In this paper we consider an SS/TDMA system with

uplink beams and

downlink beams, where uplink beam

has bandwidth β
iand downlink beam

has bandwidth α
j. The maximum traffic which can be handled by the satellite (in any given time slot) is assumed to be

. Multiplexing and demuitiplexing are also assumed. An optimal time slot assignment algorithm to minimize the total transmission time for any given traffic demand matrix is proposed and analyzed. Other system configurations of interest are also discussed.