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This article deals with the problem of bandwidth allocation in the upstream channel for Ethernet passive optical networks (EPONs). EPONs are an emerging access network technology that provides a low-cost solution for deploying optical access lines between a carrier's central office and a customer site. In particular, in this paper we evaluate a simple modification of the bandwidth allocation algorithm called multi point control protocol (MPCP). Simulations results, obtained using OPNET™ modeler, show that the modified algorithm outperform the original one in terms of maximum available bandwidth and packet wait time in upstream direction.