- 1 -

(switch)

(switch)

k (switch)

(Bernoulli)

Bernoulli

T

.

T

.

- 2 -

(LPF)

(data modem)

(noisy band-limited channel)

H(f)

W (Hz) L (Km)

W

S

N

- 3 -

(switch)

q .

Bernoulli.

.

q

.

,

,

(arrival rate)

.

.

p(k)

Bernoulli

.

- 4 -

Bernoulli Bernoulli

, Poisson

t

.

Poisson

t .

- 5 -

Poisson

0 t

T

- 6 -

=0 .

=t T > t

Bayes

(memoryless property).

0 t

T

t+

- 7 -

- Erlang B

k+1

k+1

k -1

...

k

t t+

- 8 -

k=0 P(k-1)=0

k> P(k)=0

,

.

B(A,M)

- 9 -

M - Erlang C

...

k+1

k+1

k -1

k

t t+

- 10 -

C(A,M)

( , ),

- 11 -

A

///

Kendall notation

k

(queuing systems)

: //

: //

:

: / (system RAM)

, =

Poisson (renewal processes)

- 12 -

(memoryless)

Poisson

(memoryless)

k

( )

IIIII

M/M/1/ (statistical multiplexing)

- 13 -

IIIII

IIIII

IIIII

q

1-q

, Kirchhoff, -

-

-

,

in out .

. ,

in>out

.

in

- 14 -

(memoryless)

Poisson

(memoryless)

IIIII

T

.

X

x

M/M/1/

D

M/M/1/

,

k , k

.

k=1

k=2

- 15 -

k=3

k1, , k=0,

.

- 16 -

, (t)

k

=

k

- 17 -

D=T+X

- 18 -

t

(t)

(t) k

(t) (t) IIIII

N(t)

Little

(t) :

(t) :

:

N(t)=(t)- (t) : t

:

:

:

( Little)

- 19 -

,

.

.

- 20 -

,

, W

X Y

.

- 21 -

Poisson

(memoryless)

IIIII

i

t

i+1 i+2

M/G/1/ (statistical multiplexing, error handling)

i+1,

.

i+1

i

i+1 ,

,

,

.

.

- 22 -

,

.

,

p(0)

- 23 -

- 24 -

M/G/1/ (STDM multiplexing)

G(z)

M/G/1/ Poisson

.

q( )

( )

( Poisson)

i+1 ( ), []

- 25 -

A(z)

- 26 -

Laplace

s= (1-z).

H M/G/1/ (system

state), RAM

,

G (z) z=1

. G(z)

z=1, G(z)

.

- 27 -

(1)=1 G(1)=1 z=1,

A(1) (1)

Laplace Leibnitz

- 28 -

(1) (1)

Little

- 29 -

Poisson

(memoryless)

messages/sec

packets/message

IIIII

M/G/1/ (STDM multiplexing burst arrivals)

sec

. Poisson

.

m

r

- 30 -

P r

- 31 -

-

m

Poison

Poisson (compound Poisson process) A(z)

- 32 -

M/G/1/ (system state)

- 33 -

BER

Poisson

(memoryless)

messages/sec

IIIII

t

i i+1

. . . n=1 n=2 n

M/G/1/ (ARQ1 protocols)

M/G/1/ -

ARQ

.

L bits

Poisson

.

b(t).

m

1 ARQ (error detection) - . HARQ (error correction) . HARQ 3

HSDPA (High Speed Downlink Packet Access)

4 LTE (Long Term Evolution).

- 34 -

BER (bit error rate) bit L

bits.

ACK

(stop-n-wait) ARQ (automatic repeat request)

ACK

n

(stop-n-wait) ARQ (automatic repeat

request)

ARQ n

- 35 -

x .

Laplace

.

x ,

Laplace -

,

n

Laplace

.

(stop-n-wait) ARQ ,

b()

- 36 -

,

- 37 -

= ,

- 38 -

,

Little .

- 39 -

BER

Poisson

(memoryless)

messages/sec

packets/message

IIIII

t

i i+1

. . . n=1 n=2 n

M/G/1/ (STDM multiplexing ARQ protocols)

L bits.

.

Poisson

.

.

m

r

- 40 -

BER (bit error rate) bit L

bits.

n

(stop-n-wait) ARQ (automatic repeat

request)

Q=1-P .

- 41 -

ARQ n

A(z)

i+1 .

Poisson i+1

,

Poisson (compound Poisson process)

, ,

- 42 -

- 43 -

Little

.