Abstract-Complex contemporary systems contain multiple applications, some which have firm real-time requirements while others do not. These applications are deployed on multi-core platforms with shared resources, such as processors, interconnect, and memories. However, resource sharing causes contention between sharing applications that must be resolved by a resource arbiter. Time-Division Multiplexing (TDM) is a commonly used arbiter, but it is challenging to configure such that the bandwidth and latency requirements of the real-time resource clients are satisfied, while minimizing their total allocation to improve the performance of non-real-time clients.This work addresses this problem by presenting an efficient TDM configuration methodology. The five main contributions are: 1) An analysis to derive a bandwidth and latency guarantee for a TDM schedule with arbitrary slot assignment, 2) A formulation of the TDM configuration problem and a proof that it is NP-hard, 3) An integer-linear programming model that optimally solves the configuration problem by exhaustively evaluating all possible TDM schedule sizes, 4) A heuristic method to choose candidate schedule sizes that substantially reduces computation time with only a slight decrease in efficiency, 5) An experimental evaluation of the methodology that examines its scalability and quantifies the trade-off between computation time and total allocation for the optimal and the heuristic algorithms. The approach is also demonstrated on a case study of a HD video and graphics processing system, where a memory controller is shared by a number of processing elements.