An Optimal Algorithm for Time-Slot Assignment in SS/TDMA Satellite Systems

Packet scheduling in switches plays an important role in providing guaranteed service to meet Quality-of-Service (QoS) requirements. In this paper, we revisit a historical Maximum Traffic Time-slot Scheduling (MTTS) problem for both circuit- and packet-switched traffic in SS/TDMA satellite systems proposed two decades ago by Bonuccelli et al.. They developed a two-step approach to solve the MTTS problem, which scheduled the circuit-switched traffic first into TDMA frames and then inserted packets from packet-switched traffic into empty slots in these scheduled TDMA frames as many as possible. This problem was referred as Incremental Time-slot Assignment (ITSA) Problem in their paper, and was proved to be NP-hard. Therefore, MTTS problem seems to be NP-hard due the the NP-hardness of ITSA problem induced by their two-step approach. However, in this paper, we show that MTTS problem is NOT NP-hard, since there exists an optimal algorithm for this problem. By aggregating the traffic in scheduled TDMA frames, an optimal algorithm based on network flow method is developed for MTTS problem, which can solve the MTTS problem in polynomial time. Theoretic proof for the optimality of our algorithm is given and simulations results further validate the correctness of our algorithm.