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.

he paper takes a real option approach to consider optimal capacity investment decisions under uncertainty. Besides the timing of the investment, the firm also has to decide on the capacity level. Concerning the production decision, we study a flexible and an inflexible scenario. The flexible firm can costlessly adjust production over time with the capacity level as the upper bound, while the inflexible firm fixes production at capacity level from the moment of investment onwards. We find that the flexible firm invests in higher capacity than the inflexible firm, where the capacity difference increases with uncertainty. For the flexible firm the initial occupation rate can be quite low, especially when investment costs are concave and the economic environment is uncertain. As to the timing of the investment there are two contrary effects. First, the flexible firm has an incentive to invest earlier, because flexibility raises the project value. Second, the flexible firm has an incentive to invest later, because costs are larger due to the higher capacity level. The latter effect dominates in highly uncertain economic environments.