first exploit a sample average approximate (SAA) technique and an alternating direction method of multipliers (ADMM) to tackle the indeterministic objective function and the two timescale issue. Then, a semidefinite relaxation (SDR) scheme joint with a Taylor expansion scheme are leveraged to approximate the non-convex problem as a convex one. The tightness of the SDR scheme and the error bound of the Taylor expansion are also analyzed.

The remaining of this paper is organized as follows. We review the prior arts in Section II. In Section III, we describe our system model and formulate the service multiplexing problem in Section IV. The problem-mitigating algorithm is presented in Sections V and VI. In Section VII, we give the simulation results and conclude this paper in Section VIII.

Prior arts
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Recently, many researches have been conducted to increase RA success probabilities and/or reduce the access delay of mIoT devices. They can be generally classified into two groups: traffic detection and estimation based algorithms and algorithms without traffic detection and estimation.

The fundamental idea of the traffic detection and estimation based algorithms is to design an RA algorithm based on the detected and/or estimated users’ activity and traffic congestion situation and so 