Stability of Asynchronous ALOHA System

The authors consider a pure ALOHA system involving random multiple access of packets to a shared channel with feedback. A new mathematical model of the system is proposed; it is free from a number of the restrictive assumptions that were made in [N. Abramson, IEEE Trans. Commun., 1977, vol. 25, no. 1, pp. 117–128; L. Kleinrock, Queuing Systems, Vol. 2, Wiley, New York, 1976; M. J. Ferguson, Proc. 4th Data Commun. Symp., Quebec, Canada, 1975, pp. 5.20–5.25; D. Sant, IEEE Trans. Commun., 1980, vol. 28, no. 8, pp. 1422–1425]. The stability conditions for a pure ALOHA system are obtained. The transmission rate is optimized in the case of single stations.