(3)
where m is the first moment of random variable Iin. In the presented model, it is convenient to shift the domain of function
pdfγ (x) so that the first moment of shift variable distribution is equal to 0.Wecan calculate the expected time of interception
of the information package:
E(Tin) = (1 − q) + 2q(1 − q) + 3q2(1 − q) + ・ ・ ・ =
1
1 − q
.
If we take into account (3) and E(Tout) = 1 then it is easy to obtain:
E(T ) = 1 + E([x ≥ a])−1. (4)
The random variable Iout = [Iin ≥ a] Iin has a probability density function pdfγ (x + m) which is cut off to the field [a,∞):
[x ≥ a]
E([x ≥ a])
pdfγ (x + m). (5)
If we put an expected value of random variable Iout and (4) to (2) then we get the formula for information processing
intensity:
ρ(pdfγ , a)right := ρ(a) =
∞
a x ・ pdfγ (x + m)dx
1 +
∞
a pdfγ (x + m)dx
. (6)
560 R. Jankowski et al. / Physica A 416 (2014) 558–563