<s>
A	O
nonblocking	B-Algorithm
minimal	I-Algorithm
spanning	I-Algorithm
switch	I-Algorithm
is	O
a	O
device	O
that	O
can	O
connect	O
N	O
inputs	O
to	O
N	O
outputs	O
in	O
any	O
combination	O
.	O
</s>
<s>
Historically	O
,	O
in	O
telephone	O
switches	O
,	O
connections	O
between	O
callers	O
were	O
arranged	O
with	O
large	O
,	O
expensive	O
banks	O
of	O
electromechanical	O
relays	O
,	O
Strowger	B-Device
switches	I-Device
.	O
</s>
<s>
The	O
basic	O
mathematical	O
property	O
of	O
Strowger	B-Device
switches	I-Device
is	O
that	O
for	O
each	O
input	O
to	O
the	O
switch	O
,	O
there	O
is	O
exactly	O
one	O
output	O
.	O
</s>
<s>
In	O
the	O
1940s	O
and	O
1950s	O
,	O
engineers	O
in	O
Bell	O
Lab	O
began	O
an	O
extended	O
series	O
of	O
mathematical	O
investigations	O
into	O
methods	O
for	O
reducing	O
the	O
size	O
and	O
expense	O
of	O
the	O
"	O
switched	B-Architecture
fabric	I-Architecture
"	O
needed	O
to	O
implement	O
a	O
telephone	O
exchange	O
.	O
</s>
<s>
One	O
early	O
,	O
successful	O
mathematical	O
analysis	O
was	O
performed	O
by	O
Charles	O
Clos	O
(	O
)	O
,	O
and	O
a	O
switched	B-Architecture
fabric	I-Architecture
constructed	O
of	O
smaller	O
switches	O
is	O
called	O
a	O
Clos	B-Device
network	I-Device
.	O
</s>
<s>
The	O
crossbar	O
switch	O
has	O
the	O
property	O
of	O
being	O
able	O
to	O
connect	O
N	O
inputs	O
to	O
N	O
outputs	O
in	O
any	O
one-to-one	B-Algorithm
combination	O
,	O
so	O
it	O
can	O
connect	O
any	O
caller	O
to	O
any	O
non-busy	O
receiver	O
,	O
a	O
property	O
given	O
the	O
technical	O
term	O
"	O
nonblocking	O
"	O
.	O
</s>
<s>
This	O
seemed	O
to	O
imply	O
that	O
most	O
of	O
the	O
switching	B-Architecture
fabric	I-Architecture
of	O
a	O
crossbar	O
switch	O
was	O
wasted	O
.	O
</s>
<s>
The	O
switching	B-Architecture
fabric	I-Architecture
could	O
become	O
very	O
efficient	O
,	O
and	O
possibly	O
even	O
be	O
created	O
from	O
standardized	O
parts	O
.	O
</s>
<s>
This	O
is	O
called	O
a	O
Clos	B-Device
network	I-Device
.	O
</s>
<s>
A	O
telephone	O
system	O
only	O
has	O
to	O
make	O
a	O
one-to-one	B-Algorithm
connection	O
.	O
</s>
<s>
This	O
algorithm	O
is	O
a	O
form	O
of	O
topological	B-Algorithm
sort	I-Algorithm
,	O
and	O
is	O
the	O
heart	O
of	O
the	O
algorithm	O
that	O
controls	O
a	O
minimal	O
spanning	O
switch	O
.	O
</s>
<s>
It	O
's	O
not	O
difficult	O
to	O
make	O
composite	O
switches	O
fault-tolerant	B-General_Concept
.	O
</s>
<s>
The	O
eventual	O
result	O
was	O
the	O
Bell	O
1ESS	B-Device
.	O
</s>
<s>
This	O
was	O
controlled	O
by	O
a	O
CPU	O
called	O
the	O
Central	O
Control	O
(	O
CC	O
)	O
,	O
a	O
lock-step	B-General_Concept
,	O
Harvard	B-Architecture
architecture	I-Architecture
dual	O
computer	O
using	O
reliable	O
diode	B-General_Concept
–	I-General_Concept
transistor	I-General_Concept
logic	I-General_Concept
.	O
</s>
<s>
In	O
the	O
1ESS	B-Device
CPU	O
,	O
two	O
computers	O
performed	O
each	O
step	O
,	O
checking	O
each	O
other	O
.	O
</s>
<s>
The	O
1ESS	B-Device
switch	I-Device
was	O
still	O
in	O
limited	O
use	O
as	O
of	O
2012	O
,	O
and	O
had	O
a	O
verified	O
reliability	O
of	O
less	O
than	O
one	O
unscheduled	O
hour	O
of	O
failure	O
in	O
each	O
thirty	O
years	O
of	O
operation	O
,	O
validating	O
its	O
design	O
.	O
</s>
<s>
In	O
a	O
modern	O
digital	O
telephone	O
switch	O
,	O
application	O
of	O
two	O
different	O
multiplexer	B-Protocol
approaches	O
in	O
alternate	O
layers	O
further	O
reduces	O
the	O
cost	O
of	O
the	O
switching	B-Architecture
fabric	I-Architecture
:	O
</s>
<s>
space-division	O
multiplexers	B-Protocol
are	O
something	O
like	O
the	O
crossbar	O
switches	O
already	O
described	O
,	O
or	O
some	O
arrangement	O
of	O
crossover	O
switches	O
or	O
banyan	O
switches	O
.	O
</s>
<s>
8000	O
times	O
per	O
second	O
,	O
the	O
connection	O
is	O
reprogrammed	O
to	O
connect	O
particular	O
wires	O
for	O
the	O
duration	O
of	O
a	O
time	B-Protocol
slot	I-Protocol
.	O
</s>
<s>
Design	O
advantage	O
:	O
In	O
space-division	O
systems	O
the	O
number	O
of	O
space-division	O
connections	O
is	O
divided	O
by	O
the	O
number	O
of	O
time	O
slots	O
in	O
the	O
time-division	B-Protocol
multiplexing	I-Protocol
system	O
.	O
</s>
<s>
This	O
dramatically	O
reduces	O
the	O
size	O
and	O
expense	O
of	O
the	O
switching	B-Architecture
fabric	I-Architecture
.	O
</s>
<s>
time-division	B-Protocol
multiplexers	I-Protocol
each	O
have	O
a	O
memory	O
which	O
is	O
read	O
in	O
a	O
fixed	O
order	O
and	O
written	O
in	O
a	O
programmable	O
order	O
(	O
or	O
vice	O
versa	O
)	O
.	O
</s>
<s>
This	O
type	O
of	O
switch	O
permutes	O
time-slots	O
in	O
a	O
time-division	B-Protocol
multiplexed	I-Protocol
signal	I-Protocol
that	O
goes	O
to	O
the	O
space-division	O
multiplexers	B-Protocol
in	O
its	O
adjacent	O
layers	O
.	O
</s>
<s>
Design	O
advantage	O
:	O
Time-division	B-Protocol
switches	O
have	O
only	O
one	O
input	O
and	O
output	O
wire	O
.	O
</s>
<s>
First	O
,	O
it	O
is	O
typical	O
to	O
"	O
fold	O
"	O
the	O
switch	O
,	O
so	O
that	O
both	O
the	O
input	O
and	O
output	O
connections	O
to	O
a	O
subscriber-line	O
are	O
handled	O
by	O
the	O
same	O
control	B-General_Concept
logic	I-General_Concept
.	O
</s>
<s>
Then	O
,	O
a	O
time-division	B-Protocol
switch	O
is	O
used	O
in	O
the	O
outer	O
layer	O
.	O
</s>
<s>
The	O
control	B-General_Concept
logic	I-General_Concept
has	O
to	O
allocate	O
these	O
connections	O
,	O
and	O
the	O
basic	O
method	O
is	O
the	O
algorithm	O
already	O
discussed	O
.	O
</s>
<s>
The	O
computer	O
code	O
decomposes	O
larger	O
multiplexers	B-Protocol
into	O
smaller	O
multiplexers	B-Protocol
.	O
</s>
<s>
Switches	O
typically	O
interface	O
to	O
other	O
switches	O
and	O
fiber	O
optic	O
networks	O
via	O
fast	O
multiplexed	O
data	O
lines	O
such	O
as	O
SONET	B-Protocol
.	O
</s>
<s>
Multiplexer	B-Protocol
lines	O
are	O
allocated	O
in	O
a	O
first-in-first	O
out	O
way	O
,	O
so	O
that	O
new	O
connections	O
find	O
new	O
switch	O
elements	O
.	O
</s>
<s>
They	O
are	O
being	O
replaced	O
by	O
high-speed	O
Internet	B-Protocol
Protocol	I-Protocol
routers	O
.	O
</s>
