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This paper explores criticality-based real-time scheduling of neural-network-based machine inference pipelines in cyber-physical systems (CPS) to mitigate the effect of algorithmic priority inversion. We specifically focus on the perception subsystem, an important subsystem feeding other components (e.g., planning and control). In general, priority inversion occurs in real-time systems when computations that are of lower priority are performed together with or ahead of those that are of higher priority. In current machine perception software, significant priority inversion occurs because resource allocation to the underlying neural network models does not differentiate between critical and less critical data within a scene. To remedy this problem, in recent work, we proposed an architecture to partition the input data into regions of different criticality, then formulated a utility-based optimization problem to batch and schedule their processing in a manner that maximizes confidence in perception results, subject to criticality-based time constraints. This journal extension matures the work in several directions: (i) We extend confidence maximization to a generalized utility optimization formulation that accounts for criticality in the utility function itself, offering finer-grained control over resource allocation within the perception pipeline; (ii) we further instantiate and compare two different criticality metrics (distance-based and relative velocity-based) to understand their relative advantages; and (iii) we explore the limitations of the approach, specifically how inaccuracies in criticality-based attention cueing affect performance. All experiments are conducted on the NVIDIA Jetson AGX Xavier platform with a real-world driving dataset. [ABSTRACT FROM AUTHOR]