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The increasing applications of networking have caused limitation of dynamic bandwidth allocation (DBA) in next generation access networks such as Ethernet passive optical network (EPON). In this paper, Arishtat, a novel EPON-based DBA method has been proposed that shows advantages over currently available methods. In Arishtat, which is based on the auction theory, optical line terminal runs an auction-based process to effectively register optical network units bandwidth requests and allocates the highest bidders based on the amount of available bandwidth. Simulation results indicate significant improvements comparing to Fair sharing using dual-service-level agreements, and `limited service` interleaved polling with adaptive cycle time methods regarding quality of service parameters such as packet loss, throughput, line utilisation and the execution time of running method.