2 4 1 3
2 2
4 4 2 5
3 3
4 4 5 6 3 3
6 6 4 3
5 2
6 3 5 5
Node 4
Destination Next node
1 1
2 2
Node 2 Node 5
3 3
Destination Next node Destination Next node
5 5
1 1 6 3 1 4
3 1 2 2
4 4 3 4
5 5 4 4
6 5 6 6
Non-Hierarchical Addresses and
Routing
0000 0001
0111 0100
1010 1 4 1011
1101 1110
3
R1 R2
2 5
0011 0011
0110 0000 1 0001 4 0101
1001 0111 1 0100 4 1000
1100 1010 1 1011 4 1111
… … … …
No relationship between addresses & routing
proximity
Routing tables require 16 entries each
Hierarchical Addresses and
Routing
0000 0100
0001 0101
0010 1 4 0110
0011 0111
3
R1 R2
2 5
1000 1100
1001 00 1 00 3 1101
1010 01 3 01 4 1110
1011 10 2 10 3 1111
11 3 11 5
Prefix indicates network where host is attached
Routing tables require 4 entries each
Specialized Routing
Flooding
Useful in starting up network
Useful in propagating information to all nodes
Flooding
Send a packet to all nodes in a network
No routing tables available
Need to broadcast packet to all nodes (e.g., to
propagate link state information)
Approach
Send packet on all ports except one where it
arrived
Exponential growth in packet transmissions
1 3
6
4
2
5
Flooding is initiated from Node 1: Hop 1 transmissions
1 3
6
4
2
5
Flooding is initiated from Node 1: Hop 2 transmissions
1 3
6
4
2
5
Flooding is initiated from Node 1: Hop 3 transmissions
Chapter 7
Packet-Switching
Networks
Shortest Path Routing
Shortest Paths & Routing
Many possible paths connect any given source
and to any given destination
Routing involves the selection of the path to be
used to accomplish a given transfer
Typically it is possible to attach a cost or
distance to a link connecting two nodes
Routing can then be posed as a shortest path
problem
Routing Metrics
Means for measuring desirability of a path
Path Length = sum of costs or distances
Possible metrics
Hop count: rough measure of resources used
Reliability: link availability; BER
Delay: sum of delays along path; complex & dynamic
Bandwidth: “available capacity” in a path
Load: Link & router utilization along path
Cost: $$$
Shortest Path Approaches
Distance Vector Protocols
Neighbors exchange list of distances to destinations
Best next-hop determined for each destination
Bellman-Ford (distributed) shortest path algorithm
Link State Protocols
Link state information flooded to all routers
Routers have complete topology information
Shortest path (& hence next hop) calculated
Dijkstra (centralized) shortest path algorithm
Distance Vector
Do you know the way to San Jose?
San Jose 392
San Jose 596
Distance Vector Algorithm
Local Signpost Table Synthesis
Direction Neighbors exchange
Distance table entries
Determine current best
Routing Table next hop
For each destination list: Inform neighbors
Periodically
Next Node
After changes
Distance dest next dist
Shortest Path to SJ
Focus on how nodes find their shortest
path to a given destination node, i.e., SJ San
Jose
Dj
Cij
j
i
Di If Di is the shortest distance to SJ from i
and if j is a neighbor on the shortest path,
then Di = Cij + Dj
But we don’t know the shortest
paths
i only has local info
from neighbors San
Dj' Jose
j'
Cij'
Dj
Cij j
i
Cij” Pick current
Di j"
Dj" shortest path
Why Distance Vector Works SJ sends
accurate info
San
2 Hops
1 Hop
From SJ
Jose
3 Hops From SJ
From SJ
Hop-1 nodes
calculate current
(next hop, dist), &
Accurate info about SJ send to neighbors
ripples across network,
Shortest Path Converges
Bellman-Ford Algorithm
Consider computations for one destination d
Initialization
Each node table has 1 row for destination d
Distance of node d to itself is zero: Dd=0
Distance of other node j to d is infinite: Dj=, for j d
Next hop node nj = -1 to indicate not yet defined for j d
Send Step
Send new distance vector to immediate neighbors across local link
Receive Step
At node j, find the next hop that gives the minimum distance to d,
Minj { Cij + Dj }
Replace old (nj, Dj(d)) by new (nj*, Dj*(d)) if new next node or distance
Go to send step
Bellman-Ford Algorithm
Now consider parallel computations for all destinations d
Initialization
Each node has 1 row for each destination d
Distance of node d to itself is zero: Dd(d)=0
Distance of other node j to d is infinite: Dj(d)= , for j d
Next node nj = -1 since not yet defined
Send Step
Send new distance vector to immediate neighbors across local link
Receive Step
For each destination d, find the next hop that gives the minimum
distance to d,
Minj { Cij+ Dj(d) }
Replace old (nj, Di(d)) by new (nj*, Dj*(d)) if new next node or distance
found
Go to send step
Iteration Node 1 Node 2 Node 3 Node 4 Node 5
Initial (-1, ) (-1, ) (-1, ) (-1, ) (-1, )
1
2
3
Table entry Table entry
@ node 1 @ node 3
for dest SJ for dest SJ
2 3
1 1 San
5 2
4
Jose
3 1 3 6
2
2 5
4
Iteration Node 1 Node 2 Node 3 Node 4 Node 5
Initial (-1, ) (-1, ) (-1, ) (-1, ) (-1, )
1 (-1, ) (-1, ) (6,1) (-1, ) (6,2)
2
3
D3=D6+1
n3=6
D6=0
2 3 1
1 1
5 2
0
4 San
3 6
1 3
Jose
2 5 2
4
2
D5=D6+2 D6=0
n5=6
Iteration Node 1 Node 2 Node 3 Node 4 Node 5
Initial (-1, ) (-1, ) (-1, ) (-1, ) (-1, )
1 (-1, ) (-1, ) (6, 1) (-1, ) (6,2)
2 (3,3) (5,6) (6, 1) (3,3) (6,2)
3
3 1
2 3
1 1
5 2
3 0
4 San
3 6
1 3
Jose
2 2
5
4
6 2
Iteration Node 1 Node 2 Node 3 Node 4 Node 5
Initial (-1, ) (-1, ) (-1, ) (-1, ) (-1, )
1 (-1, ) (-1, ) (6, 1) (-1, ) (6,2)
2 (3,3) (5,6) (6, 1) (3,3) (6,2)
3 (3,3) (4,4) (6, 1) (3,3) (6,2)
1
3 2 3
1 1
5 2
3 0
4 San
3 6
1 3
Jose
2
2 5
4
4 4 2
Iteration Node 1 Node 2 Node 3 Node 4 Node 5
Initial (3,3) (4,4) (6, 1) (3,3) (6,2)
1 (3,3) (4,4) (4, 5) (3,3) (6,2)
2
3
1 5
3 2
3
1 1
5 2
3 0
4 San
3 6
1 3
Jose
2
2 5
4 4
2
Network disconnected; Loop created between nodes 3 and 4
Iteration Node 1 Node 2 Node 3 Node 4 Node 5
Initial (3,3) (4,4) (6, 1) (3,3) (6,2)
1 (3,3) (4,4) (4, 5) (3,3) (6,2)
2 (3,7) (4,4) (4, 5) (5,5) (6,2)
3
5
37 2
3
1 1
5 53 2
0
4 San
3 6
1 3
Jose
2
2 5
4
4 2
Node 4 could have chosen 2 as next node because of tie
Iteration Node 1 Node 2 Node 3 Node 4 Node 5
Initial (3,3) (4,4) (6, 1) (3,3) (6,2)
1 (3,3) (4,4) (4, 5) (3,3) (6,2)
2 (3,7) (4,4) (4, 5) (5,5) (6,2)
3 (3,7) (4,6) (4, 7) (5,5) (6,2)
5 7
7 2 3
1 1
5 2
5 0
4 San
3 6
1 3
Jose
2 5 2
4
46 2
Node 2 could have chosen 5 as next node because of tie
Iteration Node 1 Node 2 Node 3 Node 4 Node 5
1 (3,3) (4,4) (4, 5) (3,3) (6,2)
2 (3,7) (4,4) (4, 5) (2,5) (6,2)
3 (3,7) (4,6) (4, 7) (5,5) (6,2)
4 (2,9) (4,6) (4, 7) (5,5) (6,2)
79 2 7
3
1 1
5 2
5 0
4 San
3 6
1 3
Jose
2
2 5
4
6 2
Node 1 could have chose 3 as next node because of tie
Counting to Infinity Problem
(a) 1 2 3 4
1 1 1 Nodes believe best
path is through each
(b) 1 2 3 X 4 other
1 1
(Destination is node 4)
Update Node 1 Node 2 Node 3
Before break (2,3) (3,2) (4, 1)
After break (2,3) (3,2) (2,3)
1 (2,3) (3,4) (2,3)
2 (2,5) (3,4) (2,5)
3 (2,5) (3,6) (2,5)
4 (2,7) (3,6) (2,7)
5 (2,7) (3,8) (2,7)
… … … …
Problem: Bad News Travels Slowly
Remedies
Split Horizon
Do not report route to a destination to the
neighbor from which route was learned
Poisoned Reverse
Report route to a destination to the neighbor
from which route was learned, but with infinite
distance
Breaks erroneous direct loops immediately
Does not work on some indirect loops
Split Horizon with Poison Reverse
(a) 1 2 3 4
1 1 1 Nodes believe best
path is through
(b) 1 2 3 X 4 each other
1 1
Update Node 1 Node 2 Node 3
Before break (2, 3) (3, 2) (4, 1)
After break (2, 3) (3, 2) (-1, ) Node 2 advertizes its route to 4 to
node 3 as having distance infinity;
node 3 finds there is no route to 4
1 (2, 3) (-1, ) (-1, ) Node 1 advertizes its route to 4 to
node 2 as having distance infinity;
node 2 finds there is no route to 4
2 (-1, ) (-1, ) (-1, ) Node 1 finds there is no route to 4
Link-State Algorithm
Basic idea: two step procedure
Each source node gets a map of all nodes and link metrics
(link state) of the entire network
Find the shortest path on the map from the source node to
all destination nodes
Broadcast of link-state information
Every node i in the network broadcasts to every other node
in the network:
ID’s of its neighbors: Ni=set of neighbors of i
Distances to its neighbors: {Cij | j Ni}
Flooding is a popular method of broadcasting packets
Dijkstra Algorithm: Finding
shortest paths in order
Find shortest paths from Closest node to s is 1 hop away
source s to all other
destinations 2nd closest node to s is 1 hop
away from s or w”
3rd closest node to s is 1 hop
w' away from s, w”, or x
z
w
x
s z'
w"
x'
Dijkstra’s algorithm
N: set of nodes for which shortest path already found
Initialization: (Start with source node s)
N = {s}, Ds = 0, “s is distance zero from itself”
Dj=Csj for all j s, distances of directly-connected neighbors
Step A: (Find next closest node i)
Find i N such that
Di = min Dj for j N
Add i to N
If N contains all the nodes, stop
Step B: (update minimum costs)
For each node j N
Dj = min (Dj, Di+Cij) Minimum distance from s to
Go to Step A j through node i in N
Execution of Dijkstra’s algorithm
2 2
1 3 1 1 3 1
6 6
5 2 5 2
3 3
1 4 1 4 2
2
3 3
2 2
4 5 4 5
Iteration N D2 D3 D4 D5 D6
Initial {1} 3 2 5
1 {1,3} 3 2 4 3
2 {1,2,3} 3 2 4 7 3
3 {1,2,3,6} 3 2 4 5 3
4 {1,2,3,4,6} 3 2 4 5 3
5 {1,2,3,4,5,6} 3 2 4 5 3
Shortest Paths in Dijkstra’s
Algorithm
2 3 1 2 3 1
1 1
6 6
5 2 5 2
3 3
1 4 2 1 4 2
3 3
2 2
4 5 4 5
2 3 1 2 3 1
1 1
6 6
5 2 5 2
3 3
1 4 2 1 4 2
3 3
2 2
4 5 4 5
2 3 1 2 3 1
1 1
6 6
5 2 5 2
3 3
1 4 2 1 4 2
3 3
2 2
4 5 4 5
Reaction to Failure
If a link fails,
Router sets link distance to infinity & floods the network
with an update packet
All routers immediately update their link database &
recalculate their shortest paths
Recovery very quick
But watch out for old update messages
Add time stamp or sequence # to each update message
Check whether each received update message is new
If new, add it to database and broadcast
If older, send update message on arriving link
Why is Link-State Algorithm Better?
Fast, loopless convergence
Support for precise metrics, and multiple
metrics if necessary (throughput, delay, cost,
reliability)
Support for multiple paths to a destination
algorithm can be modified to find best two paths
READING
Read the sections covered in class
