RFID Anti-collision algorithm Based onBi-directional Binary Exponential Index

YU Song-sen, ZHAN Yi-ju, WANG Yong-hua

Contents

1.Introduction 2.Algorithm Principle 3.Mathematical Analysis 4.The Simulated Analysis of the

Algorithmic Model 5.Conclusion

1.Introduction Problem:tag collision

Stochastic collision algorithm ： ALOHA ； Slotted-ALOHA resolutions deterministic collision algorithm ： tree searching algorithm

Our proposed algorithm bi-directional binary exponential index that comes from the binary exponential backoff algorithm of the computer network IEEE802.3 protocol is belongs to Stochastic collision algorithm.

2.Algorithm Principle

2.1 Algorithm Definitions (1)Interval :The period from the reader sending out request order to

tag answering information is called an interval.

request answer

t request t answer

t interval

Fi gure 1 the composi ti on of i nterval

(2)Request order: Request_under_success, Request_under_failure, Request_under_idle

(3)Shield command――Shield (EPC)

2.1 Algorithm Definitions (4)tag’s state:Active state and shielded state . (5) The probability of the tag’s answer is a series of discrete values.

In this paper:

1[ , , , , , , , , , , , ]

2 4 8 16 32 64 128 256 2k

q q q q q q q q qp q

q presents a constant. The adjust principal : While the reader sends Request_under_idle command, the

probability of tag doubles; While the reader sends Request_under_success command, the

probability of tag doesn’t change; While the reader sends Request_under_failure command, the

probability of tag is cut half.

2.2Algorithm Description Firstly, the reader sends request command at each

interval to ask the tags to answer, and decides the next request command according to the tags answering; at the same time, if the reader successfully identifies a tag, it will sent a shield command to shield the tag.

Secondly, the tags monitor the reader’s request command and adjust the answering probability, then answer at the probability in the answering period.

While the tags continuously enter into the reader’s district, the radio frequency identifying process of this algorithm is showed in the figure 2:

2.2Algorithm Description

TR1

n1

p1

TR2

n2

p2

TR3

n3

p3

TRm

nm

pm

TRK-2

nK-2

pK-2

TRK-1

nK-1

pK-1

tags

Answeri ng probabi l i ty

TRk

reader

Fig.2 Anti-collision algorithm Based on bi-directional Binary Exponential Index

3 Mathematical Analysis

From the model of the algorithm it can be seen that the state of the tag is stochastic, and the state from this interval to next interval will stochastically change according to some probability, and the state of next interval only lies in the state of this interval and the transfer probability. Therefore the model of this algorithm is a typical model of Markov chain.

Additionally, the final aim of the tag is to be identified by the reader, and once being identified it will keep silent. So, this Markov chain is an absorbing chain.

3 Mathematical Analysis

Converting the time into discrete intervals, for each m (m=0,1,2,…), the state of the tag is expressed as the stochastic variable .

mTR

lnmTR l

lp

Obviously, the commonly process of the reader identifying the tags is that there are tags in each state of , and the tags in this state will answer at the probability .

ln

mTRl lpmTR

l

is the number of the tags whose tag state variable is ; is the probability of the tags whose tag state variable is .

mTR i 1mTR j 1( | )ij m mq Q TR j TR i From to the probability marks as that is the transfer probability.

mTR( ) ( )i ma m Q TR i

mTRAssume the has k discrete values ( =1,2,…,k), and marks that , that is the state probability.

3 Mathematical Analysis

1coll idle sucp p p The probability of the channel collision:

111

1 1,

( (1 ) (1 ) )l i

kkn n

suc l l l il i i l

p n p p p

The probability of the channel successfully identifying a tag:

(2)

1

1

(1 ) i

kn

idle ii

p p

The probability of idle channel: (1)

3 Mathematical Analysis in the situation that the channel successfully

identified a tag, the probability of this tag coming from the state is:

(3)mTR l

11

1,( / ) 11

1

1 1,

(1 ) (1 )

( (1 ) (1 ) )

l i

m

l i

kn n

l l l ii i l

TR l succ kkn n

l l l il i i l

n p p p

pn p p p

1 l k

( / ) ( / )( 1) (1 )(1 0)

0 (1 0)

m ml suc TR l succ l suc TR l succl

l l

l

n p p n p pl k and n

u n

l k and n

＝

the probability that tags whose state is are still in state （ ） in the next interval is :

(4)

mTR l

3 Mathematical Analysis

( 1 1)

( 1)

( 1 )

idle

ij i

coll

p i j and j k

q u i j and j k

p i j and j k

1

2

2

According to the principal of the bi-directional binary exponential index and the adjustable rules of the tags answering probability, we can get that:

(6)

( / )11 0)

0 1 0)

msuc TR l succl

l l

l

p pl k and n

v n

l k and n

（

（

The probability that tags, whose state are , are in state （ ） in the next interval is:

(5)

lnmTR l

k 1mTR k

3 Mathematical Analysis

Therefore, the state transfer matrix of the algorithm is:

(8)

1

1

( 1 1)

( 1)

0 ( | 2 , [1, 1])

0 ( 1)

( 1 1)

1 ( )

idle

i

ij

k coll

u p i and j

v j k and i k

i j and i j kq

i k and j k

u p i k and j k

i k and k

1

|

1

j

11 12 13 1 1 1

21 22 23 2 2 2

31 32 3

1

1 2

, 0 0

, , ,0

0 ,

, ,

k idle coll

k idle coll

idle

idle k coll

k k kk

q q q q u p p

q q q q p u p

q q p uQ

p u p

q q q

v， ， ， ，，v， ， ，

， ，＝

，1

0 0, 0 0 1kv

， ，，

Additionally:

(7)

3 Mathematical Analysis

1

( 1) ( ) 1,2, ,k

i j jij

a m a m q i k

＋ ，

Therefore, if the original state has been presented, the state of any interval m can be calculated by the expressions （ 8 ）～（ 11 ） , and the intervals that the system need to identify all the tags can be calculated, then we can know the efficiency of the identification.

( 1) ( )a m a m Q Then the basic equation （ 9 ） can be expressed as: (11)

1 2( ) ( ( ), ( ), , ( ))ka m a m a m a m The state probability vector (row vector) is used as the following: (10)

The basic state probability equation of the model is:

(9)

4.The Simulated Analysis of the Algorithmic

Model

The difference of this algorithmic model to common Markov chain model is that: of different states at different intervals will dynamically change, it will result in that the value of transfer matrix is different at different interval, therefore the analysis of the efficiency can’t be deduced directly from the mathematical way. So we used the experimental measure and the computer simulation to analyze some typical applied example.

ln

In the following analysis of the model, it assumes that is twelve, the result is the average value after the model run ten thousand times.

k

4.1tags entering dynamically by the linear function

in the rapid operative product line,the process of the tags passing the reader can be abstracted as the linear function:

presents the discrete interval

s n t t

Firstly, it assumes that the linear velocity of the tags entering is 0.1 、 0.15 、…、 0.95 、 1 、 2 、…、 10 in turn, the total number of tags is 20, the original answer probability of tags is = 1/16 . Its identified probability , which is equal to the total number of tags, comparing to the total number of consumed intervals is showed in the figure 3:

4pefficp

in the begin, the velocity of tag entering is low and the is comparatively low;

00. 050. 1

0. 150. 2

0. 250. 3

0. 35Peffic

n

Figure 3 the identifying efficiency that the linear velocity n changes

efficp

This indicated that this algorithm has a strong self-adaptability.

efficpafter that the dropped little, and finally kept at 0.321. The reason is that the probability of tags can diffuse dynamically according to the congested situation of current signal channel; consequently the whole capability of reader can stay in the saturated state.

efficpwith the velocity of tag increasing, the was improved gradually and reached the culmination 0.3273 while n is 0.4;

Figure 4 the identifying efficiency that the number of tags change

00. 050. 1

0. 15

0. 20. 250. 3

0. 35

5 45

85

125

165

205

245

285

325

365

405

445

485

Peffic

tags

It can be seen from figure 4 that: along with the number of tag increasing, the identifying efficiency of reader didn’t decrease and stabilized at 0.322. This also indicated that this algorithm was very stable.

Secondly, it assumes that the linear velocity of the tags entering is 0.35, the total number of tags is 5 、 10 、…、 500 in turn, the original answering probability of tags is , the identified probability is showed in the figure 4:

4.2 tags entering abruptly by impulse

function There will be the situation that a batch of tags enter

abruptly, that can be abstracted as impulse function:

m is the discrete interval

( )s n m

It assumes that the original answering probability of tags is ,the number of tags is 5 ～ 500, the successfully identifying probability is showed in the figure 6:

4pefficp

Figure 6 the identifying efficiency that the number of tags change

0

0. 1

0. 2

0. 3

0. 4

0. 5

5 50

95

140

185

230

275

320

365

410

455

500

Peffic

tags

It can be seen From figure 6 that: while the tags enter abruptly, the efficiency was the highest in the range of 36.2~41.3% when n was lower than 15. Thereafter, the efficiency decreased slowly while the number of tags increasing; but it decreased by a certain value, the efficiency didn’t decrease with the number of tags increasing, and finally stabilized at 0.322.

Assuming the number of tags is 20, the original answering probability of tags is , the changes from 0.3 to 0.95, the successful identifying probability is showed in the figure 7:

0. 3430. 3440. 3450. 3460. 3470. 3480. 3490. 35

0. 3510. 352

Peffic

P1

Figure 7 the identifying efficiency that the P1 changes from 0.3 to 0.95

It can be seen from figure 7 that :while the is 0.45 ～0.75, the efficiency was the highest and above 0.35, when the original answering probability of tags was in the two side value, the efficiency was a little lower; the fluctuating range didn’t exceed 1.43%.

1p

4p 1pefficp

5 Conclusion

From our analysis, the features of this algorithm included:

(1) In the ideal static state, the efficiency of this algorithm was lower than that of tree searching algorithm, but was higher than that of dynamic slotted- ALOHA algorithm.

(2) In the dynamic situation, the efficiency of this algorithm was higher than that of dynamic slotted-ALOHA algorithm, and extraordinarily higher than that of tree searching algorithm.

5 Conclusion

(3) The performance of this algorithm was very stable. While tags entered with different original answering probability, the efficiency of identification fluctuated little. When the number of tags increased greatly, the efficiency of identification dropped slowly in the beginning, but quickly attained to a stable value and didn’t decrease again, unlike that of the ALOHA algorithm drops sharply.

(4) This algorithm is impartial to all the tags. The case that while adopting the binary exponential backoff algorithm in the IEEE802.3 protocol the tag entering latter will be identified firstly didn’t exist. Selecting the original answering probability properly, it is useful to form the situation that the one entering first is identified first. This is also superior to the all-equal service of the ALOHA algorithm.

THANKS!