[17], the author proposed a different way to estimate the number of tags. If we know
the frame size and the number of tags, we can calculate the expected value of readable
slots, idle slots, and collided slots. This expectation is a function of frame size and the
number of tags. We can create a vector using the three values earlier. We could also create
another vector that consists of the actual value of readable slots, idle slots, and collided
slots in the previous frame. By using Chevyshevs inequality, we can make tag estimation
function as
Vogt2: Estimation function ?? min
Ntag
SEXP(F,Ntag)
CEXP(F,Ntag)
IEXP(F,Ntag) 0@
1A
S
C
I 0@
1A
: (9:2)
We refer to these methods using the author name, Vogt1 and Vogt2, respectively. Vogt1
can easily estimate the number of tags. However, as the number of tags increases, the
number of errors increases accordingly. On the contrary, when the number of tags is small,
Vogt2 has a large error rate. Vogt2 can estimate the number of tags precisely, but it may
have larger computational complexity.
9.4.2 Dynamic Framed Slotted ALOHA
The probability mass function of the number of reacting tags in a slot can be obtained by
using a binomial distribution. Given the number of tags and the frame size, we can
compute the probabilities of the occurrences of readable, idle, and collision slots.
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