Triple Pattern Fragments (TPFs) are a novel interface for accessing data in knowledge graphs on the web. Up to this date, work on performance evaluation and optimization has focused mainly on SPARQL query execution over TPF servers. However, in order to devise querying techniques that efficiently access large knowledge graphs via TPFs, we need to identify and understand the variables that influence the performance of TPF servers on a fine-grained level. In this work, we assess the performance of TPFs by measuring the response time for different requests and analyze how the requests' properties, as well as the TPF server configuration, may impact the performance. For this purpose, we developed the Triple Pattern Fragment Profiler to determine the performance of TPF server. The resource is openly available at https://github.com/Lars-H/tpf_profiler. To this end, we conduct an empirical study over four real-world knowledge graphs in different server environments and configurations. As part of our analysis, we provide an extensive evaluation of the results and focus on the impact of the variables: triple pattern type, answer cardinality, page size, backend and the environment type on the response time. The results suggest that all variables impact on the measured response time and allow for deriving suggestions for TPF server configurations and query optimization.