CSMA Multi-stage Anti-collision Protocol for Active

RFID Systems

Alejandro Palomo-L´opez, M. Victoria Bueno-Delgado, Esteban Egea-L´opez

Juan J. Alcaraz-Esp´ın and Javier Vales-Alonso

Department of Information Technologies and Communications

Technical University of Cartagena

Plaza del Hospital 1, 30202, Cartagena, Spain

Abstract. Current anti-collision protocols for active RFID systems stem from

the ISO-18000-7 standard, which selects Frame Slotted Aloha as the underly-

ing Medium Access Control protocol. However, these approaches neglect the

possibility of using the Listen-Before-Talk mechanism already available in ac-

tive RFID tags. In this work, a Carrier Sense Multiple Access mechanism with

Multi-Stage, (CSMA/MS), derived from the quasi-optimal Sift distribution, is de-

veloped in order to substitute the anti-collision procedure in active tags. The key

of CSMA/MS is to concatenate various contention windows, where only win-

ners contend in the next contention windows. We demonstrate that this approach

nearly achieves a 100% of identiﬁcation probability per slot, improving Sift re-

sults and outperforming standard procedure.

1 Introduction

Radio Frequency Identiﬁcation (RFID) systems are one of the enabling technologies for

the ubiquitous computing paradigm [1]. Its foreseen applications cover from replace-

ment of bar-code systems to location of containers in large cargo vehicles. All of them

share a common architecture: a basic RFID cell consists of a reader device and a (po-

tentially large) set of RFID tags, which reply to the queries or enforce the commands

from the interrogator. RFID devices are classiﬁed according to the source of energy

of the tags: passive ones do not have a power source and obtain the energy from the

reader signal (via induction), whereas active ones incorporate their own battery. On the

one hand, passive tags are targeted to be inexpensive and, thus, very simple, usually

read-only, devices. Their coverage typically ranges from centimeters to a couple of me-

ters. On the other hand, active tags are more complex devices, with more sophisticated

capabilities (usually integrating a microprocessor and memory) and they can be read

and written from distances in excess of 100 meters [1]. Whereas passive RFID sys-

tems are the most deployed and have been studied for years [2–4], active RFID systems

have recently been standardized [5] using Frame Slotted Aloha (FSA) as the underlying

medium access control mechanism.

Palomo-LÃ¸spez A., Bueno-Delgado M., Egea-LÃ¸spez E., Alcaraz-EspÃ n J. and Vales-Alonso J.

CSMA Multi-stage Anti-collision Protocol for Active RFID Systems.

DOI: 10.5220/0003051900660078

In Proceedings of the 4th International Workshop on RFID Technology - Concepts, Applications, Challenges (ICEIS 2010), page

ISBN: 978-989-8425-11-9

In both cases, the tag collision problem arises: in a RFID cell, if multiple tags are

to be identiﬁed simultaneously, reply messages from tags can collide and cancel each

other. Thus, an anti-collision mechanism is needed. Since, in a typical application, items

(with attached tags) enter and leave the reader coveragearea, the goal of this mechanism

is to communicate with the tags as quickly and reliably as possible, ensuring that all

tags have been identiﬁed. An additional goal for active tags is to save energy in order

to maximize the battery lifetime. Therefore, the tag identiﬁcation problem deals with

identifying multiple objects with minimal delay and power consumption, reliability,

line-of-sight independence and scalability. Unlike classical medium access protocols,

channel utilization and fairness are not usually issues in RFID systems.

DATA

1 2 k

...

Slot

Contention micro-slots

Fig.1. General identiﬁcation procedure in CSMA.

In a previous paper [6], we proposed the use of non-persistent Carrier Sense Mul-

tiple Access (CSMA) as anti-collision mechanism for active RFID tags. This protocol

can be seamlessly integrated with current active tags, since they already include the

Listen-Before-Talk capability. In this case, time is divided in slots (see Figure 1) which

include contention periods. During the contention period tags select a contention micro-

slot, and transmit their identities only if medium is empty. Contention winners (note that

if there is more than one winner a collision takes place and that tags are not aware of si-

multaneous transmissions) continue transmitting their identiﬁcations in the data period.

Our performance evaluation shown that using a classical uniform distribution for

contention micro-slots do not necessarily improves the identiﬁcation process. However,

performance is greatly improve if the micro-slot selection is based on the optimal dis-

tribution CSMA/p

∗

proposed by Tay et. al in [7]. In this work authors determines the

best probability distribution assignment if the number of contenders is known. Never-

theless, in a general situation, this parameter is unknown. Therefore, in [7] is already

proposed a distribution named Sift which nearly approximates the optimal one, and

which depend only on a maximum boundary for the number of competitors. Both dis-

tributions outperform the FSA mechanism used in active RFID systems in performance

and scalability.

The new proposal is called CSMA/Multi-Stage (henceforth, CSMA/MS) and it is

based on the concatenation of several micro-contention windows before data transmis-

sions, where only contention winners transmits in the successive windows. In this work

we show that, for an equal overall number of contention micro-slots, even though the

optimal distribution and its approximation are able to achieve almost 96% of trans-

mission success in each slot, CSMA/MS improves further the identiﬁcation process,

achieving 99% of success and, more importantly, providing linear identiﬁcation time

with the number of tags. That is, our proposal scales well to large sets of tags. Let us

remark that the optimal distribution itself cannot be improved obviously, but, combined

with the efﬁcient splitting procedure proposed the overall identiﬁcation process im-

proves. The key difference is the following: the goal of the optimal distribution p

∗

is to

minimize the latency of the ﬁrst few successful transmissions in an event-based trafﬁc

pattern, whereas in an RFID system the goal is to minimize the collision probability of

all the transmissions. The optimal distribution achieves 96% percent of success of any

transmission. This is an outstanding result but, as we say, it may be insufﬁcient in some

scenarios: we consider a scenario where a very large number of tags must be identiﬁed

as fast as possible. The optimal result that can be achieved is to identify a tag every

identiﬁcation cycle, which implies 100% of transmission success which would render a

linear identiﬁcation time.

The rest of this work is organized as follows: Section 2 describes the ISO-18000-7

standard for active RFID solutions. Section 3 discusses related works, with an em-

phasis on solutions for active RFID anti-collision protocols. Section 4 introduces the

CSMA/Multi-Stage mechanism, and describes how it can be adapted with minor modi-

ﬁcations to the ISO 18000-7 standard. Section 5 shows the performance evaluations of

CSMA/MS in comparison with CSMA/p

∗

, Sift and conventional FSA. Finally, Section

6 concludes this work.

2 ISO 18000-7

ISO 18000-7 [5] is the de facto global standard for active UHF RFID solutions. It de-

ﬁnes the Physical and the MAC layer requirements and the communication protocol for

active RFID systems communicating at 433 MHz. ISO 18000-7 was ratiﬁed in 2004,

and has undergone modiﬁcations in 2008 and 2009.

Fig.2. Anti-collision procedure of ISO/IEC 18000-7 (from [5].)

2.1 Anti-collision Procedure

The anti-collision algorithm deﬁned in ISO 18000-7 is based on a FSA procedure. Fig-

ure 2 illustrates the identiﬁcation sequence. The reader initiates the identiﬁcation proce-

dure sending a Wake-Up signal, which wakes up the N tags within its coverage range.

Tags move to idle mode, listening to the channel. Then, the reader initiates a collection

round by sending a Collection command, with two parameters:

– The time the reader will be listening to the channel, waiting for tag responses. The

standard denotes this parameter as Window Size (W

– The length of the tag responses (T

tag

), determined by the ﬁeld type in the Collection

command. Note that this parameter determines the type of tag response (e.g tag

identiﬁer ID or speciﬁc data).

After transmitting the Collection command, the reader senses carrier signals during

Windows Size time, waiting for tag responses. Every time the reader detects a tag re-

sponse, it processes the corresponding tag identiﬁer and inserted it into a buffer, called

sleep queue. After the collection round, the reader extracts the identiﬁers from the sleep

queue one by one and, for each identiﬁer, the reader transmits an unicast Sleep com-

mand (see Figure 2). When tags receive the Sleep command, they change to sleep mode

(saving energy mode) and do not participate in the next collections rounds. Afterwards,

the reader starts a new collection round, resuming the identiﬁcation process, which

eventually ﬁnishes after three consecutive collection rounds without reply.

In the identiﬁcation procedure, tags operate as follows: When they receive a Collec-

tion command, extract the value of Windows Size parameter (in seconds) and calculate

the number of slots (K) and the slot size (T

slot

). The latter is calculated as follows:

slot

= T

tag

+ T

pr oc

(1)

being T

proc

the time the reader needs to process the data received from a tag and

the time to be ready to listening to the following tag response. By default, the standard

sets T

proc

=2 ms. Once T

slot

is calculated, the tag uses it to calculate K as follows,

K =

slot

(2)

K is rounded up to the nearest integer.

The process continues with tags selecting a random slot (with uniform distribution)

to send their Response packet. Each tag controls when the slot selected starts by means

of an internal clock. Let us remark that carrier sensing is not performed in this procedure

although active tags implement this capability. When a slot selected by a determined

tag starts, this tag changes to transmit mode and sends its identiﬁer. After that, the tag

changes to receive mode and listens to the channel. If the tag is successfully identiﬁed,

it will receive a Sleep command to change to the sleep mode. Otherwise, tag will receive

a new Collection command, indicating a new slot starts.

The most extended operational mode in ISO-18000-7 is Fixed Windows Size pro-

cedure,where the reader uses the same W

in every collection round i. The general

formula to calculate W

is as follows:

i+1

= W

· 57.3 (3)

for i= 0,1,2,. . . , C. Note that C is the total number of collection rounds in a identi-

ﬁcation procedure. W

is deﬁned by the standard as the Windows Factor to adjust W

in every cycle. In Fixed Windows Size procedure, W

takes the same value for every

collision round i. The standard recommends to set W

i∈C

=1.

Fig.3. Collection command format (from [5]).

3 Related Work

There is a lack of scientiﬁc literature that speciﬁcally addresses the collision prob-

lem for active tags. The ISO 18000-7 standard [5] deals with it and proposes FSA

as an anti-collision protocol, suggesting a frame length adaption mechanism but with-

out specifying a particular one and leaving it open to the vendors. Some works suggest

improvements of ISO 18000-7 identiﬁcation procedure, such as in [10][11], where the

authors suggest new tags and readers designed to save energy, and compatible with the

standard. However, they do not propose any mechanism to improve the identiﬁcation

performance. In [12] the authors focus their proposal on the sleep round (see Figure

2), suggesting a mechanism to reduce the number of Sleep commands to exchange

between reader and tags. However, this procedure does not reduce the collisions. In

[13] it is proposed to modify the content of the Collection commands to improve the

performance. The reader, instead of sending the windows size value in the collection

command, sends the values of T

slot

and K, previously calculated by it. Hence, tags

only have to calculate the guard time T

proc

. This solution has some drawbacks: the

maximum K value is limited to 256 slots. Therefore, if the number of tags in coverage

(N) is higher than the maximum K (a likely condition due to the large communication

range of active devices), collisions will raise up and the number of collection rounds

will increase. Besides, the proposal forces tags to calculate T

proc

, though they do not

suggest any procedure to do it. Finally, [13] also suggests to use the variable window

size mechanism proposed in [14]. However, as we demonstrate in [15], it is not efﬁcient.

On the other hand, a typical active tag has the capabilities of an on-board micropro-

cessor and a sophisticated transceiver and may use Bluetooth or IEEE 802.11 protocols

or Wireless Sensor Networks (WSN) MAC protocols [9]. It is clear that these proto-

cols are designed with different requirements in mind and, at the moment, the cost of

these devices is still possibly too high. Therefore, it seems that the possible choices are:

very simple approaches also suitable for passive tags or very sophisticated proposals

designed for different purposes.

In [6] we propose the use of CSMA with the optimal probability distribution (p

∗

)

for the selection of CSMA contention micro-slots derived in [7].This distribution max-

imizes the probability of success when N stations become simultaneously backlogged,

but depends on the number of slots in use (K) and the number of nodes (N ) contending.

Since the latter is usually unknown (also in RFID), an approximation is also provided,

the Sift distribution, which not only keeps close to the optimal for a wide range of its

conﬁguration parameters but it is also scalable. The authors of reference [7] discuss

different applications in wireless sensor networks, but RFID is not mentioned. In this

paper we show that RFID is a major ﬁeld of application of this optimized distribution.

CSMA/p* and Sift [7] are probability distributions that optimize the probability

of success in a CSMA contention compared with the uniform distribution. In this pa-

per we discuss the key aspects of these distributions and make a new proposal: the

CSMA/Multi-stage protocol.

The key idea of CSMA/p* and Sift distributions is to unbalance the probability of

selecting a contention micro-slot, increasing the probability of selecting one of the last

ones available. Thus, transmission is successful when the the ﬁrst micro-slots are se-

lected by very few nodes with a higher probability. CSMA/p* is optimal, in the sense

that given K contention micro-slots, there is no other distribution that provides a higher

probability of success. However, it requires knowledge of the number of contenders.

Since usually this information is not available, it is not practical. Fortunately, the Sift

distribution approximates CSMA/p* without knowing number of contenders. It only

needs a parameter, M , that is the maximum number of contenders, and is the analog

of 802.11 maximum window size. Sift works very well, compared to the uniform dis-

tribution, and also has the desirable property it scales linearly as the maximum number

of contenders raises. That is, an exponential increase of the number of contenders only

need a linear increase of K, keeping the probability of success around 99%. In this pa-

per we propose the slotted multi-stage CSMA protocol, based on the Sift distribution,

but with an additional procedure that approximates the probability of success to 100%.

4 Slotted Multi-Stage Proposal

In this section we describe CSMA/MS algorithm. Before, the operation of CSMA-Sift

based is also introduced in depth since CSMA/MS uses also this distribution.

4.1 Sift Operation

The operation of the identiﬁcation protocol when using CSMA would be as follows:

after receiving a collection command from the reader all N tags listen to the channel for

a number of micro-slots chosen randomly from a set of K. If the channel remains idle

after the number of selected micro-slots, a node sends its ID. Otherwise, it withdraws

until the next collection command. If there is no collision, the reader sends an ACK-

Collection command, which indicates the node already identiﬁed and asks for more

IDs. The remaining nodes start the process again.

The probability of success π

(N) when N nodes select a contention micro-slot us-

ing probability distribution p, where p

is the probability each contender independently

picks slot r, is [7]:

(N) = N

K−1

s=1

(1 −

r=1

) (4)

k + k

k +1

... ... ... ...

N tags

21 K

stage 1 stage 2

poles in 1st stage

(to 2nd stage)

poles in 2nd stage

(to 3rd stage)

p(success) =

transmits data

Slot selection probability

Tags

stage G

poles in (G−1)th stage

(to Gth stage)

p(1 pole in stage G)

Fig.4. Slotted Multi Stage procedure.

Let us assume ﬁrst that the slots are chosen uniformly. In this case p

. Like

FSA, this procedure does not scale well either. In fact, its performance is worse and

together with the additional device complexity it may be one of the reasons why it has

never been proposed as an anti-collision procedure for RFID systems.

Besides, let us assume now the Sift distribution is used, which is an approximation

to the optimized distribution derived in reference [7]. In this case, p

−r

(1−α)α

1−α

for

r = 1 . . . K and α = M

−1

K−1

. M is a parameter of the Sift distribution, pre-conﬁgured

before deployment and representing the maximum number of contenders (as expected

by the designer). The results reveal [6] that the number of cycles increases almost lin-

early with the number of tags, unlike the exponential increment of FSA. Therefore, this

procedure scales well. In addition, by increasing the number of micro-slots the num-

ber of cycles tends to the minimum necessary (N cycles), but it implies increasing the

duration of a cycle and may be even counterproductive.

These results show that after choosing carefully the distribution for the contention

window CSMA becomes an scalable technique for the identiﬁcation of RFID tags. In

Section 5, the different proposals for active tags are compared and discussed.

4.2 CSMA/MS

CSMA Multi-Stage proposal is based on the idea of splitting the original contention

micro-slots (K) into G stages of respective lengths k

, k

, . . ., where k

+ k

+ ... +

=K, where tags are dropping from the contention process from one stage to the

following. The operation is as follows (see Figure 4):

– In the ﬁrst stage (of length k

), all tags select randomly (using an arbitrary distribu-

tion p) a micro-slot i, being i= 1,2,· · ·,k

. Note that one or more tags ‘win’ in this

stage selecting the same initial slot. Let us denote these tags as the poles of stage

#1. Remainder tags detects the medium busy and withdraw from contention. Note

that if the number of poles is greater than 1, a collision has taken place. Hopefully,

this collision is solved in next stage.

– In the second stage (of length k

) the poles of the ﬁrst stage contends again. Each

one select again a random micro-slot i, being i= k

+ 1, k

+ 2, · · · , k

+ k

, and

the same procedure of the ﬁrst stage takes place.

– This process continues until to stage G, where only the poles from stage M − 1

contend. In this case, if there is only one pole, or there is a single winner in this

stage, one tag can successfully transmits its identiﬁcation. Otherwise, a collision

takes place.

Let us remark that more than one tag may compete in consecutive slots since several

tags may select the same lowest slot (a collision event). Moreover, the overall collision

probability depends on the number of stages and its relative length, henceforth let us

denote CSMA/MS(k

+ · · · + k

) to the speciﬁc conﬁguration selected for the MS

protocol. Also note that at each stage, a micro-slot can be chosen with any arbitrary

distribution. We propose to use the Sift distribution since it is quasi-optimal for a single-

stage scenario. Therefore, in each stage, the Sift distribution is conﬁgured using two

parameters, the number of k

micro-slots in this stage, and the parameter M . In the ﬁrst

stage, M is the maximum number of contenders, as shown in [7], but in the following

ones the number of contenders that reach a stage i is a random variable N

i−1

, which

depends on the number of contenders that have reached the previous stage, and the

number of micro-slots of that stage. Usually, as we will be discuss in section 5, the

highest probability corresponds to a single tag reaching to the next stage. So in stages

2, · · · the Sift parameter M is set at 2 (note that Sift does not allow M=1).

4.3 Modiﬁed Anti-collision Algorithm

The adaptation of the mechanism proposed in the previous section the ISO 18000-7

involves minor modiﬁcations in the anti-collision algorithm of the current standard,

without adding extra hardware in readers or tags. The operational mode is as follows:

The reader transmits the Collection command indicating, not only the Windows Size,

but also the number of stage (s ∈ 1, 2, . . . , S). The latter is sent to the tags in the

reserved byte ﬁeld of Collection command (see Figure 3).

If s=1, tags in coverage which were not identiﬁed previously calculate the number

of contention micro-slots of that stage using the same procedure deﬁned by the stan-

dard and select one of them randomly using the Sift distribution. Each tag listens to

the channel (Carrier Sense) until the number of micro-slot chosen starts. If the channel

remains idle after the number of selected micro-slot, the tag sends its ID. If there is no

collision, the reader sends an command, which conﬁrms the tag has won the contention

and it can send its Data. After that, the reader asks for more IDs using a new Col-

lection command setting s=1 (see Figure 4). The tag identiﬁed changes to sleep mode

(saving energy mode) and the remaining tags start the process again. Otherwise, if two

or more tags select the same micro-slot, a collision occurs. Then, the procedure works

as follows:

– Colliding tags do not detect the collision because they were in transmitting mode.

Hence, they keep waiting for a reader response.

– Those tags listening the channel while the collision was happening, do not partici-

pate in the identiﬁcation process until they receive a new Collection command with

s=1.

– Reader, that has also detected the collision, send a new Collection command, indi-

cating a new Windows size and a new stage, s=2. Colliding tags receive the com-

mand and compete again.

Fig.5. Collection command with Data format (from [5]).

The contention procedure continues until the maximum s value conﬁgured in the

reader. If, after S stages no new tags are identiﬁed, the reader starts a new Collection

command, setting s=1, and provoking all tags in coverage not identiﬁed previously

compete again.

Note that the duration of each micro-slot (denoted as T

m−slot

) depends on the dura-

tion and accuracy of carrier sensing Clear Channel Assessment (CCA), which depends

on the technology, device and implementation [18]. There are many possibilities, but

we assume that devices use coherent CCA, that is, the channel is busy when the packet

preamble is detected. Thus, we set the micro-slot time as follows:

m−slot

= T

+ T

preamble

(5)

being (T

preamble

) the duration of the preamble and T

the time a tag needs to start

transmitting its identiﬁer. ISO 18000-7 ﬁxes T

preamble

=1 ms and T

=1 ms [5]. Hence,

m−slot

=2 ms can be considered a conservative value, since current devices can per-

form this task in less time [18].

Tags calculate the number of contention micro-slots K

m−slot

in every stage as fol-

lows,

m−slot



− T

tag

− T

proc

m−slot



(6)

As in the standard, W

and T

tag

values are extracted from Collection command. K

is rounded up to the nearest integer.

In summary, our proposal only involves the use of the reserved ﬁeld of the typical

Collection command (see Figure 3) and a slight modiﬁcation of the Collection with data

format command deﬁned by the standard (see Figure 5) to be used as ACK-Collection

command. Figure 6 shows how the Start Address and Number of Data bytes ﬁelds of

Collection with data format command are replaced by Tag ID ﬁeld.

Fig.6. ACK-Collection command.

5 Simulation Results

As stated in the previous section, CSMA/MS performance depends on the number of

stages and on their size. We evaluated the performance of different conﬁgurations by

means of Montecarlo methods using Matlab. For each point (conﬁguration) evaluated

100000 samples has been averaged. In addition, CSMA/MS has been compared with

CSMA/p

∗

, Sift and a uniform selection of slots in a single stage CSMA protocol. Let

us remark that the total available micro-slots does not change among these options,

only its distribution in different stages (for CSMA/MS) or the probability function used

to select the micro-slot. Of the different conﬁgurations possibilities of CSMA/MS the

conﬁguration (7+7+7+7) has been selected for these tests. Besides, for CSMA/MS the

parameter M is adjusted as explained in section 4. In this case, for the ﬁrst stage M =

250, and the following ones sets M = 2.

Figures 7 and 8 show the identiﬁcation success probability for each one of these op-

tions (note that 8 providesa zoom viewof 7). Clearly, conﬁguration CSMA/MS(7+7+7+7)

improves the success ratio, and sets it nearly optimal. Moreover, the uniform distribu-

tion is evidently disastrous.

0 50 100 150 200 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Number of tags

Probability of succes

CSMA/p*

Uniform distribution

SMS(14+14)

SMS(7+7+7+7)

Sift distribution

Fig.7. Identiﬁcation success probability.

Besides, Figure 9 shows the overall identiﬁcation delay (in time slots) as a function

of the number of initial contenders. CMSA/MS(7+7+7+7) improves Sift by a 15%,

and it is slightly better than CSMA/p

∗

(however let us remarks that CMSA/p

∗

can be

implemented in actual systems as discussed in the introduction).

Finally, Figure 10 shows the mass probability function of the random variable “num-

ber of contenders at stage i” for the different stages i = 1, · · · , 4. Note how the system

behaves as a ﬁlter, removing in each stage a signiﬁcant ratio of the tags contending,

increasing the probability of having a winner at the end.

50 100 150 200 250

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

Number of tags

Probability of succes

SMS(14+14)

CSMA/p*

Uniform distribution

SMS(7+7+7+7)

Sift distribution

Fig.8. Identiﬁcation success probability (zoom view).

50 100 150 200 250

100

150

200

250

300

350

Number of tags

Average time (timeslots)

CSMA/p*

SMS(14+14)

Uniform distribution

SMS(7+7+7+7)

Sift distribution

+15%

Fig.9. Identiﬁcation time.

2 4 6 8

0.2

0.4

0.6

0.8

Tags

mpf poles in 1st stage

2 4 6 8

0.2

0.4

0.6

0.8

Tags

mpf poles in 2nd stage

2 4 6 8

0.2

0.4

0.6

0.8

Tags

mpf poles in 3rd stage

2 4 6 8

0.2

0.4

0.6

0.8

Tags

4th stage: p(success) = p(1 tag)

Fig.10. Mass probability function for CSMA/MS(7+7+7+7).

6 Conclusions and Further Works

In this work we have demonstrated how a multi-stage strategy which uses CSMA-Sift

distribution at different contention windows improves the identiﬁcation delay of a pop-

ulation of tags. By means of simulation an evaluation was carried out for a 4-stage

conﬁguration with 7 micro-slots each, which outperforms FSA and uniformly selected

micro-slots CSMA. This distribution also improves a Sift distribution of 28 micro-slots,

yielding to a feasible MAC strategy. A discussion is also developed on how to seam-

lessly adapt our approach to ISO-18000-7 compliant systems.

Several question remain open: given a number of K micro-slots which are the op-

timal number of stages, and which slot distribution is optimal? which is the analytical

expression for the probability of success and for the identiﬁcation delay of a population

of N tags?.

Acknowledgements

This work has been supportedby project DEP2006-56158-C03-03/EQUI,funded by the

Spanish Ministerio de Educacion y Ciencia, projects TEC2007-67966-01/TCM (CON-

PARTE-1), TSI-020301-2008-16(ELISA)and TSI-020301-2008-2(PIRAmIDE), funded

by the Spanish Ministerio de Industria, Turismo y Comercio and is also developed

within the framework of ”Programa de Ayudas a Grupos de Excelencia de la Region

de Murcia”, funded by Fundacion Seneca, Agencia de Ciencia y Tecnologia de la Re-

gion de Murcia (Plan Regional de Ciencia y Tecnologia 2007/2010).

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