SWITCH-BASED DYNAMIC
INTERCONNECTION
NETWORKS
(single-stage, and
multistage)
Mariam A. Salih
 Single
stage network
 Multi-stage network
 Blockage in Multistage Interconnection
Networks
Single-Stage Networks

In this case, a single stage of switching elements (SEs) exists
between the inputs and the outputs of the network.

The simplest switching element that can be used is the 2 x 2
switching element (SE).

The connection in a 2×2 switch will either be straight, exchange,
lower broadcast or upper broadcast as shown in the Figure.

Straight; the upper input is transferred to the upper output and
the lower input is transferred to the lower output.

Exchange; the upper input is transferred to the lower output and
the lower input is transferred to the upper output.

Upper-broadcast; the upper input is broadcast to both the
upper and the lower outputs.

Lower-broadcast; the lower input is broadcast to both the upper
and the lower outputs.

A two function switch box can assume either the straight or
exchange state
A four function switch box can be any of the four legitimate
state

CONCEPT OF PERMUTATION NETWORK
 In
permutation interconnection networks
the information exchange requires data
transfer from input set of nodes to output
set of nodes and possible connections
between edges are established by
applying various permutations in available
links.

Let us look at the basic concepts of permutation with
respect to interconnection network. Let us say the
network has set of n input nodes and n output nodes.
Permutation P for a network of 5 nodes (i.e., n = 5) is written as follows:
The permutations can be combined. Where two or
more permutations are applied in sequence, e.g. if P1
and P2 are two permutations defined as follows:
1
1
1
2
2
2
3
3
3
A single stage network
 To
establish communication between a
given input (source) to a given output
(destination), data has to be circulated a
number of times around the network.
1)Shuffle-Exchange
A
well-known connection pattern for
interconnecting the inputs and the
outputs of a single-stage network is
the Shuffle-Exchange.
2) Butterfly permutation:

This permutation is obtained by interchanging the
most significant bit in address with least significant bit.
Multistage Networks

Multistage interconnection networks (MINs)
were introduced as a means to improve some
of the limitations of the single bus.

The most undesirable single bus limitation that
MINs is set to improve is the availability of only
one single path between the source and the
destination modules.
Multistage Networks

a general MIN consists of a
number of stages each
consisting
of
a
set
of
switching elements.

Stages are connected to
each other using Inter-stage
Connection (ISC) Pattern.

There are few Inter-stage
Connection are provided by
hardware.
1) Multistage butterfly
2) The Omega Network
 The
Omega Network represents another wellknown type of MINs. (Shuffle– Exchange
networks)
 Number
of stages log2 (n)
 Number of switches in each stage n/2
 Total number of switches (n/2)*log2(n)
Example:

Figure illustrates the case of an N = 8 Omega
network. As can be seen from the figure, the
inputs to each stage follow the shuffle
interconnection pattern.
Final design
3)Clos network:
 This
network was developed by Clos (1953).

Consider an I input and O output network Number N is
chosen such that (I= n.x) and (O=p.y).

In Clos network input stage will consist of X switches each
having n input lines and z output lines.

The last stage will consist of Y switches each having m input
lines and p output lines

the middle stage will consist of z crossbar switches, each of
size X × Y.

To utilize all inputs the value of Z is kept greater than or equal
to n and p.
 The
connection between various stages is made
as follows: all outputs of 1st crossbar switch of first
stage are joined with 1st input of all switches of
middle stage.
 all
outputs of 2nd crossbar switch of first stage are
joined with 2nd input of all switches of middle
stage, and so on…
 Similar
connections are made between middle
stage and output stage.
 Example
: Consider a Clos network with, 3
stages and 3×3 switches in each stage
4) The Banyan Network

In the banyan If the number of inputs, for example,
processors, in an MIN is N and the number of
outputs, for example, memory modules, is N,
the number of MIN stages is log2 (N)
 and the number of SEs per stage is N/2,


Each stage use inverse shuffle permutation.
Destination-tag routing
 In
destination-tag routing, switch settings are
determined by the message destination.
 The most significant bit of the destination address is
used to select the output of the switch in the first
stage;
if the most significant bit is 0, the upper output is
selected,
 if it is 1, the lower output is selected.
The next-most significant bit of the destination address is
used to select the output of the switch in the next stage,
and so on until the final output has been selected.


Example of tag Routing
destined = 4 (= 100 )
0
1
2
0
4
1
2
2
3
3
4
4
5
5
6
6
7
7
Example of tag Routing
destined = 4 (= 100 )
0
1
2
0
4
1
2
2
3
3
4
4
5
5
6
6
7
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4
4
5
5
6
6
7
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4
4
5
5
6
6
7
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4
4
5
5
6
6
7
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4 4
5
5
6
6
7
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4
5
5
6
7
4
6
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
4
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
4
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4
5
5
6
7
4
6
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4
5
4
5
6
6
7
7
Example of tag Routing
destined = 4 (= 100 )
2
0
0
1
1
2
2
3
3
4
4 4
5
5
6
6
7
7
Multiple Concurrent Paths
0
1
0
5
2
3
1
2
7
3
4
4
5
5
6
6
7
7
Multiple Concurrent Paths
0
1
0
5
2
3
1
2
7
3
4
4
5
5
6
6
7
7
Multiple Concurrent Paths
0
0
1
1
2
2
3
3
4
5
5
6
7
4
5
7
6
7
Multiple Concurrent Paths
0
0
1
1
2
2
3
3
4
5
4
5
5
6
6
7
7
7
Multiple Concurrent Paths
0
0
1
1
2
2
3
3
4
5
4
5
5
6
6
7
7
7
Multiple Concurrent Paths
0
0
1
1
2
2
3
3
4
4
5
5 5
6
6
7
7 7
Multiple Concurrent Paths
0
1
0
5
2
3
1
2
7
3
4
4
5
5
6
7
1
6
7
Multiple Concurrent Paths
0
1
0
5
2
3
1
2
7
3
4
4
5
5
6
7
1
6
7
Multiple Concurrent Paths
0
0
1
1
2
2
3
1
3
4
5
4
5
6
7
5
7
6
7
Multiple Concurrent Paths
0
0
1
1
2
1
3
3
4
2
5
4
5
5
6
6
7
7
7
Multiple Concurrent Paths
0
1
0
1
1
2
2
3
3
4
5
4
5
5
6
6
7
7
7
Multiple Concurrent Paths
0
0
1
1 1
2
2
3
3
4
4
5
5 5
6
6
7
7 7
Source (000) -> destination (101)
Source (101) -> destination (011)
Source (110) -> destination (010)
Blockage in Multistage Interconnection
Networks
A number of classification criteria exist for MINs. Among these
criteria is the criterion of blockage.

Blocking Networks; Blocking networks possess the property
that in the presence of a currently established
interconnection between a pair of input/output, the arrival
of a request for a new interconnection between two
arbitrary unused input and output may or may not be
possible.

Nonblocking
Networks;
Nonblocking
networks
are
characterized by the property that in the presence of a
currently established connection between any pair of
input/output, it will always be possible to establish a
connection between any arbitrary unused pair of
input/output. The Clos is a well-known example of
nonblocking networks.
Output Port Contention
0
1
0
4
1
2
2
3
3
4
4
5
5
6
7
4
6
7
Output Port Contention
0
1
0
4
1
2
2
3
3
4
4
5
5
6
6
7
4
7
Output Port Contention
0
0
1
1
2
2
3
3
4
4
4
5
5
6
6
7
4
7
Output Port Contention
0
0
1
1
2
2
3
3
4
4
5
6
7
4
5
4
6
7
Output Port Contention
0
0
1
1
2
2
3
3
4
4
4
5
4
5
6
6
7
7
Output Port Contention
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
Output Port Contention
0
0
1
1
2
2
3
3
4
4 4
5
5
6
6
7
7
Path Contention
0
2
0
1
1
2
2
3
3
4
3
4
5
5
6
6
7
7
Path Contention
0
2
0
1
1
2
2
3
3
4
3
4
5
5
6
6
7
7
Path Contention
0
2
0
1
3
1
2
2
3
3
4
4
5
5
6
6
7
7
Path Contention
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
Path Contention
0
1
0
3
1
2
2
3
3
4
4
5
5
6
6
7
7
Path Contention
0
0
1
1
2
3
2
3
3
4
4
5
5
6
6
7
7
Path Contention
0
0
1
1
2
2
3
3 3
4
4
5
5
6
6
7
7
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
Performance Degradation
0
5
1
2
0
1
0
2
3
3
4
3
4
5
2
5
6
4
6
7
6
7
Performance Degradation
0
5
0
1
3
1
2
2
3
2
3
4
0
4
5
4
5
6
6
7
6
7
Performance Degradation
0
3
0
1
5
1
2
2
2
3
3
4
0
4
5
4
5
6
6
7
6
7
Performance Degradation
0
3
0
1
0
1
2
2
2
3
3
4
5
4
5
4
5
6
6
7
6
7
Performance Degradation
0
0
0
1
3
1
2
3
2
2
3
4
4
5
5
6
6
7
6
7
Performance Degradation
0
0
0
1
3
1
2
2
3
2
3
4
5
4
5
5
6
6
7
6
7
Performance Degradation
0
0
1
0
1
2
3
2
3
2
3
4
5
4
5
5
6
6
7
6
7
Performance Degradation
0
0 0
1
1
2
2 2
3
3 3
4
4
5
5 5
6
6 6
7
7
 Myrinet-2000
Clos Network for 128 Hosts
Network Topology
• Backplane of the M3E128 Switch
• M3-S16-8F fiber line
card (8 ports)
Simple Quiz..