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In this study, the problem of optimal resource allocation in real-time systems is studied. A recently proposed resource allocation approach called Q-RAM (Quality of Service based Resource Allocation Model) is investigated in detail. The goal of the Q-RAM based approaches is to minimize the execution speed in real-time systems while meeting resource constraints and maximizing total utility. Phased array radar system is an example of a system. In this system, multiple targets are tracked by the radar system simultaneously requiring processor and energy resources of the radar system. In the present study, first, the Q-RAM solution approach to the radar resource allocation problem with single resource type is extended to give a global optimal solution in all possible termination cases. For the case of multiple resource types, the Q-RAM approach can only generate near-optimal results. In this study, for the formulated radar resource allocation problem with multiple resource types, the Methods of Feasible Directions are considered as an alternative solution approach.