Environmental Decision-Making - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 240

capacity intended for the delays. Therefore it is necessary to obtain an assessment for
the probability of appearance of errors and to find memory capacities for delays

M 1 þþ M k \ , t K .

Let selection bi i be realized in the volume sample in i , basing each selection on Ni i
reasonable values bi i . In this case, the non-anomalous value bi i is taken as the
anomalous value with probability

M and for the distribution of time delay intervals t 1 , …

α i and it is rejected with probability 1 − α i . The

probability of appearance of “ candidates ” during time ti i =r i α i S i is given by:

g ¼ C S i

S i i 1 a i r i S i

P f l i ¼ S i

r i a

ð Þ ¼ m i S ðÞ:

When ʼ i ≤ r i α i , the “ candidates ” arrive rarely and have time to be processed

” f b i g arrive often and do not have time
to be analyzed before the arrival of f b i þ 1 g . Therefore, the variants are delayed at Fi. i .
The probability that the number of

without delay. If ʼ i >r i α i , the “ candidates

“ candidates ” will not exceed the mean values ri i

α i by more than ʵ i , is given by:

g ¼ X

m ð i Þ
s¼0 m i ð s Þ;

P f l i r i a i þ e i

where m(i)=r α i + ʵ i . Considering that r i is suf ciently large and according to the

Laplace ' s limit theorem we obtain:

h i

g 1 = 2

P f l i ¼ s i g / ð s i r i a i Þ f r i a i 1 a i ð Þ ;

ðÞ

1 = 2 exp u 2

where ð Þ .

Denoting the memory capacity intended for delay of the ith component of b by
M i and

/ ðÞ ¼2 =

fixing the condition emerging from the limitation, we obtain: riαi i α i + ʵ i ≤ M i

(i =1, … , K). Then the probability of non-over fl ow of memory Mi i will be: P

{ ʼ i ≤ M i }= ʦ (u i ), (i =1, … , K), where

g 1 = 2 g 1 = 2 u i ¼ e i r i a i 1 a i f ð Þ ¼ M i r i a i ð Þ f r i a i 1 a i ð Þ ð 3 : 27 Þ

Utilizing the Boolean formula, let us calculate the probability of non-over fl ow of

memory M i on the i ' i'th component during delay with time ti i and the uninterrupted

transfer of the “ candidates ” from Fi i to F i+1 without delay. Let us denote this

probability by P(1, 2, … , N i ):

P 1 ð ; 2 ; ...; N i Þ 1 N i 1 U ½ u ðÞ ; i ¼ 1 ; ...; K ;

where N i is the number of possible variants of values bi. i .
Let this probability differ from unity by no more than ʴ i . Then we obtain an

equation for determining the delay value ti i (i =1, … , K):