As passive optical networks (PON) are increasingly deployed to provide high speed Internet access, it is important to understand their fundamental traffic capacity limits. The paper discusses performance models applicable to wavelength division multiplexing (WDM) EPONs and GPONs under the assumption that users access the fibre via optical network units equipped with tunable transmitters. The considered stochastic models are based on multiserver polling systems for which explicit analytical results are not known. A large system asymptotic, mean-field approximation is used to derive closed form solutions of these complex systems. Convergence of the mean field dynamics is proved in the case of a simple network configuration. Simulation results show that, for a realistic sized PON, the mean field approximation is accurate.