A function model for the description of distributed end-to-end computations is called a task graph. Multiple functions with different criticality levels are supported by one electronic control unit (ECU), and one function is distributed over multiple ECUs in integrated automotive architecture. Considering the inherent heterogeneity, interaction, and diverse nature of such an architecture, automotive embedded systems have evolved to automotive cyber-physical systems (ACPS), which consist of multiple distributed automotive functions with different criticality levels. Efficient scheduling strategies can fully utilize ECUs in ACPS for high performance. However, ACPS should deal with joint challenges of heterogeneity, dynamics, parallelism, safety, and criticality, and these challenges are the key issues that will be solved in the next generation automotive open system architecture adaptive platform. This study first proposes a fairness-based dynamic scheduling algorithm FDS_MIMF to minimize the individual makespans (i.e., schedule lengths) of functions from a high performance perspective. FDS_MIMF can respond autonomously to the joint challenges of heterogeneity, dynamics, and parallelism of ACPS. To further respond autonomously to the joint challenges of heterogeneity, dynamics, parallelism, safety, and criticality of ACPS, we present an adaptive dynamic scheduling algorithm ADS_MIMF to achieve low deadline miss ratios (DMRs) of safety-critical functions from a timing constraint perspective while maintaining the acceptable overall makespan of ACPS from a high performance perspective. ADS_MIMF is implemented by changing up and down the criticality level of ACPS to adjust the execution of different functions on different criticality levels without increasing the time complexity. Experimental results indicate that FDS_MIMF can obtain short overall makespan, whereas ADS_MIMF can reduce the DMR values of high-criticality functions while still keeping satisfactory performance of ACPS.