## On the Optimal Identification of Tag Sets in Time-Constrained RFID Configurations  
**[PERSON] \({}^{\star}\), [PERSON], [PERSON], [PERSON] and [PERSON]**  
Department of Information Technologies and Communications, Technical University of Cartagena,  
Plaza del Hospital 1, 30202 Cartagena, Spain; E-Mails: [EMAIL_ADDRESS] (M.V.B.D. );  
[EMAIL_ADDRESS] (E.E.L. ); [EMAIL_ADDRESS] (J.J.A. );  
[PERSON])  
\({}^{\star}\) Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS];  
Tel. : +34-968-326588; Fax: +34-968-325973. Received: 25 January 2011; in revised form: 1 March 2011 / Accepted: 2 March 2011 /  
_Published: 4 March 2011_  
**Abstract:** In Radio Frequency Identification facilities the identification delay of a set of tags is mainly caused by the random access nature of the reading protocol, yielding a random identification time of the set of tags. In this paper, the cumulative distribution function of the identification time is evaluated using a discrete time Markov chain for single-set time-constrained passive RFID systems, namely those ones where a single group of tags is assumed to be in the reading area and only for a bounded time (sojourn time) before leaving. In these scenarios some tags in a set may leave the reader coverage area unidentified. The probability of this event is obtained from the cumulative distribution function of the identification time as a function of the sojourn time. This result provides a suitable criterion to minimize the probability of losing tags. Besides, an identification strategy based on splitting the set of tags in smaller subsets is also considered. Results demonstrate that there are optimal splitting configurations that reduce the overall identification time while keeping the same probability of losing tags. **Keywords:** RFID; anti-collision protocols; time-constrained configuration; identification time; tag loss probability Introduction  
Radio Frequency IDentification (RFID) enables the identification of nearby objects or people by means of Radio-Frequency (RF) signals. The communication takes place between small and inexpensive devices called _tags_ which are attached to the items to be tracked, and _readers_ which collect and manage information about these items. This process is performed in the coverage area of the reader, or checking area. RFID is increasingly being used to identify and track objects in supply chains and manufacturing process [1]. These scenarios consider a large number of tags attached to items which pass through checking areas, usually carried in sets by conveyor belts, pallets, lorries, _etc_. According to the power supply of the tags, RFID systems are classified as active or passive. The former are used in applications which typically require to sense the environment (e.g., Wireless Sensor Networks). The latter are the most extended in logistic facilities due to their low cost. In passive systems, RFID readers continuously emit electromagnetic waves creating _reading areas_. Passing tags are thereby energized allowing them to send their identifiers back to the reader. Since the communication between tags and reader use a shared wireless channel, when multiple tags reply simultaneously to a reader, a collision occurs. Therefore, to avoid it, an anti-collision protocol is necessary, and readers implement them. Framed-slotted Aloha (FSA) is one of the most widely used anti-collision protocol by passive RFID systems [1]. As in Slotted-Aloha, time is divided into periods called slots, but all slots are confined to a super-structure called \"frame\". The reader starts an interrogation frame by sending a _Query_ packet informing the tags about the frame length \(K\) (the number of slots that make a frame). At every frame, each unidentified tag randomly selects a slot among the \(K\) slots to send its identifiers to the reader. When more than a single tag select the same slot in the frame, a collision occurs, and the reader is not able to recover the identifier of the tags involved in the collision.