The k-SIC (successive interference cancellation) technology can support at most k parallel transmissions, and thus fast media access can be provided, which is vital for real-time industrial wireless networks. However, it suffers from high power consumption because high interference caused by parallel transmissions has to be overcome. In this paper, given the real-time performance requirements, we consider a network supporting k-SIC, and study how to minimize aggregate power consumptions of user equipments for uplink transmissions by jointly addressing power allocation and user scheduling. We show that the problem is solvable in polynomial time in the case of continuous transmit powers by an algorithm with complexity of O(nlog(n)), where n is the number of user equipments. In the case of discrete transmit powers, the problem is shown to be polynomially solvable for 2-SIC, and we also propose an approximation algorithm for k-SIC where k > 2. Experimental evaluations reveal that the real-time performances have tremendous impacts on both the aggregate power consumption and the maximum of the transmit powers of user equipments. Besides, the usability of SIC in low-power applications is also shown by experimental evaluations.