## On the Optimal Identification of Tag Sets in Time-Constrained RFID Configurations
Variations of FSA are used for instance by ISO/IEC 18000-6C, ISO/IEC 18000-7 [2] and EPCGlobal Class 1 Gen 2 (EPC-C1G2) [3], used by most commercial passive and active RFID systems. Three different classes of scenarios of practical interest arise in RFID facilities, according to the way the tags behave in the reading areas:  
1. **Static scenario**: a group of tags enters the reading area and remains there until all of them have been successfully identified. Other tags do not enter during that time. As an example, let us think about a conveyor belt controlled by a reader: as long as the reader detects collisions, the conveyor is stopped. Once the reader does not detect tags contending, the conveyor belt runs again, allowing new tags to enter. The goal in the static scenario is usually to minimize the average identification time. A thorough evaluation of this case can be found in our previous paper [4]. 2. **Flow scenario**: tags are continuously entering and leaving the checking area, according to some scenario dynamics that defines the arrival process. For example, a conveyor belt continuously running with tags randomly scattered on it. In this case, some tags may leave the reader coverage area unidentified. Thus minimizing the average identification time (as in the prior case) should not be optimization goal--instead it is critical to minimize the probability of losing tags. This case has been evaluated in [5] and [6]. 3. **Mixed scenario**: in this case a group of tags enter the checking area and stay there only for a certain time (sojourn time). No more groups enter the checking area until the previous one has left. For example, consider a moving truck with tags grouped in boxes, which are uniformly spaced. Like in the flow scenario some tags may leave the reader coverage area unidentified. This is the case addressed in this paper. Our goal is to compute the minimum suitable sojourn time that guarantee that the percentage of groups correctly identified is above some level. In this paper, this level is termed Identification Confidence Level (ICL). To conduct the study of mixed scenarios a _Discrete Time Markov Chain_ (DTMC) is used to obtain the cumulative distribution function of the identification time of a group of tags of size \(N\). From it the ICL is computed as a function of the sojourn time. Moreover, based on the previous results, a splitting strategy of the tag set is considered. That is, given a number of tags \(N\) entering the checking area we seek to find which is the best size of subsets that minimizes the global duration of the identification process guaranteeing the ICL level. Overall, the results provided in this paper are useful to help manufacturers and system operators to improve the RFID system performance in mixed scenarios. Designers must rely on physical parameters to control the performance of the system, such as, conveyor belt speed, coverage range, _etc._ The usefulness of the results of this paper is twofold. First, given an ICL bound and a packet tag size \(N\) the minimum sojourn time is computed in Section 3 and from it the physical parameters of the facility (e.g., conveyor belt speed) can be determined. Second, if tags repackaging is possible the optimal packet size is derived from the results exposed in Section 5. Let us remark that the results derived are valid for any FSA protocol with fixed frame size. This includes most active and passive RFID standards used in logistic currently. The rest of the paper is organized as follows: a review of the related work is provided in Section 2. The analysis of mixed scenarios is addressed in Sections 3 and 4. Section 5 discusses the feasibility of a splitting strategy in the tag set. Finally, Section 6 points out the main conclusions of the work.