1. Computer Networks: Switching and Queuing
Ivan Marsic
Rutgers University
Chapter 4 – Switching and Queuing Delay Models

2. Switching and Queuing Delay Models
Chapter 4

3. Topic: Packet Switching in Routers
 Router Architecture
 Forwarding Table Lookup
 Switching Fabric Design
 How Queuing Happens

4. Why Routers? (Recall Chapter 1)
Avoid needing direct link between all hosts (totally connected graph)
Redundancy: If one path fails, find an alternative path

5. Routing Delays

6. Router Components

7. How Router Forwards Packets

8. Services to Incoming Packets
Receiving and storing packets
Forwarding decision for packets
Moving packets from input to output port
Transmission of packets

9. Distribution of Protocol Layers
Note that router has a single (common) Network Layer protocol,
but each connection has a dedicate Link Layer protocol

10. Forwarding Algorithms

11. Router Architectures First generation router Second generation router
Third generation router

12. Switching via Memory / via Bus
First generation router
Second generation router

13. Crossbar Switch Fabric
Input
N x N switching elements
allows N simultaneous packets switched (in the best case when all packets going to different outputs)
Output

14. Goal: Reduce # Switching Elements
System bus (in 1st and 2nd generation arch’s) allows only one packet switched at a time
Crossbar allows up to N packets switched at a time
Something in the middle? (+cheaper!)

15. Banyan Switch Fabric (b) (a) (c)
8x8 Banyan has only 12 switching elements (while 8x8 crossbar requires 64)
But, much greater likelihood of collisions…
(c)

16. Reducing Collisions (Show slide with a collision example)
Collisions can be reduced if packets are ordered on input ports by their output port number
The router cannot choose the ordering of arriving packets, but we can insert a sorting hardware between the input network ports and the switching fabric …

17. Batcher Network
(b)
(a)
(c)

18. Batcher-Banyan Network

19. Why Batcher-Banyan Network
This figure is meant to illustrate why a concentrator is needed, because otherwise the gap in the input sequence will cause collision in the Banyan, but the example does not work for a 4x4 network -- need an 8x8 network example!!!!

20. Topic: Router Delays & Queuing Models
Where & Why Queuing Happens
Little’s Law
Queuing Models
M / M / 1, M / M / 1/ m, M / G / 1
Networks of Queues

21. Delay Components in Forwarding

22. Road Intersection Analogy
Head of Line Blocking

23. Where & Why Queuing Happens
At input ports, Head Of Line queuing
At output ports, if output link is “too narrow” (low data rate) for incoming traffic
Inside switch fabric, if collision occurred

24. An Input-queued Switch

25. General Service Model

26. Simple Queuing Model

27. Delay Time

28. Why Queuing Happens?

29. Arrival Sequences

30. Birth and Death Processes30

31. Little’s Law
Average number of packets in the system = arrival rate  average time that packet spends in the system
N =   T
Problem
We would like to know more, such as what are the probabilities of finding different number of customers on arrival, etc.

32. Intuition for the Balance Principle
See: Global Balance Equations

33. Transition Probability Diagram

34. M/G/1 Example

35. Expected Residual Time