Centralized control functions for the IEEE802.11 family of WLAN standards are vital for the distribution of traffic with stringent Quality of Service (QoS) requirements. These centralized control functions overlay a time-based organizational "super-frame" structure on the medium, allocating part of the super-frame to polling traffic and part to contending traffic. This allocation directly determines how well the two forms of traffic are supported. Given the vital role of this allocation in the success of a system, we must have confidence in the configuration used, beyond that provided by empirical simulation results. Formal mathematical methods are a means to conduct rigorous analysis that will permit us such confidence, and the Petri-net formalism offers an intuitive representation with formal semantics. We present an extended Petri-net model of the super-frame, and use this model to assess the performance of different super-frame configurations and the effects of different traffic patterns. We believe that using such a model to analyze performance in this manner is new in itself.