Switching Networks
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Stanisław Stoch Switching Systems 1
General (theoretical) model of the exchange Extended (practical) model of the exchange
Serving Serving
Line Unit Line Unit
Switching Network Concentrator Switching Network
Unit Unit
LU LU
(SN)
SU SU
inside
Connecting
LU LU
Paths
SU SU
SN (Sieć Dróg SN
Rozmównych)
TU SU TU SU
to other to other
exchanges exchanges
TU TU
Trunk Trunk
Unit Unit
CU CU CU CU
CU
CU
Control Unit
Control Unit
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Number of terminals involved in the connection Number of terminals involved in the connection
In digital telephony a conference is task of a  conference
bridge and NOT  of the SN. From the SN point of view,
conference of N subscribers is set of N single connections
 single connection
between subscribers and the  conference bridge .
In digital telephony  multicast is to be found only
 multiconnection
by delivering of signalling from one tone generator
(=conference)
to multiple subscribers (or tone receivers).
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One-sided vs. two-sided units Possible misunderstanding
local connection
Line
 Two-sided = rectangular
Trunk
(is able to connect only
to other
input with output) offices
transit connection
outgoing or incoming
 One-sided = triangular
connection
(homogeneous terminals,
Symbol of triangle is used for one-sided units in theoretical documents only.
In the documentation of switching systems all units are drawn as rectangles.
not divided into some groups)
The real  triangular nature of one-sided unit is to deduce from text description.
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The same switching unit drawn as a triangle Number of inputs to number of outputs ratio
Line
 traffic compression
2:1 or greater, e.g. 8:1
local connections
 traffic expansion
( Line-Line )
1:2 or lesser, e.g. 1:8
outgoing and incoming
 traffic distribution
connections ( Line-Trunk )
between 2:1 and 1:2
transit connections ( Trunk-Trunk )
to other
offices
sub.A sub.B
Trunk
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Transmission directionality
exchange exchange exchange
telephone circuit telephone circuit (transmissionally bidirectional)
made on made on
pusty
bidirectional path two unidirectional paths
trunk exchange
hybrid hybrid
(centrala
(rozgałęz
nik) (rozgałęz
nik)
międzymiastowa)
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Digital  elementary switch Digital two-sided (rectangular) switch
" transmisionally bidirectional 
telephony service is bidirectional
" transmisionally unidirectional 
because of digital technology
" two-sided (rectangular) 
switching
partition into inputs and outputs
memory
is the result of unidirectional transmission
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Digital one-sided (triangular) switch Digital one-sided (triangular) switch
 Looping of certain circuit
" transmisionally bidirectional 
is practically used in switching equipment
telephony service is bidirectional
to check partly set connection path.
4 3 2 1 4 3 2 1
1 1
1 1
2 2
2 2
switching switching
memory memory
3 3
3 3
4 4
4 4
Stanisław Stoch Switching Systems 15 Switching Systems 16
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Switching directionality Switching directionality
control
seizure is possible
unit Y
by control unit Y only
exchange exchange exchange
sub.A sub.B unidirectional circuits
Because every telephone circuit
seizure is possible
control
by control unit X only
unit X
must be transmissionally bidirectional,
designation of directionality of telephone circuit
bidirectional circuits
refers always to switching directionality.
Switching directionality of a circuit is a matter of
control signaling control
control units abilities
unit X unit Y
(avoids danger of
and signaling between them. double seizure)
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Structures of stepping and crossbar exchanges Structures of digital exchanges
5ESS
FS GS
to other offices
to other offices
LF GS
EWSD
to other offices
to other offices
In the past almost all circuits (excluding subscriber lines) were unidirectional
Today almost all telephone circuits are bidirectional (switching and transmission
(switching unidirectionality), so practically all units were two-sided (rectangular).
directionality)  so typical are one-sided (triangular) units.
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Final remarks
Explanation of the difference
Possible reasons to differentiate terminals,
5ESS
what implies switching unit to be bidirectional
(rectangular):
 unidirectional transmission
to other offices
 switching unidirectional
EWSD
circuits
to other offices
 position in the
switching network
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Chicken diagram (symbolika szwedzka) Chicken diagram (cont.)
25 circuits
25 Out
1 circuit 25 circuits 25 circuits 1 circuit 10 circuits
10 In
1 25 25 1
10 25
1 25 25 1
10 25
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Joinig of inputs Joining of outputs
10 25 10 25
25 25
50 20
25 50 10
25 10 In 10 In
20 In
10 50 20 25
10 In
10 25 25 10 10 25
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Joinig of inputs and outputs
10 25
25
25
50
25
10
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10 In 10 In
20 In
10 10 25 25
Stanisław Stoch Switching Systems 27
Single-stage network (example no. 1) Single-stage one-sided network
N2 Out
N
N1 N2 N
" Number of crosspoints is a reasonable
N1 In
approximate indication of the network cost :
" To make one connection  only one crosspoint
L = N " (N  1) / 2 ( L ~ N2 )
(punkt komutacyjny) should be closed
For two-sided and one-sided networks:
" All outputs are fully available
" Number of crosspoints is a reasonable " Preserving full availability 
approximate indication of the network cost:
" we seek an opportunity to reduce the cost L.
L1 = N1 " N2 (for N1= N2: L1 = N2 )
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Two-stage network (example no. 2) Calculating number of crosspoints
n1 1 1 n2 n1 1 r2 r1 1 n2
N1 = n1 " r1 N2 = n2 " r2 N1 = n1 " r1 N2 = n2 " r2
n1 r1 r2 n2 n1 r1 r2 r1 r2 n2
1. stage 2. stage 1. stage 2. stage
one switch: n1" r2 r1" n2
" between each switch of 1. stage
one stage: (n1" r2)" r1 (r1" n2)" r2
and each switch of 2. stage
there exists exactly one link
L2 = r1" r2" (n1 + n2) = N1/n1 " N2/n2 " (n1 + n2) =
" for single chosen input and single chosen
= N1" N2" (n1 + n2) / n1" n2 = N1" N2 " (1/n1 + 1/n2)
output there exists only one possibility
to connect them (using two crosspoints)
Typical value of n was =20, is: 8" 30 = 240, so L2 « L1
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Two-stage network  example of blocking
a a
In1 Out1
b c
In2 Out2



1 2 3 1 2 3
not possible
c b
d d
3 6
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4 5 6 4 5 6
2 5
In Out
1 4
Two-stage network
1 2 3
a b
with full availability
(compared to single-stage
c d
network) is cheaper (L2 < L1),
but blocking can appear.
4 5 6
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Switching network with doubled links  blocking
Network with doubled links (example no. 3)
In1 Out1
n1 1 1 n2
In2 Out2
In3 Out3


N1 = n1 " r1 N2 = n2 " r2 1 2 3 1 2 3
not possible
n1 r1 r2 n2
3 6
1. stage 2. stage
2 5
4 5 6 4 5 6
" between each switch of 1. stage
1 4
In Out
and each switch of 2. stage
Network with multiple links
there exist exactly two links
1 2 3
between switches
of adjacent stages is called
" to connect chosen input to chosen output
incomplete network.
there exist two possibilities
This is very ineffective
" L3 = 2 " L2 4 5 6
method to reduce blocking.
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Three-stage network (example no. 4) Three-stage network  chicken diagram
3. stage
n1 1 1 1 n2
m n2
N1 N2
r2
n1 r1 m r2 n2
1. stage 2. stage 3. stage
n1
" between individual switches of adjacent
stages there exists exactly one link r1
" to connect single input to single output
there exist  m independent paths
1. stage
" we denote that network: ½
½(m,n1,r1,n2,r2)
½
½
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Clos Theorem  for ½(m,n1,r1,n2,r2) Clos network Example cost comparison
½
½
½
n1-1
n2-1
n1 1 1 1 n2 no. of terminals of the network
N 800 115 200
no. of terminals of one switch
only one only one n 20 240
free input free output
no. of side-stage switches
r 40 480
no. of middle-stage switches
m 39 479
one-stage network (nonblocking)
L1 640 000 13 271 040 000
two-stage network (blocking)
L2 64 000 110 592 000
two-stage incomplete n. (blocking)
L3 128 000 221 184 000
m
Clos network (nonblocking)
L4 124 800 220 723 200
" To avoid blocking, there must be:
m e" (n1-1) + (n2-1) + 1 i.e. m e" n1 + n2 - 1
e"
e"
e"
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One-sided (triangular) Clos network Clos theorem for one-sided network ½
½(m,n,r)
½
½
n 1
1
n r
m
" Physically it s a two-stage network.
(same as for two-sided network)
" For r > 3: m e" 2n - 1
e"
e"
e"
" From the traffic point of view
(round down
3n
" For r = 3: m e" to integer
e"
e"
e"
it s a three-stage network
2
= truncate)
(three crosspoints constitute the path
" For r = 2: m e" n
e"
e"
e"
connecting two terminals).
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2. stage
The worst state of the network
" Choose two terminals of different switches and hold
them free.
" Make connections taking subsequent terminals of the
same switches, as previously chosen free terminals.
" If connection path goes through two sections, try to
make all connections using the same link group.
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If connection path goes through three sections, try to
make subsequent connections through different
middle-stage switches to other side-stage switches,
than switches chosen at the beginning.
" After connecting all other terminals, return to
previously chosen free terminals, and try to connect
them. If it is not possible  the network is blocking.
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The worst state of the network  example The worst state of the network  example
n=3 r=4 m=4 (non-blocking m e" 2n 1 = 5)
n=4 f=4 (non-blocking f e" n = 4)
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Selection types Distibution of trunks of the same group
K1
RULE:
to K1
" P-P - Point - Point (to individual circuit)
Trunks of the
to K1
not possible
" P-G - Point - Group (to any circuit of a group)
same group
(leading to
K2
" P-A - Point - All (to any of all circuits)
the same
destination)
should be
K1
distributed
to K1
K2
as equally
to K1
sub.A sub.B
as possible
among all
P-A P-G P-G P-G P-P
output
switches.
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External blocking Internal blocking (of 1. type)
In1 K1 In1 K1
In4 K1 In2 K2
In2 K1 In3 K3


1 2 3 K1 K2 K3 1 2 3 K1 K2 K3
not possible not possible
K3 K3 K3 K3
4 5 6 K1 K2 K3 4 5 6 K1 K2 K3
K2 K2 K2 K2
In Out In Out
K1 K1 K1 K1
All internal links
1 2 3 1 2 3
available to some input
None free trunks to
(i.e. all outputs of its
the desired destnation
switch) are busy.
4 5 6 4 5 6
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Internal blocking (of 2. type) Example of Benea
algorithm s use
In1 K1
In1 K1
In4 K2
In4 K2
In4 K2 should use









In4 K2
the same switch, as
In2 K2


1 2 3 K1 K2 K3 1 2 3 K1 K2 K3
previous In1 uses
not possible
K3 K3 K3 K3
4 5 6 K1 K2 K3 4 5 6 K1 K2 K3
K2 K2 K2 K2
In Out In Out
K1 K1 K1 K1
There exists free output, In that case it s possible to
1 2 3 1 2 3
free available link, but it s establish connection
not possible to establish
In2 K2
the connection.
(as well  every other).
4 5 6 4 5 6
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Benea
algorithm Rearrangeable (or repackable) network
A
In multistage networks there exist many possible paths
to connect some input to specific destination (output).
K1 K2
These paths go trough different switches of particular
stages.
1 2
B
The main idea of Benea
algorithm is not to choose
K1 K2
a completely empty middle-stage switch if it is possible
Out
to set up a call through a partially occupied switch
3 4
(making them more occupied).
In
In1 A K1 Making change:
That choice leaves in the switching network
In3 B K2 In3 A K2
maximal switching capabilities for future connections.
In2 K1 we achieve:



not possible In2 B K1
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