In recent years, machine learning has achieved remarkable success in the fields of computer vision, natural language processing and speech recognition. Since these architectures have become quite large with millions of trainable parameters, applying machine learning models such as Transformers on resource-constrained devices has been quite difficult. While inference strategies like early exiting and split computing have been analyzed in detail, there is a lack of scientific work regarding a combination of both methods. In this thesis, we introduce the Split-EE-Transformer, an Vision Transformer architecture with early exits at intermediate layers and split computing to distribute the neural network between the edge device and a cloud server. We analyzed three different exit placements in the neural network and used a UCB algorithm to decide the splitting point in the architecture dynamically and evaluated the results based on accuracy and computational cost. The combination of both inference strategies should allow an effective use of Vision Transformers in resource-constrained environment, e.g. smartphones and IoT devices.