Abstract Cloud computing technology provides the means to share physical resources among multiple users and data center tenants by exposing them as virtual resources. There is a strong industrial drive to use similar technology and concepts to provide timing sensitive services. One such domain is a chain of connected virtual network functions. This allows the capacity of each function to be scaled up and down by adding or removing virtual resources. In this work, we develop a model of such service chain and pose the dynamic allocation of resources as an optimization problem. We design and present a set of strategies to allow virtual network nodes to be controlled in an optimal fashion subject to latency and buffer constraints. Furthermore, we derive a feedback-law for dynamically adjusting the amount of resources given to each functions in order to ensure that the system remains in the desired state even if there are modeling errors or for a stochastic input.