A queue management method of an access network device includes receiving a packet, determining feasibility of a packet transmission within a delivery deadline allowed from a destination if the received packet is for real-time transmission, storing the packet in the transmission queue and transmitting the packet in sequential order of the storage when the packet transmission within the delivery deadline is feasible, and dropping the packet instead of storing the packet in the transmission queue when the packet transmission is determined infeasible. Accordingly, resources required for the packet transmission are saved.