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We consider the rate allocation problem when two users (each one associated with one receiver) send packets through a symmetric broadcast channel. Under the assumption that the packet lengths are exponentially distributed, we establish the delay optimality of the Best User Highest Possible Rate (BUHPR) scheduling policy. Such a policy always allocate the whole possible rate to the non-empty queue serving the user with the minimum average packet length. Our analysis can be generalized to the symmetric multiuser broadcast channel.