1. EE 122: Review for 1st Midterm
Computer Science Division
Department of Electrical Engineering and Computer Science
University of California, Berkeley,
Berkeley, CA
September 28, 2004

2. Outline Performance Metrics; Router vs. Switch
Layering and End-to-End Arguments
Queueing Theory: Little Theorem and M/M/1 Queue
Routing: Distance Vector and Link State protocol
Router Architecture

3. Definitions
Link bandwidth (capacity): maximum rate (in bps) at which the sender can send data along the link
Propagation delay: time it takes the signal to travel from source to destination
Packet transmission time: time it takes the sender to transmit all bits of the packet
Queuing delay: time the packet need to wait before being transmitted because the queue was not empty when it arrived
Processing Time: time it takes a router/switch to process the packet header, manage memory, etc

4. Sending One Packet R bits per second (bps) Bandwidth: R bps
Propagation delay: T sec
T seconds
P bits
time
Transmission time = P/R T
Propagation delay =T = Length/speed_of_light
1/speed = 3.3 nsec in free space
4 nsec in copper
5 nsec in fiber

5. Router: Store and Forward
A packet is stored (enqueued) before being forwarded (sent)
10 Mbps
5 Mbps
100 Mbps
10 Mbps
Receiver
Sender
time

6. Switch: Cut-Through
A packet starts being forwarded (sent) as soon as its header is received
R1 = 10 Mbps
R2 = 10 Mbps
Receiver
Sender
Header
time
What happens if R2 > R1 ?

7. Outline Performance Metrics; Router vs. Switch
Layering and End-to-End Arguments
Queueing Theory: Little Theorem and M/M/1 Queue
Routing: Distance Vector and Link State protocol
Router Architecture

8. Layering: The Problem (cont’d)
HTTP
Application
Telnet
FTP
NFS
Coaxial
cable
Fiber
optic
Packet
radio
Transmission
Media
Re-implement every application for every technology?
No! But how does the Internet architecture avoid this?

9. Layering: Solution
Introduce an intermediate layer that provides a single abstraction for various network technologies
New application just need to be written for intermediate layer
New transmission media just need to provide abstraction of intermediate layer
Application
SMTP
SSH
NFS
HTTP
Intermediate
layer
Coaxial
cable
Fiber
optic
Packet
radio
Transmission
Media

10. Layering Layering is a particular form of modularization
System is broken into a vertical hierarchy of logically distinct entities (layers)
Service provided by one layer is based solely on the service provided by layer below
Rigid structure: easy reuse, performance suffers

11. ISO OSI Reference Model for Layers
Application
Presentation
Session
Transport
Network
Datalink
Physical

12. OSI Model Concepts Service: what a layer does
Service interface: how to access the service
Interface for layer above
Peer interface (protocol): how peers communicate
Set of rules and formats that govern the communication between two network boxes
Protocol does not govern the implementation on a single machine, but how the layer is implemented between machines

13. Layering: Internet Universal Internet layer:
Internet has only IP at the Internet layer
Many options for modules above IP
Many options for modules below IP IP
LAN
Packet
radio
TCP
UDP
Telnet
FTP
DNS
Application
Transport
Internet
Net access/
Physical

14. Hourglass

15. Implications of Hourglass
Single Internet layer module:
Allows networks to interoperate
Any network technology that supports IP can exchange packets
Allows applications to function on all networks
Applications that can run on IP can use any network
Simultaneous developments above and below IP

16. E2E Arguments: Where to Place Functionality?
Most influential paper about placing functionality is “End-to-End Arguments in System Design” by Saltzer, Reed, and Clark
“Sacred Text” of the Internet
Endless disputes about what it means
Everyone cites it as supporting their position

17. E2E Arguments: Moderate Interpretation
Think twice before implementing functionality in the network
If hosts can implement functionality correctly, implement it a lower layer only as a performance enhancement
But do so only if it does not impose burden on applications that do not require that functionality

18. Outline Performance Metrics; Router vs. Switch
Layering and End-to-End Arguments
Queueing Theory: Little Theorem and M/M/1 Queue
Routing: Distance Vector and Link State protocol
Router Architecture

19. Little’s Theorem Assume a system at which packets arrive at rate λ
Let d be mean delay of packet, i.e., mean time a packet spends in the system
Q: What is the mean (average) number of packets in the system (N) ?
d = mean delay
λ – mean arrival rate
system
A: N = λ x d

20. Example λ = 1 N = λ x d = 5 d = 5 N = 5 packets packets time d = 5 1 21 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

21. Queueing: M/M/1 Queue
λ – mean arrival rate (1/λ – mean inter-arrival time)
µ - mean service rate (1/ µ - mean service time)
d – mean delay
d = (1/µ)/(1 – u) d
1/µ 1
u (load)

22. Queueing: More Intuition
Q: Why does the delay increases so much when u  1?
A: Because in general the arrival process is bursty not uniform

23. Queueing: Uniform Arrival
(a) λ = 0.1 packets/sec; a packet arrives every 10sec
µ = 0.2 packets/sec; a packet is transmitted in 5sec
(assume all packets have the same size)
u = λ/µ = 0.5
red – packet arrival; blue – number of bits in the queue
bits
in queue
d = 5 sec …. 15 25 35 45 55 65 5 10 20 30 40 50 60
time (sec)
Packet
size
Packet transmission
starts
ends 5
delay

24. Queueing: Uniform Arrival
(b) λ = packets/sec; a packet arrives every 8 sec
bits
in queue
d = 5 sec …. 5 8 13 16 19 24 29 32 37 40 45 48 53
time (sec)
(c) λ = 0.2 packets/sec; a packet arrives every 5 sec
bits
in queue
d = 5 sec …. 5 10 15 20 25 30 35
time (sec)
With uniform traffic delay remains constant when utilization <= 1

25. Queueing: Bursty Arrival
During each 50sec interval:
- send packets at rate 2λ in the first 25sec (busy period)
- no packets during the last 25sec (idle period)
Note: average arrival rate still λ
(a) λ = 0.1 packets/sec; during busy period a packet arrives every 5 sec
bits
in queue
d = 5 sec 5 10 15 20 25 50 55 60 65 70 75
time (sec)

26. Queueing: Bursty Arrival
(b) λ = packets/sec (u=0.625); during busy period
a packet arrives every 4 sec
d = 8sec
bits
in queue 4 8 12 16 20 24 50
time (sec) 5 10 15 20 25 30 35
d = ((5-0) + (10-4) + (15-8) + (20-12) + (25-16) + (30-20) + (35-24))/7 =
= ( )/7 = 8

27. Queueing: Bursty Arrival
(c) λ = 0.2 packets/sec (u = 1); during busy period
a packet arrives every 2.5 sec
d = 16.25sec
bits
in queue … 5 10
22.5
time (sec)
2.5
7.5 5 10 15 20 25 30 35 40 45 50
d = ((5-0) + (10-2.5) + (15-5) + (20-7.5) + (25-10) + … )/10
= ( )/10 = 10
With bursty traffic delay increases as utilization increases

28. Queueing: Uniform vs. Bursty Arrivald
16.25 8 5
u (load)
0.5
0.625 1
With M/M/1 things get even worse as:
Busy periods get larger as load increases
Packets have different size (exponentially distributed sizes)

29. Outline Performance Metrics; Router vs. Switch
Layering and End-to-End Arguments
Queueing Theory: Little Theorem and M/M/1 Queue
Routing: Distance Vector and Link State protocol
Router Architecture

30. Routing Problem Assume
A network with N nodes, where each edge is associated a cost
A node knows only its neighbors and the cost to reach them
How does each node learns how to reach every other node along the shortest path? A E D C B F 2 1 3 5

31. Routing Protocols Compute and maintain routing tables
A node’s routing table contains the information on how to reach every other node in the network
Two routing algorithms
Distance vector
Link state

32. Distance Vector: Control Traffic
When the routing table of a node changes, the node sends its table to its neighbors
A node updates its table with information received from its neighbors
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

33. Example: Distance Vector Algorithm
Node A
Node B
Dest.
Cost
NextHop B 2 C 7 D ∞ -
Dest.
Cost
NextHop A 2 C 1 D 3 3 B D 2 1 1 A C 7
Node C
Node D
1 Initialization:
2 for all neighbors V do
if V adjacent to A
D(A, V) = c(A,V);
5 else
D(A, V) = ∞; …
Dest.
Cost
NextHop A 7 B 1 D
Dest.
Cost
NextHop A ∞ - B 3 C 1

34. Example: 1st Iteration (C  A)
Node A
Node B
Dest.
Cost
NextHop B 2 C 7 D ∞ -
Dest.
Cost
NextHop A 2 C 1 D 3 3 B D 2 1 1 A C 7
(D(C,A), D(C,B), D(C,D)) …
7 loop:
12 else if (update D(V, Y) received from V)
for all destinations Y do
if (destination Y through V)
D(A,Y) = D(A,V) + D(V, Y);
else
D(A, Y) = min(D(A, Y),
D(A, V) + D(V, Y));
18 if (there is a new minimum for dest. Y)
send D(A, Y) to all neighbors
20 forever
Node C
Node D
Dest.
Cost
NextHop A 7 B 1 D
Dest.
Cost
NextHop A ∞ - B 3 C 1

35. Example: 1st Iteration (C  A)
Node A
Node B
Dest.
Cost
NextHop B 2 C 7 D 8
Dest.
Cost
NextHop A 2 C 1 D 3 3 B D 2 1 1 A C 7
D(A, D) = min(D(A, D), D(A, C) + D(C,D)
= min(∞ , 7 + 1) = 8 …
7 loop:
12 else if (update D(V, Y) received from V)
for all destinations Y do
if (destination Y through V)
D(A,Y) = D(A,V) + D(V, Y);
else
D(A, Y) = min(D(A, Y),
D(A, V) + D(V, Y));
18 if (there is a new minimum for dest. Y)
send D(A, Y) to all neighbors
20 forever
(D(C,A), D(C,B), D(C,D))
Node C
Node D
Dest.
Cost
NextHop A 7 B 1 D
Dest.
Cost
NextHop A ∞ - B 3 C 1

36. Example: 1st Iteration (C  A)
Node A
Node B
Dest.
Cost
NextHop B 2 C 7 D 8
Dest.
Cost
NextHop A 2 C 1 D 3 3 B D 2 1 1 A C 7 …
7 loop:
12 else if (update D(V, Y) received from V)
for all destinations Y do
if (destination Y through V)
D(A,Y) = D(A,V) + D(V, Y);
else
D(A, Y) = min(D(A, Y),
D(A, V) + D(V, Y));
18 if (there is a new minimum for dest. Y)
send D(A, Y) to all neighbors
20 forever
Node C
Node D
Dest.
Cost
NextHop A 7 B 1 D
Dest.
Cost
NextHop A ∞ - B 3 C 1

37. Example: 1st Iteration (BA, CA)
Node A
Node B
Dest.
Cost
NextHop B 2 C 3 D 5
Dest.
Cost
NextHop A 2 C 1 D 3 3 B D 2 1 1 A C 7 …
7 loop:
12 else if (update D(V, Y) received from V)
for all destinations Y do
if (destination Y through V)
D(A,Y) = D(A,V) + D(V, Y);
else
D(A, Y) = min(D(A, Y),
D(A, V) + D(V, Y));
18 if (there is a new minimum for dest. Y)
send D(A, Y) to all neighbors
20 forever
D(A,D) = min(D(A,D), D(A,B) + D(B,D))
= min(8, 2 + 3) = 5
D(A,C) = min(D(A,C), D(A,B) + D(B,C))
= min(7, 2 + 1) = 3
Node C
Node D
Dest.
Cost
NextHop A 7 B 1 D
Dest.
Cost
NextHop A ∞ - B 3 C 1

38. Example: End of 1st Iteration
Node A
Node B
Dest.
Cost
NextHop B 2 C 3 D 5
Dest.
Cost
NextHop A 2 C 1 D 3 B D 2 1 1 A C 7 …
7 loop:
12 else if (update D(V, Y) received from V)
for all destinations Y do
if (destination Y through V)
D(A,Y) = D(A,V) + D(V, Y);
else
D(A, Y) = min(D(A, Y),
D(A, V) + D(V, Y));
18 if (there is a new minimum for dest. Y)
send D(A, Y) to all neighbors
20 forever
Node C
Node D
Dest.
Cost
NextHop A 3 B 1 D
Dest.
Cost
NextHop A 2 B 3 C 1

39. Example: End of 3nd Iteration
Node A
Node B
Dest.
Cost
NextHop B 2 C 3 D 4
Dest.
Cost
NextHop A 2 C 1 D 3 B D 2 1 1 A C 7 …
7 loop:
12 else if (update D(V, Y) received from V)
for all destinations Y do
if (destination Y through V)
D(A,Y) = D(A,V) + D(V, Y);
else
D(A, Y) = min(D(A, Y),
D(A, V) + D(V, Y));
18 if (there is a new minimum for dest. Y)
send D(A, Y) to all neighbors
20 forever
Node C
Node D
Dest.
Cost
NextHop A 3 B 1 D
Dest.
Cost
NextHop A 4 C B 2 1
Nothing changes  algorithm terminates

40. Link State: Control Traffic
Each node floods its local information to every other node in the network
Each node ends up knowing the entire network topology  use Dijkstra to compute the shortest path to every other node
Host A
Host B
Host E
Host D
Host C N1 N2 N3 N4 N5 N7 N6

41. Link State: Node State Host A Host B Host E Host D Host C N1 N2 N3 N4

42. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A
D(B),p(B)
2,A
D(C),p(C)
5,A
D(D),p(D)
1,A
D(E),p(E)
D(F),p(F)
1 Initialization:
2 S = {A};
3 for all nodes v
if v adjacent to A
then D(v) = c(A,v);
else D(v) = ; … 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

43. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F) …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

44. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
ADE
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
3,E
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F)
4,E …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

45. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
ADE
ADEB
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
3,E
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F)
4,E …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

46. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
ADE
ADEB
ADEBC
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
3,E
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F)
4,E …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

47. Example: Dijkstra’s Algorithm
Step 1 2 3 4 5
start S A AD
ADE
ADEB
ADEBC
ADEBCF
D(B),p(B)
2,A
D(C),p(C)
5,A
4,D
3,E
D(D),p(D)
1,A
D(E),p(E)
2,D
D(F),p(F)
4,E …
8 Loop
find w not in S s.t. D(w) is a minimum;
10 add w to S;
update D(v) for all v adjacent
to w and not in S:
D(v) = min( D(v), D(w) + c(w,v) );
13 until all nodes in S; 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1

48. Distance Vector vs. Link State
Highly scalable
Can converge very slowly when cost of a link increase
Not robust
Link state:
Fast convergence
Robust
Less scalable (updates are flooded in the network)

49. Outline Performance Metrics; Router vs. Switch
Layering and End-to-End Arguments
Queueing Theory: Little Theorem and M/M/1 Queue
Routing: Distance Vector and Link State protocol
Router Architecture

50. IP Routers Router consists of Router implements
Set of input interfaces where packets arrive
Set of output interfaces from which packets depart
Some form of interconnect connecting inputs to outputs
Router implements
(1) Forward packet to corresponding output interface
(2) Manage bandwidth and buffer space resources
Router 5 7 4 8 6 11 10 2 13 12 3 1

51. Generic Architecture
Input and output interfaces are connected through an interconnect
Interconnect can be implemented by
Shared memory
Low capacity routers (e.g., PC-based routers)
Shared bus
Medium capacity routers
Point-to-point (switched) bus
High capacity routers
input interface
output interface
Inter-
connect

52. Interconnect
Point-to-point switch allows simultaneous transfer of packet between any two disjoint pairs of input-output interfaces
Goal: come-up with a schedule that
Provides Quality of Service
Maximizes router throughput
Challenges:
Address head-of-line blocking at inputs
Resolve input/output speedups contention
Avoid packet dropping at output if possible
Note: packets are fragmented in fix sized cells at inputs and reassembled at outputs

53. Output Queued Routers Only output interfaces store packets Advantages
Easy to design algorithms: only one congestion point
Disadvantages
Requires an output speedup of N, where N is the number of interfaces  not feasible
input interface
output interface
Backplane RO C

54. Input Queued Routers Only input interfaces store packets Advantages
Easy to build
Store packets at inputs if contention at outputs
Relatively easy to design algorithms
Only one congestion point, but not output…
Need to implement backpressure
Disadvantages
Hard to achieve utilization  1 (due to output contention, head-of-line blocking)
However, theoretical and simulation results show that for realistic traffic an input/output speedup of 2 is enough to achieve utilizations close to 1
input interface
output interface
Backplane RO C

55. Head-of-line Blocking
Cell at head of an input queue cannot be transferred, thus blocking the following cells
Cannot be transferred because
is blocked by red cell
Input 1
Output 1
Cannot be
transferred
because output
buffer overflow
Input 2
Output 2
Input 3
Output 3

56. Solution to Avoid Head-of-line Blocking
Maintain at each input N virtual queues, i.e., one per output port
Input 1
Output 1
Output 2
Input 2
Output 3
Input 3

57. Midterm Information Date: 30 September 2004 Time: 6:40-8pm
Place: 277 Cory Hall
Thursday:
NO class
Extended professor office hours
Closed books; 8,5”x11” crib sheet (both sides)
No calculators, PDAs, cell phones with cameras, etc
Please use PENCIL and ERASER

58. Other Information
Ion’s office hour on Wednesday has moved from 4-5pm to 5-6pm
Lecture on October 12 will be given by Sally Floyd
She is the authority in the area of TCP