Our recent progress and results on optimal real-time resource allocation in phased array radar systems are reported. A previously proposed discrete resource allocation approach, the Quality of Service based Resource Allocation Model (Q-RAM), is analyzed and is observed to generate nonoptimal results. We identify the shortcomings of this method and first extend it using the Karush-Kuhn-Tucker (KKT) optimality conditions for the single resource type case. We obtain an algorithm that delivers a globally optimal solution. We later generalize this further for the multiple resource type case. The Q-RAM approach has its origins in the quality-of-service domain and is fundamentally limited to sampled cost functions. The availability of empirically obtained samples of convex tracking performance curves for phased array radar and the feasibility of continuous approximations to these samples lead our study to the consideration of well formulated alternative methods from the optimization literature belonging to the class of methods of feasible directions. In particular we successfully apply the gradient-projection algorithm for the more general multiple resource type case. Our experimental studies using simulated radar performance data (formulated as a calibration data set) show that superior performance can be obtained in achieving closeness to optimality, while also maintaining similar algorithm execution speeds. Performance can even be increased further if additional computational complexity can be tolerated. In particular improvements in closeness to optimality become significant for dense target scenarios with large number of targets.