Toward a Coherent Theory of CSMA and Aloha

Aloha and Carrier Sense Multiple Access (CSMA) are two representative random-access protocols. Despite their simplicity in concept, the performance analysis of Aloha and CSMA networks has long been known as notoriously difficult. Numerous models and analytical approaches have been proposed in the past four decades. Yet how to integrate them into a coherent theory remains an open challenge. Toward this end, a unified analytical framework was recently proposed in [33], based on which a comprehensive study of throughput, delay and stability performance of Aloha networks was presented. In this paper, the framework is further extended to CSMA networks. The analysis shows that both CSMA and Aloha have the same bi-stable property, and the performance of both networks critically depends on the selection of backoff parameters. Different from Aloha, however, substantial gains can be achieved in CSMA networks by reducing the mini-slot length a and the collision-detection time x. The maximum throughput with CSMA is derived as an explicit function of a and x, and shown to be higher than that with Aloha if a < e(1/e) - 1 approximate to 0.445. With a small mini-slot length a, CSMA networks are also found to be more robust than Aloha networks thanks to larger stable regions of backoff parameters. To demonstrate how to properly tune the backoff parameters to stabilize the network, the complete stable region of the initial transmission probability q(0) is characterized, and illustrated via the example of p-persistent CSMA with the cutoff phase K = 0. The optimal values of q(0) to maximize the network throughput and to minimize the first and second moments of access delay are also obtained, which shed important light on practical network control and optimization.