1. Lecture 2.
Switching of
physical circuits

2. Crossbar Switch Concept
Each egress port can select any ingress port as its source.
Broadcast- a copy is taken by all egress ports.
Multicast – a copy is taken by a set of egress ports.

3. Non-symmetric switch Ne – number of egress ports
Ni – number of ingress ports
In symmetric switch, Ne = Ni
If Ne > Ni, then the crossbar is with speedup. Increase the number of paths that a set of signals can take.
If Ne < Ni, then the crossbar is with slowdown. Decrease the number of paths that a set of signals can take.

4. Crossbar with speedup

5. Crossbar with slowdown

6. Broadcast by ingresses
Broadcast is expensive and not practical.

7. Using fanout buffers
Fanout tree amplifies a signal into N copies for each egress.

8. Cheaper Implementation

9. Single / Multi-Stage Switch
Single-stage switch (one central node) has the best performance. However building arbitrarily large single-stage switch is impossible.
We are forced to make multi-stage switches.

10. Multi-Stage Switch
A 3-stage switch with 2 rows:

11. Clos Switch Structure
Each Clos switch is represented by C(n,m,r).

12. Clos switch flow

13. Clos switch flow – cont.

14. Clos switch flow – cont

15. Clos switch with a speedup
A search for available path through stage two is more likely to succeed.
Also useful in case of link failure.
In general, speedup = m/n

16. Blocking in Clos switch
Blocking - there is no available route from free input to free output.
Clos network can suffer from blocking.
For example: (suppose two routes can not share a link)
Strict non-blocking: can find a route from free input to free output without changing existing routes.
Rearrangable non-blocking: can route any set of pairs (destroying existing state)

17. Clos network is strictly non-blocking (without rearrangement) iff m >= 2n-1.
Proof:
n-1 busy 1
n-1 busy … … …
free
free
n-1 n …
2n-2
Number of switches at stage 2 >= 2n-1
Sometimes this switch arrangement is called “2n-1 switch”
Speedup = (2n-1)/n

18. In practice, strictly non-blocking Clos is usually built with speedup = 2.

19. Clos network is rearrangable non-blocking iff m >= n
Proof: the arrangement if all the services are active- 1 2 … n
Number of switches
At stage 2 >= n.
Optimally, each building block of stage 1 has 2n ports, n ports to the outside and n ports to the stage 2, there are n building blocks at stage 2 and there are n building blocks on first and third level.

20. Algorithm to rearrange the paths
Map the network to coloring edges on a graph:

21. Solving conflict in the graph: find open path
Example:
(b)

22. (c)
(d)

23. Another example:

24. Multicast in clos networks
Multicast in Clos is harder to implement than in Crossbar.
Suppose A wants to send signal to both B and C.
There are two options:
Multiply signals at stage 1.
Multiply signals at stage 2.

25. Enhanced Multicast in Clos
Multicast branching:
Best solution in terms of replication
Harder to manage and configure the multicast trees

26. Single vs. Multi Stage There is no blocking in Single stage
Single stage is less expensive
No algorithm to find a path is need for Single stage.
There is a physical limit to implement a Single stage above certain number of ports.