Towards a Fundamental Understanding of the Stability and Delay of Offline WDM EPONs

The fundamental stability limit and packet delay characteristics of offline scheduling, an elementary scheduling mechanism in recently proposed dynamic bandwidth allocation mechanisms for Ethernet passive optical networks (EPONs) with wavelength division multiplexing (WDM), are unknown. For Poisson packet traffic and gated grant sizing, we develop an analytical framework for characterizing the stability limit and packet delay of off-line scheduling in WDM EPONs. We consider two reporting strategies: immediate reporting, whereby the report is immediately attached to an upstream data transmission, and synchronized reporting, where all reports are sent at the end of a polling cycle. We find that our analytical framework correctly characterizes the stability limit and approximates the delay of (i) synchronized reporting with arbitrary traffic loading and (ii) immediate reporting with symmetric traffic loading (where the number of equally loaded ONUs is an integer multiple of the number of upstream channels). For immediate reporting with asymmetric traffic loading, we discover and analytically characterize multicycle upstream transmission patterns that may increase or decrease the stability limit from the limit for synchronized reporting. We complement the analysis and simulation for Poisson packet traffic with simulations for self-similar packet traffic and observe that self-similar traffic results in substantially higher delays at low to medium loads as well as slightly higher stability limits than Poisson traffic.