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The next generation network employs virtualization to create on-demand virtual networks called network slices, ensuring different service categories meet their quality of service requirements. This, along with offloading schemes, requires small-scale data centers near radio base stations known as edge computing. These edge systems must effectively autoscale computing servers to handle fluctuating workloads. Radio access network (RAN) slicing involves containerized radio applications with compute-intensive functions at the physical and radio link control layers, imposing strict processing time requirements. To address delay-sensitive radio workloads, we propose a fine-grained autoscaling solution in the edge cloud. Our analytical approach dynamically tunes resource limits using stochastic decision processes to meet dynamic demands. Evaluations compare user-configured and soft-tuned resource limits, utilizing the Roofline model and Low Density Parity Check (LDPC) decoding algorithm for workload characterization. We establish processing time design constraints and discuss limitations and future research.