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# Rfid presentation in internet

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### Rfid presentation in internet

1. 1. RFID Anti-collision algorithm Based on Bi-directional Binary Exponential Index YU Song-sen, ZHAN Yi-ju, WANG Yong- hua
2. 2. Contents  1.Introduction  2.Algorithm Principle  3.Mathematical Analysis  4.The Simulated Analysis of the Algorithmic Model  5.Conclusion
3. 3. 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.
4. 4. 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 trequest 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)
5. 5. 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 q p q − ∈ L L 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.
7. 7. 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 t ags Answer i ng pr obabi l i t y TRk r eader Fig.2 Anti-collision algorithm Based on bi-directional Binary Exponential Index
8. 8. 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.
9. 9. 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 ln mTR 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 mTR l 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= = mTRAssume the has k discrete values ( =1,2,…,k), and marks that , that is the state probability.
10. 10. 3 Mathematical Analysis 1coll idle sucp p p= − − The probability of the channel collision: 11 1 1 1, ( (1 ) (1 ) )l i kk n n suc l l l i l i i l p n p p p −− − = = ≠ = • • − • −∑ ∏ The probability of the channel successfully identifying a tag:  (2) 1 1 (1 ) i k n idle i i p p − = = −∏  The probability of idle channel:  (1)
11. 11. 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= 1 1 1, ( / ) 11 1 1 1, (1 ) (1 ) ( (1 ) (1 ) ) l i m l i k n n l l l i i i l TR l succ kk n n l l l i l i i l n p p p p n p p p − − = ≠ = −− − = = ≠ • • − • − = • • − • − ∏ ∑ ∏ 1 l k≤ < ( / ) ( / )( 1) (1 ) (1 0) 0 (1 0) m ml suc TR l succ l suc TR l succ l l l l n p p n p p l k and n u n l k and n = =− • • + • • − ≤ < × × ≠ =   ≤ < × × L LLL ＝ the probability that tags whose state is are still in state （ ） in the next interval is : (4) mTR l=
12. 12. 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 = + × × ≤ < −  = = × × ≤ < −  = − × × ≤ < LL LL LL 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) ( / )1 1 0) 0 1 0) msuc TR l succ l l l l p p l k and n v n l k and n =• • ≤ < × × ≠ =   ≤ < × × = LL LLL （ （ The probability that tags, whose state are , are in state （ ） in the next interval is: (5) ln mTR l= k 1mTR k+ =
13. 13. 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 k q i k and j k u p i k and j k i k and k − + = × × =  = × × ≤ ≤ −  − ≥ × × ∈ − = = × × ≤ ≤ −  + = − × × = −  = × × = LL LLLL LLLL LLLL L LLLL 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 u Q p u p q q q − +        =       +      LL LLL LL LLLL OLLLM OLLLLLLM MLLLLOLLM LLLLOLLLLLLLM MLLLLLOLM MLLLLO LLLL ， ， ， ，，v ， ， ，v ， ， ＝ ， 1 0 0, 0 01 kv −                   LLLLLLLLL， ，， Additionally: (7)
14. 14. 3 Mathematical Analysis 1 ( 1) ( ) 1,2, , k i j ji j a m a m q i k = = =∑ L＋ ， 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= L The state probability vector (row vector) is used as the following: (10) The basic state probability equation of the model is: (9)
15. 15. 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
16. 16. 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: 4p efficp
17. 17.  in the begin, the velocity of tag entering is low and the is comparatively low; efficp This indicated that this algorithm has a strong self-adaptability. efficpafter 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. efficpwith the velocity of tag increasing, the was improved gradually and reached the culmination 0.3273 while n is 0.4;
18. 18. 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:
19. 19. 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 mδ= •  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: 4p efficp
20. 20. 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.
21. 21.  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: 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 1p efficp
22. 22. 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.
23. 23. 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.
24. 24. THANKS!