Leveraging virtualization technology, Cloud-RAN deploys multiple virtual Base Band Units (vBBUs) along with collocated applications on the same Mobile Edge Computing (MEC) server. However, the performance of real-time (RT) applications such as the vBBU could potentially be impacted by sharing computing resources with collocated workloads. To address this challenge, this paper presents a dynamic CPU sharing mechanism, specifically designed for containerized virtualization in MEC servers, that hosts both RT and non-RT general-purpose applications. Initially, the CPU sharing problem in MEC servers is formulated as a Mixed-Integer Programming (MIP). Then, we present an algorithmic solution that breaks down the MIP into simpler subproblems that are then solved using efficient, constant factor heuristics. We assessed the performance of this mechanism against instances of a commercial solver. Further, via a small-scale testbed, we assessed various CPU sharing mechanisms and their effectiveness in reducing the impact of CPU sharing on RT application processing performance. Our findings indicate that our CPU sharing mechanism reduces the worst-case execution time by more than 150% compared to the default host RT-Kernel approach. This evidence is strengthened when evaluating this mechanism within Cloud-RAN, in which vBBUs share resources with collocated applications on a MEC server. Using our CPU sharing approach, the vBBU's scheduling latency decreases by up to 21% in comparison with the host RT-Kernel.