Analysis of Cognition Completion Time in RFID Networks Supported by Static Naive MAC Scheme

We consider an RFID network that consists of a single reader and multiple tags sojourning in the vicinity of the reader. In such an RFID network, collisions occur among the packets which are simultaneously sent by two or more tags. In order to support the reader to cognize tags while resolving the collision problem, we consider a static naive MAC scheme that employs a collision arbitration method rooted in framed slotted ALOHA. A basic mission of a reader in an RFID network is to cognize every neighboring tag in a prescribed time. Thus, it is of necessity to analyze the cognition completion time, e.g., the time elapsed until the reader cognized all the tags. In this paper, we first mathematically describe the cognition completion time as a hitting time of a homogeneous non-decreasing Markov chain on a finite state space. Next, we construct a fast converging Markov chain on the same state space by using a sequence of random variables that have stochastic dominance. Finally, we propose a numerically efficient method in which the cognition completion time is approximated by a hitting time of the fast converging Markov chain. Numerical examples confirm that the approximate expected value of the cognition completion time provides a lower bound on the exact expected value.