... , , , , - .
, ... .
, ... ... . ... ... .
, :
1) , , , . ϳ 쳺 , (볺 );
2) ( , ).
3) ().
, , .
, n- ... , n- , m . m , , .
l m. n+m+1 .
Sk - k , , k = 0,..., n
Sn+i - n , i i = 1,..., m
 . 11.
|
..., .11. . .
, n P0(t), P1(t),..., Pn-1(t) , S0 Sn-1 , ... . , ...
P¢n = lPn-1(t) - (l+nm) Pn(t) + nmPn+1(t)
----------------------------------------------
P¢n+k = lPn+k-1(t) - (l+nm) Pn+k(t) + nmPn+k+1(t) (2.49)
----------------------------------------------
P¢n+m = lPn+m-1(t) - nmPn+m(t)
n . . ... .
P¢0 = lP0(t) + mP1(t)
------------------------------------
P¢k-1 = lPn-2(t) - (l+(n-1)m) Pn-1(t) + nmPn(t) (2.50)
... ,
Pk(t) = Pk P¢k = 0
(2.50)
- lP0 + mP1 = 0
---------------------------------
lPk-L -(l+Km)Pk + (K+1)mPk+1 = 0 2 < k < n-1
--------------------------------- (2.51)
lPn+s-1 -(l+nm)Pn+s + nmPn+s+1 = 0 1 < s < m-1
lPn+m-1 - nmPn+m = 0
(2.52)
(2.53)
(2.54)
(2.52) - (2.54) 
.
, 
- q = x; b1 = x
(2.55)
. = n+m = x m 
0 (2.56)
³
q = 1 - P. = 1 - 
P0 (2.57)
...
= lq = l(1 - 
P0) (2.58)
. ... , . ... , : , . k - , z - . m . , ... . .
|
|
|
q = 1 - P. = 1 - 
(2.59)
, . :
x =α/n,
(2.60)
,
(2.61)
1 (2.62)
, : 
(2.63)
.
S0, S1,,Sn+m. n S0, S1,,Sn-1 . = 0. , n , , 䳿 Sn, 
. 䳿 Sn+r, r 
(r=1,..,m-1).
(2.64)
, 
, - .
(2.65)
8. λ = 0,5 /. . ' , , . mt=1/μ=2. :
) ;
) ;
) , .
г. λ =0,5; μ =0,5; n=1; m=3; α =λ /μ=1.
a) (56) P=P1+3=1/(1+1+3)=1/5=0,2. q=1-P=0,8. =λ´q=0,5´0,8=0,4 /.
) n=2 (2.56) P=P2+3=(1/16)/(1+1+1/2+1/4+1/8+1/16)=1/47=0,021. q=1-P=0,979, 98% . =λ´q=0,49 /. ³ P0=16/47=0,34, 34% .
9. () (n=2), λ=2 /. t=2 . m=3 . , , , . ...: ; ;
1) ;
2) ;
3) .
, .
г.
λ=2; μ =0,5; n=2; m=3; α =4; x =α /n=4/2=2
1) (2.56) (2.57) P=P5=45/(232!)P0, P0=1/(1+4/2+42/2*(2-24)/(1-2))=0,008.
P=64×0,008=0,512
2) q=1-P=0,488. =λ*q=2*0,488=0,976 /.
3) ()
|
|
|
=/μ =α×q=4×0,488=1,952, .
4) (2.62)
.
5) 
.
: 
.
... λ = 2; μ = 0,5; n=1; m=3; α =4; x=α /n=4/1=4
P=P3+1=44(1-4)/(1-45)=3*256/1023=256/341=0,75.
q=1-0,75=0,25 =λ*q=0,25*2=0,5 /.
=/μ =α*q=4*0,25=1,
.
.
.
