Beamforming, user scheduling and transmit power on existing interference management schemes in multi-cell mmWave networks have been independently controlled due to the high computational complexity of the problem. In this paper, we formulate a long-term utility maximization problem where beam activation, user scheduling and transmit power are incorporated in a single framework. To develop a low-complex algorithm, we first leverage the Lyapunov optimization framework to transform the original long-term problem into a series of slot-by-slot problems. Since the computational complexity to optimally solve the slot-by-slot problem is even significantly high like existing schemes, we decompose the problem into two different time scales: (i) a subproblem to find beam activation probability with a long time-scale and (ii) a subproblem to find user scheduling and power allocation with a short time-scale. Moreover, we introduce two additional gimmicks to more simplify the problem: (i) sequentially making decisions of beam activation, user scheduling, and power allocation, and (ii) considering a critical user for power allocation. Finally, via extensive simulations, we find that the proposed CRIM algorithm outperforms existing algorithms by up to 47.4% in terms of utility.
