Lecture 2.
Switching of
physical circuits
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.
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.
Crossbar with speedup
Crossbar with slowdown
Broadcast by ingresses
Broadcast is expensive and not practical.
Using fanout buffers
Fanout tree amplifies a signal into N copies for each egress.
Cheaper Implementation
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.
Multi-Stage Switch
A 3-stage switch with 2 rows:
Clos Switch Structure
Each Clos switch is represented by C(n,m,r).
Clos switch flow
Clos switch flow – cont.
Clos switch flow – cont
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
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)
Clos network is strictly non-blocking
(without rearrangement) iff m >= 2n-1.
Proof:
n-1 busy
free
…
n-1 busy
1
…
…
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
• In practice, strictly non-blocking Clos is
usually built with speedup = 2.
Clos network is rearrangable nonblocking iff m >= n
Proof: the arrangement if all the services are activen
n
n…
1
n
2
n
…
n
…
Number of switches
At stage 2 >= n.
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.
Algorithm to rearrange the paths
Map the network to coloring edges on a graph:
Solving conflict in the graph: find open path
• Example:
(b)
(c)
(d)
Another example:
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:
1. Multiply signals at stage 1.
2. Multiply signals at stage 2.
Enhanced Multicast in Clos
Multicast branching:
•Best solution in terms of replication
•Harder to manage and configure the multicast trees
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.