Traffic capacity of large WDM passive optical networks

Abstract

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.

Stability of multi-server polling system with server limits

“…We omit the proof since it closely follows the proof of Proposition 3 in [1]. In this case, the polling system is stable if and only if ρ i < m i , for i = 1, .…”

“…Unlimited service policies The stability condition in the case of server limits and unlimited service policies can be readily derived using the same fluid limit arguments as in [1,5]. We omit the proof since it closely follows the proof of Proposition 3 in [1].…”

“…On the strength of this empirical evidence, we postulate the following. (1) holds where p i is the long run proportion of effective server visits to queue i. The (p i ) exist for all system loads.…”

“…However, for tractability reasons, it was necessary to assume a particular service policy: when any server visits a queue that already has a full complement of servers, one server is chosen at random and obliged to move to the next queue on its schedule. With the more natural policy considered here (i.e., no service hand over), simple stability conditions apply when there is unlimited gated or exhaustive service policies [1,5]. In [1], Antunes et al derived a mean field approximation for multi-server polling systems with server limits and limited service policies under the assumption that both the number of servers and the number of queues are large.…”

Vacation and Polling Models with Retrials

“…In queueing terms, this gives rise to multiserver polling models, each server representing a wavelength. We refer to [1] for the stability analysis of multiserver polling models, and to [2] for a mean field approximation of large passive optical networks. It would be very interesting to study multiserver polling models with the additional features of retrials and glue periods.…”