The Story of $1/e$: ALOHA-based and Reinforcement-Learning-based Random Access for Delay-Constrained Communications

Motivated by the proliferation of real-time applications in multimedia communication systems, tactile Internet, networked controlled systems, and cyber-physical systems, supporting delay-constrained traffic becomes critical for such systems. In delay-constrained traffic, each packet has a hard deadline; when it is not delivered before its deadline is up, it becomes useless and will be removed from the system. In this work, we focus on designing the random access schemes for delay-constrained wireless communications. We first investigate three ALOHA-based random access schemes and prove that the system timely throughput of all three schemes under corresponding optimal transmission probabilities asymptotically converges to $1/e$, same as the well-know throughput limit for delay-unconstrained ALOHA systems. The fundamental reason why ALOHA-based schemes cannot achieve asymptotical system timely throughput beyond $1/e$ is that all active ALOHA stations access the channel with the same probability in any slot. Therefore, to go beyond $1/e$, we have to differentiate active stations' transmission probabilities to reduce the competition level. However, since all stations work in a distributed manner without any coordination, we should deploy the same policy (i.e., same piece of codes in practice) to all stations under which they will automatically differentiate their transmission probabilities. Toward that end, we propose a Reinforcement-Learning-based Random Access scheme for Delay-Constrained communications, called RLRA-DC, under which different stations collaboratively attain different transmission probabilities by only interacting with the access point. Our numerical result shows that the system timely throughput of RLRA-DC can be as high as 0.8 for tens of stations and can still reach 0.6 even for thousands of stations, much larger than $1/e$.