Data Integrity - RFID: Fundamentals and Applications in Contactless Smart Cards and Identification - page 203

Table 7.1 Average time consumption for reading all transponders in the interrogation zone of
an example system

Number of transponders in
the interrogation zone

Average
(ms)

90% reliability
(ms)

99.9% reliability
(ms)

2 150 350 500

3 250 550 800

4 300 750 1000

5 400 900 1250

6 500 1200 1600

7 650 1500 2000

8 800 1800 2700

The probability p(k) of k error-free data packet transmissions in the observation
period T can be calculated from the transmission duration τ of a data packet and the
average offered load G . The probability p(k) is a Poisson's distribution 2 with the mean
value G/τ :

G · k

T
τ

− G τ

p(k) = · e ( 7 . 4 )

k !

7.2.4.2 SlottedALOHAprocedure

One possibility for optimising the relatively low throughput of the ALOHA procedure
is the slotted ALOHA procedure . In this procedure, transponders may only begin to
transmit data packets at defined, synchronous points in time (slots). The synchronisation
of all transponders necessary for this must be controlled by the reader. This is therefore
a stochastic, interrogator-driven TDMA anticollision procedure.
The period in which a collision can occur (the collision interval ) in this procedure
is only half as great as is the case for the simple ALOHA procedure.
Assuming that the data packets are the same size (and thus have the same trans-
mission duration τ ) a collision will occur in the simple ALOHA procedure if two
transponders want to transmit a data packet to the reader within a time interval
T ≤ 2 τ . Since, in the S-ALOHA procedure, the data packets may only ever begin
at synchronous time points, the collision interval is reduced to T = τ . This yields the
following relationship for the throughput S of the S-ALOHA procedure (Fliege, 1996).

S = G · e ( − G)

( 7 . 5 )

In the S-ALOHA procedure there is a maximum throughput S of 36.8% for an
offered load G (see (Figure 7.15).
However, it is not necessarily the case that there will be a data collision if several
data packets are sent at the same time: if one transponder is closer to the reader

2 A random number has a Poisson's distribution if it takes on the countable number of possible values
k =

λ k
k ! · e − λ .

0 , 1 , 2 ,... with a probability p(k) =