We introduce PONs (Passive Optical Networks), which are designed to provide high speed access to users via fiber links. The problem for the OLT (Optical Line Terminal) is to share dynamically the wavelength bandwidth among the ONUs (Optical Network Units). For that, with an optimal algorithm, the system can be modeled as a relatively standard polling system. Due to technological constraints, in the polling system, the number of servers which visit one queue at the same time is limited. The performance of the system is directly related to the stability condition of the polling model. It is unknown in general. A mean field approach provides a limit stability condition when the system gets large.