Stability Analysis of Frame Slotted Aloha Protocol

TL;DR

This paper analyzes the stability of the Frame Slotted Aloha protocol in RFID systems by modeling backlog as a Markov chain, deriving stability conditions, and examining behavior in unstable regions.

Contribution

It provides the first comprehensive stability analysis of FSA considering both single and multipacket reception models, with explicit stability conditions.

Findings

Stability region maximized when frame length equals backlog size in single packet model.

Stability region related to maximum multipacket reception capacity in multipacket model.

Backlog Markov chain is transient in the instability region.

Abstract

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 characterisation 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 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 maximised when the frame length equals the backlog size in the single packet reception model and when the ratio of the backlog size to frame length equals in order of magnitude the maximum multipacket reception capacity in the multipacket reception model. Furthermore, to characterise system behavior in the instability region, we mathematically demonstrate the existence of transience of the backlog Markov chain.