In the last years, new paradigms for network softwarization based on the adoption of cloud computing are evolving. Additionally, with the 5th generation of mobile networks enormous benefits for service providers and private persons arise. Scalability of services by segmentation into components helps cloud providers to monitor and analyze their services. Services to be provided to 5G network users are divided into independent components and instantiated in remote clouds or at the edge network. The service itself is assembled from the components to a so-called service chain. To understand the total performance, key influence factors for each component have to be examined. To analyze these factors, analytical models by means of task graph reduction can be used. In this work, each component is described by a task graph node and a processing time distribution. Out of all nodes, a task graph is created and reduced receiving one probability density function, characterizing the performance of the whole service chain. Finally, an example use case for cloud based video streaming on a 5G network is analyzed with the developed tool.