Abstract
The deployment of machine-type communications (MTC) together with cellular networks has a great potential to create the ubiquitous Internet-of-Things environment. Nevertheless, the simultaneous activation of a large number of MTC devices (named UEs herein) is a situation difficult to manage at the evolved Node B (eNB). The knowledge of the joint probability distribution function (PDF) of the number of successful and collided access requests within a random access opportunity (RAO) is a crucial piece of information for contriving congestion control schemes. A closed-form expression and an efficient recursion to obtain this joint PDF are derived in this paper. Furthermore, we exploit this PDF to design estimators of the number of contending UEs in an RAO. Our numerical results validate the effectiveness of our recursive formulation and show that its computational cost is considerably lower than that of other related approaches. In addition, our estimators can be used by the eNBs to implement highly efficient congestion control methods.
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