Download 1B. Communication System - Review - Circuit Switching PDF

Title1B. Communication System - Review - Circuit Switching
TagsDigital Electronics Computer Hardware Network Switch Telecommunications Infrastructure Telephone Exchange
File Size710.5 KB
Total Pages14
Document Text Contents
Page 1

1

COMMUNICATION SYSTEM
REVIEW

CIRCUIT SWITCHING

The N2 Problem

 For N users to be fully connected directly

 Requires N(N – 1)/2 connections

 Requires too much space for cables

 Inefficient & costly since connections not always on

N = 1000
N(N – 1)/2 = 499500

1

2

34

Page 2

2

Circuit Switching

 Patchcord panel switch invented in 1877

 Operators connect users on demand

 Establish circuit to allow electrical current to flow
from inlet to outlet

 Only N connections required to central office

1

2
3

N – 1

N

Manual Switching

Page 7

7

nk

nk

nk

nk

N/n  N/n

N/n  N/n

N/n  N/n

kn
1

2

N/n

N
inputs

1

2

3 3

N/n

N
outputs

1

2

k

2(N/n)nk + k (N/n)2 crosspoints

kn

kn

kn

… … …

Multistage Space Switch

Large switch built from multiple stages of small switches
The n inputs to a first-stage switch share k paths through intermediate
crossbar switches
Larger k (more intermediate switches) means more paths to output
In 1950s, Clos asked, “How many intermediate switches required to
make switch nonblocking?”

Clos Non-Blocking Condition:
k=2n-1

Request connection from last input to input switch
j to last output in output switch m
Worst Case: All other inputs have seized top n-1
middle switches AND all other outputs have
seized next n-1 middle switches
If k=2n-1, there is another path left to connect
desired input to desired output

Page 8

8

nxk

nxk

nxk

N/n x N/n

N/n x N/n

N/n x N/n

kxn
1

N/n

Desired
input

1

j m

N/n

Desired
output

1

2n-1

kxn

kxn

n-1

N/n x N/n
n+1

N/n x N/n
2n-2

Free path Free path

n-1
busy

n-1
busy


… …



Clos Non-Blocking Condition:
k=2n-1

# internal links =
2x # external links

C(n) = number of crosspoints in Clos switch

= 2Nk + k( )2 = 2N(2n – 1)+(2n – 1)( )2

Differentiate with respect to n:

0 = = 4N – + ≈ 4N – ==> n ≈ √

The minimized number of crosspoints is then:

C* = (2N + )(2( )1/2 – 1) ≈ 4N √ 2N = 4 √ 2N1.5

This is lower than N2 for large N

Minimum Complexity Clos Switch

N2

N/2

2N2

n2
2N2

n3
2N2

n2

N
2

C
n

N
n

N
n

N
2

Page 13

13

n  k N/n  N/n

N/n  N/n

N/n  N/n

k  n
1 1

2

N/n

1

2

k

k  n

k  n

n  k
2

n  k
N/n

First slot

kth slot

First slot

kth slot

… … …

Flow of time slots between
switches

Only one space switch active in each time slot

nxk

nxk

nxk

nxk

N/n x N/n
Time-shared
space switch

kxn
1

2

N/n

N
inputs

1

2

3 3

N/n

N
outputs

TDM
n slots

n slots

n slots

n slots

kxn

kxn

kxn

TDM
k slots

TDM
k slots

TSI stage TSI stageSpace stage

… …

Time-Share the Crossbar Switch

Interconnection pattern of space switch is reconfigured
every time slot
Very compact design: fewer lines because of TDM &
less space because of time-shared crossbar

Page 14

14

2x3

2x3

3x2
1

2

1

2
3x2D1

B1 A1B2 A2

C1D2 C2

B1 A1

C1D1

A1

B1

C1

D1

A1 C1

B1 D1

(b)

A

B

C

D

(a)

C

A

D

B

Example: A→3, B→4, C→1, D→3





Example: T-S-T Switch Design

For = 960
 Single stage space switch ~ 1 million crosspoints
 T-S-T

 Let = 120 = 8 TSIs
 = 2 – 1 = 239 for non-blocking
 Pick = 240 time slots
 Need 8x8 time-multiplexed space switch

For = 96,000
 T-S-T

 Let = 120 = 239
 / = 800
 Need 800x800 space switch

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