For many cyber-physical systems, e.g., IoT systems and autonomous vehicles, offloading workload to auxiliary processing units has become crucial. However, since this approach highly depends on network connectivity and responsiveness, typically only non-critical tasks are offloaded, which have less strict timing requirements than critical tasks. In this work, we provide two protocols allowing to offload critical and non-critical tasks likewise, while providing different service levels for non-critical tasks in the event of an unsuccessful offloading operation, depending on the respective system requirements. We analyze the worst-case timing behavior of the local cyber-physical system and, based on these analyses, we provide a sufficient schedulability test for each of the proposed protocols. In the course of comprehensive experiments, we show that our protocols have reasonable acceptance ratios under the provided schedulability tests. Moreover, we demonstrate that the system behavior under our proposed protocols is strongly dependent on probability of unsuccessful offloading operations, the percentage of critical tasks in the system, and the amount of offloaded workload.