Constructing deliberative real-time AI systems is challenging due to the high execution-time variance in AI algorithms and the requirement of worst-case bounds for hard real-time guarantees, often resulting in poor use of system resources. Using a motivating case study, the general problem of resource usage maximization is addressed. We approach the issues by employing a hybrid task model for anytime algorithms, which is supported by recent advances in fixed priority scheduling for imprecise computation. In particular, with a novel scheduling scheme based on Dual Priority Scheduling, hard tasks are guaranteed by schedulability analysis and scheduled in favor of optional and anytime components which are executed whenever possible for enhancing system utility. Simulation studies show satisfactory performance on the case study with the application of the scheduling scheme. We also suggest how aperiodic tasks can be scheduled effectively within the framework and how tasks can be prioritized based on their utilities by an efficient algorithm. These works form a comprehensive package of scheduling model, analysis, and algorithms based on fixed priority scheduling, providing a versatile platform where real-time AI applications can be suitably facilitated.