Online control of random access with splitting

For slotted random access systems, the slotted ALOHA protocol provides the maximum throughput of 0.368 (packets/slot) while in the category of splitting (or tree) algorithms, the maximum achievable throughput can reach up to 0.487 with the first-come first-serve (FCFS) algorithm. It has been so far demonstrated that the FCFS algorithm can achieve this maximum throughput only for Poisson traffic. This may limit its application in practical systems, where packet arrivals may not be Poissonian. In this paper, we propose a novel online transmission control framework that introduces random splitting upon collisions and controls the transmission probabilities optimally at each slot by estimating the number of active users in the system. The proposed algorithm is said to be online as it estimates the number of active users slot by slot recursively, and thus can adapt to network dynamics. We first show that the splitting algorithm of our interest can achieve the throughput of 0.532 if the number of users involved in a collision could be known, which serves as a guideline for the upper limit for the random access systems with splitting. Then, when the information on the number of collided users is not available, we show that the proposed algorithm can achieve the maximum throughput of 0.487 for Poisson arrivals while achieving shorter access delay than FCFS. When more bursty traffic than Poisson process is applied, the proposed algorithm shows much better throughput and delay performance than FCFS.