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

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 Typi

TỔNG ĐÀI &

KỸ THUẬT CHUYỂN MẠCH

Chương 2: Kỹ thuật chuyển mạch kênh

TRƯỜNG ĐẠI HỌC ĐIỆN LỰC KHOA ĐIỆN TỬ - VIỄN THÔNG

Giảng viên: Phan Thị Thanh Ngọc

Chuyển mạch ngang – dọc (Cross-bar)

Sô lượng chuyển mạch = n * m

Chuyển mạch 2 cấp

20

*5 20

*5 20

*5 20

*5 20

*5

20

*5 20

*5 20

*5 20

*5 20

*5

1

100

1

100 Dung lượng chuyển mạch= 5*20*10 = 1000 <<< 10 000

(chuyển mạch ở đây là chuyển mạch khối)

Chuyển mạch 3 cấp

n*

k 1

N

N/n*

N/n

N/n*

N/n

N/n*

N/n

n*

k

1

N

N/n

N*k k*N k 2 /n 2

N/n

N*k

Các chuyển mạch 3 cấp

n*

k

N/n*

N/n

N/n*

N/n

N/n*

N/n

n*

k

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

k

A

B

Three Level Switches

Optimal non-blocking N*N switch

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 ~  Sopt = 4N( - 1)

Example : N=100, S ~ 5200 N/2

2N

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/km 2

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.

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:

A 0 = offered traffic

A c = carried traffic

A c = A o if capacity is sufficient

A l = A o - A c = Lost traffic

B = A l / A 0 = Blocking probability

or Grade of Service (GoS)

10 J.Tiberghien - VUB

The Erlang B law

Hypothesis :

Infinite number of sources.

Arrival = Poisson distribution.

Duration = h = Exponential distribution

B(n,A 0 ) =

Often n is wanted as a function of A 0 and B.

B(n,A 0 ) is tabulated, so that n can be found,

but often n should be multiple of 30 !

!

! 2

! 1 1

!

0

2 0 0

0

n

A A

A

n

A

n n









The Erlang B law

N

5 10 30 60 75 90 120 180

A0

1.36 4.46 20.3 46.9 60 74.7 103 160.4

B = 1%

Probability

Graphs

(Lee Graphs)

p = probability 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 = p n

IF m serial links are needed to complete a call

Blocking probability B = 1 - q m

This supposes all probabilities are independent

Three Level Switches

With blocking probability

p'

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

n lines

Three Level Switches

With blocking probability

B

N

128 512

2 048

8 192

32 768

131 072

n

8 16 32 64 128 256

k

15 31 63 127 255 511

S

7 680

63 488

516 096 4.2 10 6

33 10 6

268 10 6

k

5 7 10 15 24 41

S

2 560

14 336

81 920

491 520 3.1 10 6

21.5 10 6

p = 0.1

B = 0.002

Non-blocking

Multi-stage

Switch

Time Division

Switching

Telephone channels multiplexed in 30 channel frames

1

8

(*) (*)

(*) Delay = 125 S

Time Division

Switching

MUX , Time Switch & DEMUX

Dual access RAM memory

32 bytes

Slot Counter

M U X

Control store 32 addresses

Read Address Write

Address

Hybrid Switching

Hybrid Switching

Telephone Exchange

(Conceptual Model)

Switching Matrix

Line Circuit

Line Circuit

Line Circuit

Line Circuit

Line Circuit

Control Computer

trunk lines +

Inter-office signaling

Register Register Register Register