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Narrowband Internet of Things (NB-IoT) is a new cellular technology introduced by the third generation partnership (3GPP) providing low-power and wide-area coverage for IoT. In this paper, we consider the scenario that NB-IoT is deployed in an heterogeneous network and the quality of the direct link from the NB-IoT user equipment (TIE) to the serving base station (BS) cannot satisfy the quality of service requirement for transmission of vital sensing data. Thereupon, device-to-device (D2D) communication is adopted as a routing extension to NB-IoT systems, and thus, enables two-hop routes between NB-IoT TIE and the serving BS via a set of D2D relays. As the candidate TIE relays work in duty cycle to save energy, we derive a model to select a set of TIE relays and perform opportunistic D2D communication according to a working schedule. Two optimization problems are formulated aiming at achieving optimal …