Geoscience Reference
In-Depth Information
P
t
¼ 1
Y
K
Q
ð
1
;
2
; ...;
N
i
Þ
i¼1
Let us consider another variant of constant delay:the delay of a constant number
of
“
candidates
”
. The expectation time for a complete
filling of this delay is a
random value with a Pascal distribution:
¼ C
m
i
1
m
i
i
R
i
m
i
s
i
¼ t
i
P
R
i
1
a
ð
1
a
i
Þ
;
where R
i
¼ t
i
=
n
i
is the number of bi
i
variants surveyed for time ti
i
and n
i
is the
sample capacity.
In the case of
˄
i
≥
m
i
n
i
/
α
i
, the variants from Fi
i
enter F
i+1
more rarely than on
average. According to the matching condition of the whole
fl
flow, they have time to
α
i
, the b
i
variants do not have time to be
processed at F
i+1
and are delayed at Fi.
i
. It is necessary to determine the numerical
values of mi
i
(i =1,
pass by without delay. At
˄
i
< m
i
n
i
/
M
i
and in the process of an exhaustive search
for the ith component there should be a de
…
, K) so that m
i
≤
nite probability of no over
fl
ow and no
delay emptying.
Let us take advantage of the approximate expression of Pascal
'
s distribution via
distribution (
3.12
). When R
i
α
i
≫
1, the following expression is known
¼
a
i
m
1
s
i
¼ t
i
P
w
c
i
ð
y
i
Þ
i
ow of Mi
i
memory, it is
necessary to choose m
i
in such a way that the time between the arrivals of the
“
To ensure the predetermined probability of non-over
fl
candidates
”
should be close to average. Let us calculate the probability that
˄
i
exceeds the value m
i
n
i
/
α
i
by more than some constant d
i
Þ
m
i
n
1
P
f
s
i
m
i
n
i
=a
i
d
i
g
¼ 1
W
c
i
b
m
i
n
i
d
i
a
i
ð
c
ð
3
:
33
Þ
i
lling inequality (
6.33
) during the whole
procedure of an exhaustive search for values of the ith component has the evaluation:
The Q(1, 2,
…
, N
i
) probability of ful
Þ
m
1
i
n
1
i
Q
ð
1
;
2
; ...;
N
i
Þ
1
N
i
W
c
i
b
m
i
n
i
d
i
a
i
ð
c
e
i
.
Then the equation for determining the delay value mi
i
will take the following form:
Let us try to make this probability differ from unity by not less than the value of
¼
e
i
=
Þ
m
i
n
1
W
c
i
m
i
n
i
d
i
a
i
ð
N
i
ð
3
:
34
Þ
i
At c
i
> 0, involving the designated approximation of the normal distribution
function, we have mi
i
≈
ʵ
i
)]
-
1/2
/n
i
(i =1,
, K). Furthermore, let us
demand that the probability of appearance during time m
i
n
i
/
d
i
α
i
[2c
i
ln(Ni/εi)]
i
/
…
α
i
—
d
i
being greater than
M
i
“
”
candidates
be anywhere near zero. Then we have:
Search WWH ::
Custom Search