Điện tử viễn thông c2 1 ky thuat chuyen mach kenh ditel khotailieu

TRƯỜNG ĐẠI HỌC ĐIỆN LỰC
KHOA ĐIỆN TỬ - VIỄN THÔNG

TỔNG ĐÀI &
KỸ THUẬT CHUYỂN MẠCH

Chương 2: Kỹ thuật chuyển mạch kênh

Giảng viên: Phan Thị Thanh Ngọc

1

EPU - 2012


Chuyển mạch ngang – dọc (Cross-bar)

Sô lượng chuyển mạch = n * m
2

J.Tiberghien - VUB


Chuyển mạch 2 cấp
1

100

20
*5

20
*5

20
*5

20
*5

20
*5

20
*5

20
*5

20
*5

20
*5

20
*5

1

100

Dung lượng chuyển mạch= 5*20*10 = 1000 <<< 10 000
(chuyển mạch ở đây là chuyển mạch khối)
3

J.Tiberghien - VUB


Chuyển mạch 3 cấp
1

n*
k

N/n*
N/n

n*
k

1

N/n*
N/n

N/n*
N/n

N
N/n

N*k
4

k
k*N2/n2

N
N/n
N*k
J.Tiberghien - VUB


Các chuyển mạch 3 cấp
A

n*
k

N/n*
N/n

n*
k

k
N/n*
N/n
B
N/n*
N/n

5

In both A & B, n-1 lines busy
None of the busy lines of A communicating with B
Free line of A wants to communicate with free line of B
Non blocking condition : k >= (n-1)+(n-1)+1 = 2n -1

J.Tiberghien - VUB


Three Level Switches
Optimal non-blocking N*N switch

6

Total Number of Switches S = 2Nk + kN2/n2
Non blocking
: k = 2n-1
S = 2N(2n-1) + (2n-1) N2/n2
S = 4Nn - 2N + 2N2/n - N2/n2
How to choose n to minimize S ?
dS/dn = 0
4N-2N2/n2+2N2/n3 = 0
(1-1/n)N/n2 = 2
for large n : n ~ 
2N - 1)
N/2 Sopt = 4N(
Example : N=100, S ~ 5200

J.Tiberghien - VUB


Traffic 
Intensity 

Traffic Intensity on a single line =
Fraction of time the line is busy
Expressed in Erlang (Danish mathematician)
Typical residential line (no internet) : 0.05 Erlang
Typical business line
: 0.2 Erlang
Typical GSM
: 0.035 Erlang
Traffic intensity in exchange =  Traffic on lines
e.g. Exchange with 10 000 residential lines
Traffic = 500 Erlang
Capacity of a GSM cell expressed in Erlang/km2
7

J.Tiberghien - VUB


Little formula 
h = mean duration of a call (line holding time)
λ = Call’s rate = number of calls per time unit
If T2 is the observation time and T1 the
occupancy time during T2, then
Number of calls during T2 = λ * T2
Occupancy time T1 during T2 = λ * T2 * h

Traffic = T1/T2 = λ * h
Example:
h = 4min; λ = 30 calls/min; A = 120 E.
h = 1min; λ = 120 calls/min; A = 120 E.
8

J.Tiberghien - VUB


Blocking 
If the number of servers (i.e. lines) is smaller than
the number of users trying to make a call, some
traffic will be lost:
A0 = offered traffic
Ac = carried traffic
Ac = Ao if capacity is sufficient
Al = Ao - Ac = Lost traffic
B = Al / A0 = Blocking probability
or Grade of Service (GoS)
9

J.Tiberghien - VUB


The Erlang B law 
Hypothesis :
Infinite number of sources.
Arrival = Poisson distribution.
Duration = h = Exponential distribution
A0n

B(n,A0) =
1

10

A0
1!



n!
A02
2!

 ... 

A0n
n!

Often n is wanted as a function of A0 and B.
B(n,A0) is tabulated, so that n can be found,
J.Tiberghien - VUB
but often n should be multiple of 30 !


The Erlang B law 
B = 1%
N
A0

5
10
30
60
75
90
120
180
11

1.36
4.46
20.3
46.9
60
74.7
103
160.4

J.Tiberghien - VUB


Probability 
Graphs

p = probability (Lee Graphs)
that a link is busy (0..1)
= Traffic intensity on that link (Erlang)
q = probability that a link is idle
q=1-p

IF any of n links can be used to complete a call
Blocking probability B = pn
IF m serial links are needed to complete a call
Blocking probability B = 1 - qm
This supposes all probabilities are independent
12

J.Tiberghien - VUB


Three Level 
Switches

With blocking probability 
p'
p'
B
p
k
p
n lines

p' = p (n/k) = p/
B = probability all paths busy
B = (probability that arbitrary path busy)k
B = (1 -q'2)k = [1 - ( 1- p/)2]k
given p and B , this is a relation between k and n
13

J.Tiberghien - VUB

Three Level 
Switches

With blocking probability 
Nonp = 0.1
blocking
B=B
0.002
N

n

k

S

k

S

8 5
2 560 15
7 680
128
512 16 7 14 336 31 63 488
2 048 32 10 81 920 63 516 096
8 192 64 15 491 520 127 4.2 106
33 106

32 768 128 24 3.1 106 255
131 072 256 41 21.5 106 511 268 106
14

J.Tiberghien - VUB


Multi­stage 
Switch

15

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Time Division 
Switching
Telephone channels
multiplexed in 30 channel frames
8 7 6 5 4 3 2 1

8 7 2 5 6 3 4 1

1

(*)
(*)

8

(*) Delay = 125 S
16

J.Tiberghien - VUB


Time Division 
MUX , Switching
Time Switch & DEMUX
Dual
access
RAM
memory
32 bytes

M
U
X
Write
Address
Slot
Counter

17

Read
Address
Control
store
32

addresses
J.Tiberghien - VUB


Hybrid 
Switching
Space
- Time - Space

18

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Hybrid 
Switching
Time
- Space - Time

19

J.Tiberghien - VUB


Telephone Exchange
(Conceptual Model)

Line Circuit

trunk lines +

Inter-office
signaling
Register

Line Circuit
Line Circuit
Line Circuit
Line Circuit

Switching
Matrix

Register
Register
Register

Control Computer
20

J.Tiberghien - VUB