A Theoretical Framework for Random Access: Stability Regions and Transmission Control

As one of the two fundamental types of multiple access, random access has been widely adopted in various communication networks, and expected to play an increasingly central role owing to the rising popularity of Machine-to-Machine (M2M) communications. Despite decades of successful applications, the theory of random access has long been underdeveloped, with key fundamental issues unresolved. Among them, stability of random-access networks is the most long-standing one that has received continuous attention for almost half a century. The challenge lies in establishing an analytical framework where the coupled service processes of nodes' queues can be characterized. In this paper, by extending our previously proposed analytical framework from the symmetric scenario to the general one, we tackle three open questions: 1) How to characterize the coupled service rates of nodes? 2) How to determine the stability region of input rates, only within which the network can be stabilized? 3) For given input rates within the stability region, how to tune the transmission probabilities of nodes to stabilize the network? We demonstrate that the key to characterizing the coupled service rates lies in properly establishing and solving the fixed-point equations of steady-state probabilities of successful transmission of Head-of-Line (HOL) packets of nodes. For the stability region of input rates, which closely depends on the definition of stability, two types of stability, i.e., queue-stability and throughput-stability, are considered, and both stability regions are shown to be determined by the sufficient and necessary condition of the existence of positive real roots of the fixed-point equations. To characterize the operating regions of transmission probabilities, constraints need to be further developed to ensure that the network operates at the specific steady-state point. The analysis shows that to stabilize the network, the transmission probabilities of nodes can be tuned only based on their long-term traffic input rates. Although the main results are illustrated based on Aloha with Constant Backoff, discussions on how to incorporate a general backoff function and other features of random access are also presented.