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Different from existing MOT (Multi-Object Tracking) techniques that usually aim at improving tracking accuracy and average FPS, real-time systems such as autonomous vehicles necessitate new requirements of MOT under limited computing resources: (R1) guarantee of timely execution and (R2) high tracking accuracy. In this paper, we propose RT-MOT, a novel system design for multiple MOT tasks, which addresses R1 and R2. Focusing on multiple choices of a workload pair of detection and association, which are two main components of the tracking-by-detection approach for MOT, we tailor a measure of object confidence for RT-MOT and develop how to estimate the measure for the next frame of each MOT task. By utilizing the estimation, we make it possible to predict tracking accuracy variation according to different workload pairs to be applied to the next frame of an MOT task. Next, we develop a novel confidence-aware real-time scheduling framework, which offers an offline timing guarantee for a set of MOT tasks based on non-preemptive fixed-priority scheduling with the smallest workload pair. At run-time, the framework checks the feasibility of a priority-inversion associated with a larger workload pair, which does not compromise the timing guarantee of every task, and then chooses a feasible scenario that yields the largest tracking accuracy improvement based on the proposed prediction. Our experiment results demonstrate that RT-MOT significantly improves overall tracking accuracy by up to 1.5x, compared to existing popular tracking-by-detection approaches, while guaranteeing timely execution of all MOT tasks.