. , , , , ( , 0, t ), ( ). .
, .
:
0- ;
1- , ;
2-
4.5.
4.5.
( t→ ∞)
P0 = 1 - , (4.28)
P1 = 1 - , (4.29)
P2 = 1 - , (4.30)
ν=1 ‑ ;
ν=0 ‑ .
K=1 P2 = . (4.31)
, .
4.3 [21]
3. , . λ = 0,4 10-5 -1, μ = 0,5 -1. .
.
:
0- , 1- , 2- .
.5.6.
4.6. . 5.12- |
0 1 , 2 - . .
0 (0) = 1, P1(0) = 2 (0) = 0. ,
i(ε) . , i(ε)= Di/D, D - , 0(ε), 1(ε), 2(ε); Di - , i-o .
|
|
, 2 (t). D D2.
D = D2 = .
:
2 ( ) =2λ2/ [ε2 + 3(λ + μ)ε + 2 2 + 4λμ + 2 2].
,
K (t) = 2 (t) = λ2/(λ+μ)2{ 1‑2 [- ( + μ)t] + [‑2( + (μ)t]}.
t →∞ :
K = λ2/(λ+μ)2 = (4 10-3)2(4 10-3 + 0,5)2= 1,57 10-2.
4. , ( ). .
.
(c. 4.7.).
4.7.
,
K = 0 + 1 = (μ2 + λμ)/(μ2 +λμ + λ2).
, , [19]. 4.8.
4.8.
:
K= 1 ‑ . (4.32)
K = 1 ‑ . (4.33)
n m . , . ψ = 0, 1,..., n + m. :
= (4.34)
= (4.35)
λ μ , , , , , .
.
1. λ1 μ1, ( λ2 μ2), > < - 4.9.
|
|
. 4.9.
0 1 1 2 ( t: )
P∞ =
(4.36)
0(0) = 1, , 0 + 1 + 2= 1, (4.36),
(∞) = . (4.37)
( t→∞)
P∞ = .
,
(4.38)
0 + 1 + 2 = 1,
∞ = , (4.39)
.
[21]
5. 1 2 3. 2, 2 3. . λ1 - λ2. . .
.
, , . 4 :
0- 1
1- 2,
2- ,
3- .
4.10.
4.10. |
, .
0 + 1 + 2 + 3 = 1.
0 (t) t 0 (t) = . 0 (0) = 1. ,
(t) = ‑ λ21 +λ1
1(0) = 0.
P1(t) = ‑
,
(t) =‑ λ22 (t) + ‑
2 (0) = 0
P2(t) = + ‑
3(t)
P0+ P1+ P2+ P3 = 1.
P3 = 1‑P0(t)P1(t)P2(t) = 1
( ). , . .
4.11.
( )
( 4.11.) , .
:
P∞ = .
,
(4.40)
, [21], ,
|
|
K∞ = P0 + P1 + P2 = . (4.41)
( ).
4.12.
.4.12. ,
:
0- ;
1- , , ;
2- , , ;
3- .
( t →∞)
P∞ = .
( t→∞)
∞ = . (4.43)
(). , . , , ( ).
.
[21]
6. - , . - λ = 4 ‑1 μ = 5 ‑1. . .
.
:
0 - ,
1 ,
2- .
4.13.
4.13.
0 (0) = 1, P1 (0) = 2 (0) = 0. , 2 (t) (t)
P2(t) = 1 ‑ ,
(t) = ,
= 0,5
T1 = = =3175 .
, , . , . [6]: , ; . ( ), . .
|
|
. , , . , n n‑1 . . .
, .