Efficient time slot assignment algorithms for TDM hierarchical and non-hierarchical switching systems

Two efficient heuristic time slot assignment (TSA) algorithms, called the 2-Phase algorithm for the non-hierarchical and the 3-Phase algorithm for the hierarchical TDM switching systems, are proposed. Their time complexities are O(LN²) and O(LM²) respectively, where L is the frame length, N is the switch size and M is the number of input/output sources connected to a hierarchical TDM switch. The simple idea behind these two algorithms is to schedule the traffic on the critical lines/trunks of a traffic matrix first. Extensive simulations reveal that the two proposed algorithms are very efficient. For non-hierarchical TDM switching systems, P_F the probability that the 2-Phase algorithm failed to generate optimal TSAs is found to be 3×10^-5 and independent of switch size. For hierarchical switching systems, the percentage increase in frame length as a result of non-optimal TSA by the 3-Phase algorithm is about 0.1%. That means on the average only one extra time slot is required for a frame of 1000 time slots