We consider two end users which have asymmetric traffic requirements in terms of both data rate and outage probability. They exchange information in Rayleigh flat-fading channels, and a half-duplex relay node is employed to assist the bidirectional communication between them, using the analog network coding (ANC) protocol. The provision of power levels for each node is investigated so as to minimize the total energy consumed to satisfy the asymmetric traffic requirements. By comparing energy consumptions between ANC strategy and direct transmission strategy, the relay operating region is also identified in which relay-assisted transmission can yield higher energy efficiency than direct transmission. It also indicates that the relay node is best positioned at the middle point of the two end nodes for any asymmetric traffic requirements from the perspective of energy consumption minimization.