In this paper we consider an SS/TDMA system with M uplink beams, N downlink beams, and K connection points. We first assume that the downlink is a times faster than the uplink, and a simple time multiplexing scheme is employed. An optimal time slot assignment algorithm for any M, N, a, and K, 1≤K≤ min (M, αN), and for any traffic matrix is presented, where optimality means achieving the minimal possible total transmission time for the given traffic matrix. The number of switching matrices generated by the algorithm never exceeds MN + Kα + 1. Extensive simulation results on randomly generated matrices are carried out, showing that the average number of switching matrices generated is substantially lower than the upper bound. The case when the uplink is faster than the downlink is also considered. Copyright © 1981 by The Institute of Electrical and Electronics Engineers, Inc.