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This paper presents a study on resource control for autoscaling virtual radio access networks (RAN slices) in next-generation wireless networks. The dynamic instantiation and termination of on-demand RAN slices require efficient autoscaling of computational resources at the edge. Autoscaling involves vertical scaling (VS) and horizontal scaling (HS) to adapt resource allocation based on demand variations. However, the strict processing time requirements for RAN slices pose challenges when instantiating new containers. To address this issue, we propose removing resource limits from slice configuration and leveraging the decision-making capabilities of a centralized slicing controller. We introduce a resource control agent (RC) that determines resource limits as the number of computing resources packed into containers, aiming to minimize deployment costs while maintaining processing time below a threshold. The RAN slicing workload is modeled using the Low-Density Parity Check (LDPC) decoding algorithm, known for its stochastic demands. We formulate the problem as a variant of the stochastic bin packing problem (SBPP) to satisfy the random variations in radio workload. By employing chance-constrained programming, we approach the SBPP resource control (S-RC) problem. Our numerical evaluation demonstrates that S-RC maintains the processing time requirement with a higher probability compared to configuring RAN slices with predefined limits, although it introduces a 45% overall average cost overhead.