, ( , ), :
(3.6)
(3.7)
h, g - ; , z, , .
, , , . , . , .
:
.
, , (3.6) (3.7) , .
.
3.3. - (F -)
- () () , , .
() , . F -:
F = < z, x, y, j, y, z 0>, (3.8)
z, x, y , () (). z 0 Î Z ; j(z, x) ; y(z, x) . , , .. , , . .
t, z (t), x (t) y (t) = y[ z (t), x (t)], z (t + 1) = j[ z (t), z (t)], z (t) Î Z; y (t) Î Y; x (t) Î X. z 0, x (0), x (1), x (2), ( ), y (0), y (1), y (2), ( ).
:
1) F - 1- ( ), :
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z (t + 1) = j[ z (t), z (t)], t = 0, 1, 2, (3.9)
y (t) = y[ z (t), x (t)], t = 0, 1, 2, ; (3.10)
2) F - 2- :
z (t + 1) = j[ z (t), z (t)], t = 0, 1, 2, (3.11)
y (t) = y[ z (t), x (t 1)], t = 1, 2, 3, ; (3.12)
3) F - 2- , x (t) ( ):
z (t + 1) = j[ z (t), z (t)], t = 0, 1, 2, (3.13)
y (t) = y[ z (t)], t = 0, 1, 2, ; (3.14)
, (3.9-3.14), F -, :
, (3.15)
, , , , , t ;
, (3.16)
S , x.
. , ( ) . (3.10) , x (t) y (t), .. :
y (t) = y[ x (t)], t = 0, 1, 2,
, X Y, x y, 2- .
() F - . , , . . F - , , x, , 3.8-3.14, , , .
F - F = < z, x, y, j, y, z 0>, .. , , . F - , .
, , . 1- z 0. i - j - j(zk, xi) , y(zk, xi) . F - , , zk , , , (3.14), y(zi).
F - j y 3.1, F - 3.2.
3.1 | 3.2 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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. , , . xk zi zj, , zi zj, xk. , . : xk zi, , zi xk; y = y(zi, xk). : xk, , zj, , zj xk, y = y(zj, xk). . 3.1 F - F 1 F 2 .
. 3.1. () ()
. , , . cij = xk / ys xk, zi zj, ys, . F 1, , :
.
zi zj , cij / , .
F - cij (zi zj), :
,
i - , zi.
. , F - 2 , . C .
F - zk , xi Î X, j(zk, xi) = zk y(zk, xi) = yk. , F - , zk Î Z .
, , , . .
zk xs zs (s ¹ k), zk zk.
F - , , , . F - . , .
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4. - (Q -)
(queuing systems), Q -.
. .
(, ) . (, ) , , , .. .