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Motivated by the proliferation of real-time applications in multimediacommunication systems, tactile Internet, and cyber-physical systems, supportingdelay-constrained traffic becomes critical for such systems. Indelay-constrained traffic, each packet has a hard deadline; when it is notdelivered before its deadline is up, it becomes useless and will be removedfrom the system. In this work, we focus on designing random access schemes fordelay-constrained wireless communications. We first investigate threeALOHA-based schemes and prove that the system timely throughput of all threeschemes under corresponding optimal transmission probabilities asymptoticallyconverges to $1/e$, same as the well-known throughput limit fordelay-unconstrained ALOHA systems. The fundamental reason why ALOHA-basedschemes cannot achieve asymptotical system timely throughput beyond $1/e$ isthat all active ALOHA stations access the channel with the same probability inany slot. To go beyond $1/e$, we propose a reinforcement-learning-based schemefor delay-constrained wireless communications, called RLRA-DC, under whichdifferent stations collaboratively attain different transmission probabilitiesby only interacting with the access point. Our numerical result shows that thesystem timely throughput of RLRA-DC can be as high as 0.8 for tens of stationsand can still reach 0.6 even for thousands of stations, much larger than $1/e$.

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