Along with the growing diversity and complexity of real-time embedded systems, it is becoming common that different types of tasks, periodic tasks and aperiodic tasks, reside in a system. In such systems, it is important that schedulability of periodic tasks is maintained and at the same time response times to aperiodic requests are short enough. Total Bandwidth Server (TBS) is one of convincing task scheduling algorithms for mixed task sets of periodic and aperiodic tasks. This paper proposes a method of using predictive execution times instead of worst-case execution times for deadline calculations in TBS to obtain shorter deadlines and reducing response times of aperiodic execution, while maintaining the schedulability of periodic tasks. From the evaluation by simulation, the proposed method combined with a resource reclaiming technique exhibits better average response times for aperiodic tasks, in case of a heavy load, by up to 39%.