Achieving 100% throughput in WDM-PON under the SUCCESS-HPON architecture

In this paper we study the tunable resources scheduling problem for WDM-PON under the Stanford University aCCESS-Hybrid WDM/TDM PON (SUCCESS-HPON) architecture, a next generation optical access network. In SUCCESS-HPON a few tunable transmitters and receivers at the OLT are shared by all the users for both downstream and upstream transmission using a centralized light sources approach. Each ONU is assigned a single wavelength for both downstream and upstream data transmission; for the latter, a continuous wave is provided by the OLT for the ONUs to amplitude-modulate upstream data onto it and send it back to the OLT. Through the use of novel scheduling algorithms, it is possible to provide service to all users in the network with just a few tunable transmitters and receivers, making the network very cost-efficient. The performance of these algorithms has been extensively studied through simulations. In this paper we attempt to prove 100% throughput guarantee on a particular scheduling algorithm. We show that the Maximum Weight Matching (MWM) algorithm for admissible traffic with the Strong Law of Large Numbers property is stable and can guarantee 100% throughput in a simplified model of SUCCESS-HPON. We derive this result by converting the scheduling problem under consideration to a generalization of the well-known crossbar input-queued switch scheduling problem, and then use a fluid model of a discrete time switch together with the extended Birkhoff-von Neumann (BvN) Decomposition Theorem. The MWM algorithm can be easily implemented on the SUCCESS-HPON architecture since the number of wavelengths, which determines the complexity of implementation of MWM algorithm, is usually small. This proof of MWM in SUCCESS-HPON is meaningful in that it suggests a practical scheduling algorithm with 100% throughput guarantee as well as determines a theoretical bound. As a byproduct of this research, we prove the extended BvN Decomposition Theorem, which may be useful in proving 100% throughput guarantee of MWM algorithm in resource scheduling (allocation) problems where certain number of users share the same kind of resources, for example, as in the case that K users are sharing N type-A resources and M type-B resources.