This paper presents a combinatorial model and approximation formulas to estimate the average number of successful and collided users for a one-shot random access in finite-user multichannel slotted ALOHA systems. The proposed model and approximation can be used to evaluate the performance of group paging for machine-type communication (MTC) in 3GPP LTE. Numerical results demonstrate the applicable range of the approximation formulas and the accuracy of the derived performance metrics.
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Wei et al. (2012) studied this question.
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