The Optimization of Framed Aloha based RFID Algorithms

Transcription

1 The Optimization of Framed Aoha based RFID Agorithms Lei Zhu The Chinese University of Hong Kong Shatin, ew Territory Hong Kong, China Tak-Shing Peter Yum The Chinese University of Hong Kong Shatin, ew Territory Hong Kong, China ABSTRACT The anti-coision mechanism is a very important part in Radio-frequency Identification RFID systems. Among a the agorithms, the Framed Aoha based FA ones are most widey used due to simpicity and robustness. Previous works mainy focused on the tag popuation estimation, but determined the reading strategy based on the cassica resuts of Random Access RA systems. We show that a new theory is needed for the optimization of the RFID systems as they have characteristics very different from the RA systems. In this paper, We propose a new approach to minimize the tota expected reading time by choosing the most suitabe frame size based on the tag popuation distribution. We show that the optima strategy can be used in different appications. The mathematica anaysis and computer simuation show our approach outperforms the previous optimization works in the iterature. Categories and Subject Descriptors F.. [Anaysis of Agorithms and Probem Compexity]: onnumerica Agorithms and Probems; G.3 [Probabiity and Statistics]: Distribution functions, Markov processes Genera Terms Agorithms, Design, Performance, Theory Keywords Agorithm, RFID, Framed Aoha, Optimization 1. ITRODUCTIO In Radio-frequency Identification RFID systems, tags share a common communication channe. Therefore, if mutipe tags transmit at the same time, their packets wi coide and get ost [1]. Passive tags have bare-bone functionaity and no embedded power suppy. They cannot sense the media or cooperate with one another. The RFID reader needs to coordinate their transmissions to avoid coisions. The communication time between tags and readers are sotted. But Permission to make digita or hard copies of a or part of this work for persona or cassroom use is granted without fee provided that copies are not made or distributed for profit or commercia advantage and that copies bear this notice and the fu citation on the first page. To copy otherwise, to repubish, to post on servers or to redistribute to ists, requires prior specific permission and/or a fee. MSWiM 09, October 6 9, 009, Tenerife, Canary Isands, Spain. Copyright 009 ACM /09/10...$ Figure 1: and tags The communication between the reader unike CSMA system, tags need to reserve the channe before transmission. The tota communication time therefore incudes the contention time and the operation time. To iustrate, consider the tag reading operation in EPCgoba standards [] as shown in Figure 1. Within a contention sot, the reader broadcasts a trigger command Query or QueryRep. After receiving this command, each tag runs a random function to decide whether to repy or not. Tags ony repy a short packet named R16 random number 16 bits. It is used as the temporary ID for this tag. If mutipe tags repy or no tag repies, the reader sends an trigger command again. If ony one tag repies, the reader can receive the packet successfuy and operate on this tag by its R16 after this sot. The operation may incude reading data, writing new data, changing password, etc. Since the operation sot is coision-free, the tota operation time does not depend on the reading strategy. Therefore, the performance of anti-coision agorithms is conventionay evauated by the average contention time measured by the number of contention sots. In iterature, the sot usuay refers to the contention sot whie the reading time usuay refers to the contention time measured in contention sots. foow this convention in this paper. We Depending on working principes, RFID anti-coision agorithms can be divided into three main types: Tree based agorithms [5][6], Framed Aoha based FA agorithms [8-16] and Interva based agorithms [7]. Different types usuay require different hardware and software design of both the reader and the tags. Among a the types, FA agorithms are most widey used in RFID communication standards [- 4] due to simpicity and robustness. In most appications, the number of tags are unknown before identification. So a proper FA agorithm aways contains two parts: Popuation Estimation part and Reading Strat- 1

2 egy Determination part. The first part is for estimating the tag popuation based on tags repies whie the second part is for adjusting the command parameters, such as the frame size, based on the estimation. Previous works [8-16] emphasized Popuation Estimation methods and designed reading strategies based on the cassic resuts of Random Access RA Systems [10]. Since RFID systems and RA systems are fundamentay different the detais are in section 3, the use of RA resuts wi not ead to the optima reading strategy in RFID systems. In this paper, we mode the reading process as a Markov Chain and derive the optima reading strategy through first-passage-time anaysis. We show that the optima strategy can be easiy incorporated into the different appications to give significant performance improvement, especiay when the variance of tag popuation is arge. In section, we introduce the basic ideas of the FA agorithms. In section 3, we give a survey of the traditiona strategies of FA agorithms and point out an unjustified assumption used in previous attempts of reading strategy optimization. In section 4, a new mode is proposed to derive the optima reading strategy. In section 5, we show the appications of the optima strategy and compare its performance with the previous works.. FRAMED ALOHA-BASED RFID SYSTEMS Framed Aoha FA is a variation of sotted Aoha where a termina is permitted to transmit once per frame. The frame size L is broadcast by the reader at the beginning of every round; each tag randomy chooses a vaue from 0 to L 1 as its transmission deay. In RFID systems, the FA agorithms have some specia characteristics..1 Limited Choices of Frame Size Many RFID systems have imitations on the choice of frame size due to hardware constraints. For exampe, in EPCgobe standards, it is imited to ony 16 choices as Q,whereQ = 0, 1,,...,15.. Sience Command In the origina design of FA agorithms, tags do not know their transmission resuts as there is no feedback from the reader. They wi a transmit again in the next round of contention. Readers have difficuty ascertaining the end of the reading process as some tags may suffer coisions again and again tag starvation probem. This situation was changed by the introduction of the Sience Command 1 in EPCgobe standards. After identifying a tag, the reader wi broadcast its ID and ask it to keep sient..3 Reset Command As in Figure 1, the RFID reader has to broadcast a Trigger command in every time sot because tags need to extract power from the command signa to repy. The reader consequenty does not have to wait unti the end of a frame to change the repy probabiity by setting the appropriate frame size. Some designs introduce the Frame-size Reset 1 It is aso referred to as Ki command in iterature. In EPCgobe standards, it corresponds to the Seect command, which have other uses besides siencing a tag. Figure : The working mechanism of Type 4 Aohabased agorithms command to cance a running frame and initiate a new one..4 Spit Command Some FA agorithms [8] have the Spit Command of Treebased agorithms embedded. After a frame of reading, the reader may choose to initiate a new frame or just spit the coided sots. The reading process of agorithms embedded with the Spit Command is iustrated in Figure. This was shown to improve the performance at the expense of hardware compexity..5 Cassification of RFID Systems Depending on the tag-reader capabiity, or the set of commands supported, the RFID systems for FA agorithms can be cassified into four types as foows: 1: support ony Framed Aoha; : support Framed Aoha with Sience Command; 3: support Framed Aoha with Sience and Reset Command; 4: support Framed Aoha with Sience and Spit Command. ote the term Type RFID system refers to an RFID system hardware and software which supports a certain set of commands whie the term Type agorithm refers to a reading strategy which determines when and how to use these commands. In this paper, we wi focus on the Type RFID system, which is simpe enough and reativey efficient. In EPCgoba standards, it corresponds to the QueryAdjust command.

3 3. A SURVEY OF PREVIOUS WORKS FA agorithms are widey used in random-access systems. The cassica resut for throughput U with attempting terminas and frame size L is given in [10] as: U,L = L 1 1 L 1. 1 The throughput U can be optimized by setting the frame size equa to the termina number, or L =. The bound for arge is U = e 1. However, in RFID systems, the precise vaue of is usuay not avaiabe. Hence the throughput depends on the estimate of from tag repies. During the reading process, the reader can estimate the tag popuation based on the outcomes of the sots: whether they are empty, singeton or coided. There is usuay a misunderstanding that the reader shoud use severa frames of contention sots to estimate the tag popuation before the rea reading process starts. Actuay, it is ony usefu for the earier RFID systems, which do not support the reservation mechanism. Since the coision of the operation sots woud waste more time, the earier strategies prefer to use a sequence of training sots short sots to estimate the tag popuation and use it to set the frame size of the operation sots. However, in modern RFID systems, a singeton contention sot can reserve an operation sot. Tags can be identified whie the reader is doing estimation. Thus the training sequence approach is abandoned. Most agorithms do estimation throughout the reading process. Based on the estimation methods, agorithms can be divided into: the max-ikeihood approach and the probabiity distribution approach. 3.1 Max-ikeihood Approach Schoute [10] noticed that when is arge and L is suitaby chosen say L, the number of tags attempting each sot has a Poisson distribution with mean 1. The number of coided tags C at the end of a frame can be estimated as: C = round.39s c where s c is the number of coided sots in the frame. Therefore his strategy is to set L = round.39s c as the next frame size. Vogt [11] improved Schoute s strategy by using the statistics of empty sots s e and singeton sots s s in addition. Tag popuation is estimated to be the vaue that minimizes the error between the observed vaues of s e, s s, s c and their expected vaues using. Kodiaam [16] proposed an new estimation method based on the Centra Limit Theorem. That is when the number of contending tags is arge enough, the number of coision sots and empty sots in the current frame shoud obey the orma distribution. Thus using his method, one may obtain the estimation accuracy as we as the max-ikeihood tag popuation. But the frame size is aso set as L = E[]. Another exampe is the Q agorithm in EPCgoba standards []. The reader maintains a foating-point variabe Q fp. It decreases a typica vaue C when no tag repies, increases C when mutipe tags repy and stays unchanged when ony 1 tag repies. 3 The frame size is set to Q,where Q = roundq fp and wi be canceed whenever roundq fp changes. In [13][14], the efficiency of the Q agorithm was obtained with different choices of C and Q fp and some methods to improve efficiency were proposed. In summary, agorithms of this type compute the maximumikeihood tag popuation ˆ based on the reading resuts and set L = ˆ as the frame size. This approach is simpe but rough, as the expectation ony cannot fuy describe the variabe. 3. Probabiity Distribution Approach Foerkemeier [1][15] designed some new strategies based on 1. He assumes that a rough estimation of the target group size is aways avaiabe in the form of a distribution Pr = i and derives the next frame size as max L = L :max U = i, LPr = i, 3 L Υ i=0 where Υ is the set of possibe frame sizes. In every time sot, the reader updates the distribution by Bayesian method and cances the current frame whenever L changes according to 3. This approach can track the vaue of more accuratey. Since a random variabe is competey specified by its distribution and Bayesian method ensures no information oss in estimation, the Popuation Estimation part of Foerkemeier s agorithm is undisputabe, but the use of 1 in the Reading Strategy Determination part is unwise. 3.3 The eed for a ew Mode From this review, we can see that previous works focused on the Popuation Estimation, providing different ways to find a more accurate. For the Reading Strategy Determination part, they a use 1 for cacuating throughput. As we mentioned before, 1 is obtained from the theory of Random Access RA system. In RA system, the frame size is chosen to optimize the instantaneous throughput U. Sincea termina in an RA system woud sti attempts the channe after a successfu transmission, the contending group can be assumed unchange during a ong enough period. The ong-term throughput of a RA system is therefore equa to the expected instantaneous throughput U cacuated by 1. However, in RFID systems, identified tags are sienced by the reader, eading to tag popuation decrease during the reading process. When the frames are not identica, a concatenation of ocay optima soutions is not gobay optima. As an exampe, suppose the target group size is distributed as Pr = i = 0.99, i =0 0.01, i =10 From 3, the suitabe frame size shoud be L = 10, as it can maximize the throughput of the current frame. However, since this group is very ikey empty, it is better to use L =1 to check whether it contains tags or not even though the throughput of this checking frame is 0. 3 In EPCgobe standards, it is recommended that 0. C 0.5 and the initia Q fp =4 3

4 4. READIG STRATEGY OPTIMIZATIO We now present our method to find the gobay optima frame size. This method can be used for a types of FA agorithms. In this paper, We use the Type agorithm to iustrate. 4.1 The Optima Reading Strategy Since canceing a frame is not aowed in Type agorithms, the reading strategies are restricted to the choice of the next frame size. To choose a suitabe frame size L, thereader needs the information of the target group size. As discussed in Section 3, this information can be fuy described by a probabiity distribution. In appications, a rough distribution is often avaiabe as the reader has information of its previous readings. In the worst case where is competey unknown, a uniform distribution on [0, max] can be assumed as we cannot favor any vaue over the others. During the reading process, et Be denotethebeief of, or the conditiona distribution of based on a avaiabe information [17]. At the end of every frame, the beief can be updated by the Bayesian method [17]. To simpify the notation, et v n = Be = n andv =v 0,v 1,...,v max. Obviousy the accuracy of the beief affects the reading efficiency. Let T n v denote the expected contention time, measured by sots, for these n tags when the current beief is v. Then the expected finishing time is T v = max n=0 v nt n v. Our goa is to find the optima frame size L that can minimize T v for any given distribution v, or L = L : L Υ, mint v L. 4 ote 4 is different from 3 as it is designed to minimize the expected reading time T v instead of the expected instantaneous throughput U. ThusL is the gobay optima frame size. To find it, however, requires deriving the function of T v from the reading mechanism of Type agorithms. denote the set of a possibe states. For a group with the initia estimation P, et V 0 = P be the initia state and V T =1, 0, 0,...,0 be the termina state. Theorem 1. Foowing a distribution-based anti-coision agorithm, the reading process V 0V 1V...V T is a Markov Chain. Proof. At the end of frame j, etv j =v 0,v 1,...,v max V be the current state. For a distribution-based agorithm, the next frame size shoud be fixed given V j. Let V j+1 = u 0,u 1,...,u max be the beief of tag popuation at the end of frame j + 1. Obviousy it depends on the reading resuts of frame j + 1 as we as the previous beiefs. In frame j + 1, et random variabe S 0,S 1,S c denote the number of empty sots, singeton sots and coided sots. It can be proved that the position of the empty sots, singeton sots and coided sots does not matter and ony their tota numbers affect the beief. Since S 0 + S 1 + S c =, thereare at most = different outcomes. Thus for a given frame size, there are at most different choices of V j+1 that satisfy PrV j+1 V j > 0. Anaogous to the urn probem [18], the probabiity that s 1 urns contain ony 1 ba, s c urns contain more than 1 bas and the others are empty can be obtained as: PrS c = s c,s 1 = s 1 j = n, L = = s 0,s 1,s c n! n s 1! n m 1,m,...,msc, m 1 +m + +msc=n s 1 n s 1, m 1,m,...,m sc 5 where m 1,m,...,m sc denote the number of tags in each of the s c coided sots. Further, we can substitute the beief of j to obtain = PrS c = s c,s 1 = s 1 L = max n=0 v n PrS c = s c,s 1 = s 1 j = n, L =. 6 In an inteigent system, the optima decision depends ony on the current information, or the beief of a the reevant variabes [17]. Appying to RFID systems, the optima frame size depends ony on Be. 4 We et V j = Be j = v 0,v 1,...,v max denote the state of the reading process at the end of frame j, where j is unresoved tag popuation at the end of frame j. Since identified tags are sienced by the reader, we aways have j j+1. Furtheret V = v 0,v 1,...,v max v i 0, max i=0 v i =1 4 ote it is important to differentiate the unconditiona optima and the optima based on current beief. As an exampe, suppose = 10, but our current beief is Be = 9 = 1. Then the unconditiona optima frame size is 10, but the optima frame size based on the current knowedge is 9. Since the unconditiona optima frame size is not avaiabe unti the reading process is finished, in this paper we ony consider the optima one based on current beief. At the end of frame j + 1, we can obtain the vaues of s 0, s 1 and s c. By Bayes formua, the posterior distribution of j can be updated as: v i = Pr j = i S c = s c,s 1 = s 1,L= = PrSc = sc,s1 = s1 j = i, L = vi PrS c = s c,s 1 = s 1 L = As tags in the singeton sots are successfuy identified and sienced, we have j+1 = j s 1 with distribution given as 7 u i = Pr j+1 = i S c = s c,s 1 = s 1,L= = Pr j = i + s 1 S c = s c,s 1 = s 1,L= = v i+s 1, i =0, 1,,... 8 Since the transition probabiity from state V j =v 0,v 1,...,v max to V j+1 =u 0,u 1,...,u maxisjustprs c = s c,s 1 = s 1 L =, which depends ony on V j and V j+1,thestatesv 0V 1V...V T forms a Markov Chain. 4

5 For a given state V j, et VV j, V denote the set of possibe V j+1, or VV j,= V j+1 PrV j+1 V j > 0. As proved in Theorem 1, V V j, Let T OV j denote the first passage time from V j to V T using the optima reading strategy. From the theory of Markov Chain [19], we have T O V j = L + = min V j+1 VV j,l + V j+1 VV j, PrV j+1 V j T O V j+1 PrV j+1 V j T O V j+1 9 In 9, the set VV j, and the transition probabiity PrV j+1 V j are given by 8 and 6. Theoreticay speaking, it can be soved to obtain the optima frame size L. In the foowing, we show how to sove 9 anayticay and numericay. 4. The Anaytica Soution of L In this section, we show how to sove 9 by some exampes. Since 9 is a recursive function, we begin from sma max cases 4..1 Case 1: max = In this case, the tag popuation can ony be 0, 1 or. Given V j = v =v 0,v 1,v, the probabiity of different outcomes of frame j + 1 can be obtained from 6 as: PrS c =0,S 1 =0 L = = v 0; PrS c =0,S 1 =1 L = = v 1; PrS c =0,S 1 = L = = 1 v ; PrS c =1,S 1 =0 L = = 1 v. From 7 and 8, we get the distribution of j+1 as Pr j+1 =0 S c =0,S 1 = s 1,L= =1; Pr j+1 = S c =1,S 1 =0,L= =1. Thus V j+1 has ony two possibe choices as VV j,= 1, 0, 0, 0, 0, 1 and the transition probabiity is Pr 1, 0, 0 v 0,v 1,v = 1 v + v 1 + v 0 Pr 0, 0, 1 v 0,v 1,v = 1 v Substituting them into 9, we have T Ov = min + 1 0, v TO 0, 1, 10 = min + 4v where T O 0, 0, 1 = 4 is the expected reading time for a group with exacty tags, which can be obtained in Case Figure 3: The soution set for max =3case 3. Sowehave L = T Ov = 1, v < 1, v 1 1+4v, v < 1 +v, v 1 To compare, we derived the frame size and average reading time of Foerkemeier s strategy from 3 as 1, v L = 1 >v, v 1 v 1+4v, v T f v = 1 >v +v, v 1 v Therefore, when the distribution v satisfies v 1 <v < 0.5, Foerkemeier s strategy is not optima. 4.. Case : max =3 ext, we move on to max = 3 and derive the recursive function as 1v3 1 T Ov =min + + v + v3 TOu, 11 where u is the distribution of j+1 on condition that S c =1 and S 1 =0inframej +1,or v v 3 u =u 0,u 1,u,u 3= 0, 0,,. v 3 + v v 3 + v Soving 11, the optima reading strategy can be simiary obtained as: L = T O v = 1, v Φ 1, v Φ 3, v Φ 3 1+v + v 3 T v3 x v +v 3 +3v v v + v 3 T 3 x v +v v v v + v 3 T 3 x 3v +v 3 where T x is a recursive function as T xα = 8, v Φ 1, v Φ, v Φ 3 α +4, 0 <α α αtx α 9, <α<1 3 α 16 5

6 whie Φ 1, Φ and Φ 3 are distribution regions specified in Figure 3. It shows that the choice of L is determined by v and v 3 instead of E[ A]. As an exampe, suppose Group X has tag popuation distribution as 0, 0.45, 0, 0.55 and Group Y0.4, 0, 0.5, 0.1. Their expected group size are cacuated to be E[ X]=.1 ande[ Y ]=1.3, but the optima frame size for Group X is 1 whie that for Group Y is. For max > 3 cases, the optima strategies can be obtained simiary. But the computation becomes more compex. efficiency RFID systems Random Access systems 4..3 Case 3: Tag Popuation known Let T n denote the average reading time for a group with tag popuation known as n, ort n =T Ov whenv n = 1. After one frame of reading, the popuation decreases to n = n s 1,wheres 1 is the number of singeton sots. So the remaining reading time is T n s 1. Substituting T n and T n s 1into9,wehave T n = min + s 1 s 1 =0 s c=0 PrS c = s c,s 1 = s 1 T n s 1. 1 The expicit form of the system equation after rearranging is T n = 13 s 1 + PrS c = s c,s 1 = s 1 T n s 1 s 1 =1 s c=0 min. 1 PrS c = s c,s 1 =0 s c=1 Soving 13, the optima frame size is obtained as L = n. The agorithm efficiency η = isshowninfigure4. We n T n can see that η decreases with n and approaches e 1,which coincides with the efficiency upper bound of Random Access systems [10]. 4.3 The umerica Soution of L Here, we introduce a method to compute the vaues of L by running a recursive program. From the ast section, we know for a group with known popuation k, the optima frame size is L = k and the average reading time is T k. It is easy to imagine for a group with tag popuation very ikey to be k, theoptima framesizeshoudasobel = k. In other words, if the distribution of satisfying: 1. v k >v i,wherei k and 0 i max, 1 k max;. Varv <δ,whereδ is a sma enough vaue, the optima frame size is sti L = k. If it does contain k tags, obviousy, the average reading time approaches T k when δ 0, or im δ 0 T k v =T k. Butifitcontains j tags, where j k, we et im δ 0 T j v = T k j j, tag termina popuation Figure 4: The efficiency of the Optima Type FA agorithm when tag popuation is known or T k j j is the average reading time for j tags starting with the wrong information that k. Averaging a these cases, we have max max im T v = im vjt j v = δ 0 δ 0 j=0 j=0 v jt k j j, 14 where T 0 j =T j forj = k. Simiar to the derivation in Case 3, the formua for T m can be obtained as: for m<0, + T m n = m 1 k=0 n+m S 1 =0 and for m 0, L + L X S 1 =1 S c=0 PrS c,s 1 L T m n S 1 PrS c = n S 1 k,s 1 L T k n S 1 X 1 1 PrS c = s c,s 1 =0 L, 15 s c=1 L + T m n = L L S 1 S 1 =1 S c=0 PrS c,s 1 L T m n S 1 L 1 PrS c,s 1 =0 L S c=1, 16 where L = m + n and X =minl S 1, n S 1. Limited by space, we skip the mathematica detais. With the above formuas, the computer program is designed as foows 5 : 5 This program is designed for S L = 1,, 3, 4,... case. If L is imited to the powers of, the program is simper. 6

7 Figure 5: State machine uniform distributed in [1, 5] ================================== Function [T v,l v]=optimaaohav // reaize9 if varv <δ // the stopping condition T v = T v; // using 14 L v = E[]; return; end if =rounde[]; T v = ; for L t = Δ : +Δ // numericay find L temp =0; for s 1 =0:L t for s c =1:L t s 1 Cacuate Prs c,s 1 L t from 6 Cacuate b from 7 and 8; [T u,l u]=optimaaohau; temp=temp+ Prs c,s 1 L tt u; end for end for ift v >temp T v=temp; L v = L t; end if end for ================================== The input is a vector v representing the distribution. The program first checks its variance. If it is smaer than a threshod δ our experiment shows δ 0.4 is enough, the optima frame size is E[] and the average reading time is cacuated from 14; if not, it is numericay resoved. Since the variance of the input distribution decreases as the program is recursivey used, the stopping condition wi be fufied after severa oops. For impementation, these resuts can be precacuated and stored in database. There is no need to do any computation during the reading process. For exampe, when tag popuation is uniformy distributed from 1 to 5, the optima strategy is shown in Figure 5 as a state machine. 5. APPLICATIO EXAMPLES In a modern supermarket where a the merchandize are tagged, customers just need to wak their carts through a door for a items to be identified. Let denote the num- Figure 6: The frame size for different vaue of α ber of items in one customer s cart. Athough the precise vaue of is usuay unknown, a distribution of is often avaiabe from the past saes statistics. For a given distribution, most of the previous agorithms cangivetheoptimaframesizewhenthevarianceof is sma. But when the variance of is arge, the frame size is often inappropriatey chosen. Here we use a simpe exampe to show that the optima agorithm we proposed sti works efficienty for arge-variance sampes. Consider an express check-out supermarket counter where each customer is aowed to checkout no more than 0 items, or 0. To iustrate the effect of popuation variation on reading performance, we set E[] = 10 and change the variance. Var[] = 0 when a customers buy exacty 10 items each. Var[] is maximized when haf of them buy 0 items whie the other haf buy nothing. In our experiment, we choose: 1 Pr = n = n 10 + Z 10α, 0 n 0, 0, others where Z is the normaization constant and α is a variabe. Thevarianceof A increase with α whie E[] = 10 is independent of α. Specificay, when α,var approaches 0; when α =0, is uniformy distributed in [0, 0]; and when α,var is maximum. ote that this distribution is chosen for simpicity. Other distributions we tried give simiar resuts. Foowing Schoute s and Vogt s strategies L = E[], the suitabe frame size is just 10 regardess the choice of α. 6 For distribution-sensitive agorithms Foerkemeier s agorithm and the Optima Type agorithm, the choices of frame size are isted in Figure 6. The frame size of both agorithms start with 10 for sma variance cases, but diverge to 0 and 1 respectivey as the 6 We do not simuate Kodiaam s agorithm [16], because in his agorithm the reader uses severa training frames to estimate tag popuation before the rea reading process starts. As mentioned in section 3, this is not efficient for modern RFID systems. Thus its reading time woud be much onger compared other agorithms. 7

8 Figure 7: The average reading time from simuation variance increases. Figure 7 shows the average reading time of four strategies from computer simuation the average of 1 miion sampes for each point as a function of Var. We observe: The performance of Schoute s and Vogt s agorithms are barey distinguishabe. Foerkemeier s agorithm is marginay better than Schoute s when α<, or Var < 4 but poorer when above. The Optima Type agorithm is the best for a vaues of α and the performance gain increases with the variance of tag popuation; The minimum performance gain is obtained at α, orvar = 0, where the average reading time of the Optima Type agorithm is 4. sots, the same as that of Foerkemeier s agorithm. The maximum performance gain is obtained at α, where the average reading time of the Optima Type agorithm is reduced from 35.3 sots to 6.3 sots when compared to Foerkemeier s agorithm. The Optima Type agorithm is ony marginay better for sma variance cases, because it is usuay easier to find the suitabe frame size when the target group size does not change dramaticay. However, as the variance increases, traditiona agorithms fai to make suitabe choices whie the optima agorithm can sti work efficienty. Since the sampes to identify usuay have arge variance in rea appication, the improvement is considerabe. 6. SUMMARY In this paper, we proposed a new optimizing method for Framed Aoha based RFID anti-coision agorithms. It makes gobay optima decisions based on the current information. The optima parameters can be obtained by running an iterative program and adopted to different appications. Simuation resuts show that significant improvement was obtained, especiay when the variance of tag popuation is arge. 7. ACKOWLEDGMETS This work was partiay supported by the Competitive Earmarked Research Grant Project umber CUHK estabished under the University Grant Committee of the Hong Kong Specia Administrative Region, China. 8. REFERECES [1] K. Finkenzeer. RFID handbook - Second Edition. JOH WILEY & SOS, 003. [] EPCgoba. EPCgoba Cass 1 Generation UHF Air Interface Protoco Standard Version 1.0.9, [3] Internationa Organization for Standardization. Information technoogy - RFID for item management - Part 6: Parameters for air interface communications at 860 MHz to 960 MHz, 004. [4] Phiips Semiconductor. I-CODE1 Labe ICs Protoco Air Interface Datasheet, January 005. [5] J. Myung, W. Lee, J. Srivastatva, T.K. Shih. Tag-Spitting: Adaptive Coision Arbitration Protocos for RFID Tag Identification. IEEE Transactions on Parae and Disitributed Systems, Vo 18, o.6, June 007. [6] K.W. Chiang, C.Q. Hua and T.S.P. Yum. Prefix-Randomized Query-Tree Protoco for RFID Systems. IEEE ICC, 006 [7] P. Popovski, F.H.P. Fitzek, R. Prasad. Batch Confict Resoution Agorithm with Progressivey Accurate Mutipicity Estimation. ACM DIALM-POMC Oct [8] J.Park, M.Y. Chung and T.J. Lee. Identification of RFID Tags in Framed-Sotted ALOHA with Tag Estimation and Binary Spitting, Communications and Eectronics, 006 [9] J. Mosey, P.A. Humbet. A Cass of Efficient Contention Resoution Agorithms for Mutipe Access Channes. IEEE Transactions of communications, Vo. Com-33, o., Feb [10] F.C.Schoute. Dynamic Frame Length ALOHA. IEEE Transactions on Communications, COM-314: , Apr [11] H. Vogt. Efficient Object Identification with Passive RFID Tags. First Internationa Conference, PERVASIVE 00, voume 414 of Lecture otes in Computer Science LCS, pages , Zurich, Switzerand, August 00. Springer-Verag. [1] C. Foerkemeier. Transmission contro scheme for RFID object identification. Proceedings of the Pervasive Wireess etworking Workshop at IEE PERCOM 006, Pisa, Itay, 006 [13] B. Zhen, M. Kobayashi, M. Shimizu. Framed Aoha for Mutipe RFID objects Identification. IEICE Transactions of comminication. Vo.E88-B, o.3, March 005 [14] M. Buettner, D. Wethera. An Empirica Study of UHF RFID Performance. MobiCom, San Francisco, Caifornia, USA, 008 [15] C. Foerkemeier. Bayesian Transmission strategy for Framed ALOHA Based RFID Protocos. IEEE Internationa Conference on RFID, GayordTexanResort, Grapevine, TX, USA, March, 007 [16] M. Kodiaam, T. andagopa. Fast and Reiabe Estimation Schemes in RFID Systems. MobiCom, Los Angees, Caifornia, USA, Sepetember, 006 [17] J. Pear. Probabiistic Reasoning in Inteigent Systems: etworks of Pausibe Inference, Morgan Kaufmann Pubishers. [18] W. Feer. An Introduction to Probabiity Theory and Its Appications, Second edtion, Vo I, John Wiey. [19] S.M. Ross. Introduction to Probabiity Modes, Seventh Edition, Chapter 6, Academic Press. 8