This work seeks to support the validation of large eddy simulation models used to simulate fire suppression. The emphasis in the present study is on the prediction of flame extinction and the prevention of spurious reignition using a fast chemistry, mixing-controlled combustion model applicable to realistic fire scenarios of engineering interest. The configuration provides a buoyant, turbulent methane diffusion flame within a controlled co-flowing oxidizer. The oxidizer allows for the supply of a mixture of air and nitrogen, including conditions for which oxygen-dilution in the oxidizer leads to flame extinction. Measurements to support model validation include local profiles of thermocouple temperature and oxygen mole fraction, global combustion efficiency, and the limiting oxygen index. The present study evaluates the performance of critical-flame-temperature-based extinction and reignition models using the Fire Dynamics Simulator, an open-source fire dynamics solver. Alternate model cases are explored, each offering a unique treatment of extinction and reignition. Comparisons between simulated results and experimental measurements are used to evaluate the capability of these models to accurately describe flame extinction. Of the considered cases, those that include provisions to prevent spurious reignition show excellent agreement with measured data, whereas a baseline case lacking explicit reignition treatment fails to predict extinction.