Network utility maximization (NUM) models have been successfully applied to address multiple resource- allocation problems in communication networks. This paper explores, for the first time to our knowledge, their application to modeling the bandwidth-allocation problem in passive optical networks (PONs) and long-reach PONs. Using the NUM model, we propose the FEx-DBA (fair excess-dynamic bandwidth allocation) algorithm, a new DBA scheme to allow a fair and efficient allocation of the upstream channel capacity. The NUM framework provides the mathematical support to formally define the fairness concept in the resource allocation and the guidelines to devise FEx-DBA. A simulation study is conducted, whereby FEx-DBA is compared to a state-of-the-art proposal. We show that FEx-DBA (i) provides bandwidth guarantees to the users according to the service level agreement (SLA) contracted and fairly distributes the excess bandwidths among them; (ii) has a stable response and fast convergence when traffic or SLAs change, avoiding the oscillations appearing in other proposals; (iii) improves average delay and jitter measures; and (iv) only depends on a reduced set of parameters, which can be easily tuned.
