Stability Analysis of Frame Slotted Aloha Protocol

Frame Slotted Aloha (FSA) protocol has been widely applied in Radio Frequency Identification (RFID) systems as the
de facto
standard in tag identification. However, very limited work has been done on the stability of FSA despite its fundamental importance both on the theoretical characterization of FSA performance and its effective operation in practical systems. In order to bridge this gap, we devote this paper to investigating the stability properties of
$p$
-persistent FSA by focusing on two physical layer models of practical importance, the models with single packet reception and multipacket reception capabilities. Technically, we model the FSA system backlog as a Markov chain with its states being backlog size at the beginning of each frame. The objective is to analyze the ergodicity of the Markov chain and demonstrate its properties in different regions, particularly the instability region. By employing drift analysis, we obtain the closed-form conditions for the stability of FSA and show that the stability region is maximized when the frame length equals the number of packets to be sent in the single packet reception model and the upper bound of stability region is maximized when the ratio of the number of packets to be sent to frame length equals in an order of magnitude the maximum multipacket reception capacity in the multipacket reception model. Furthermore, to characterize system behavior in the instability region, we mathematically demonstrate the existence of transience of the backlog Markov chain. Finally, the analytical results are validated by the numerical experiments.