Concurrent data transmission from massive Machine Type Communications (MTC) devices makes the traffic pattern of MTC more bursty, which invalidates the commonly-used methodologies of traffic engineering for multichannel S-ALOHA under the assumption of homogeneous or compound Poisson process. By usage of the number of contending devices that transmit the j-th preamble at the i-th Random Access (RA) slot as state variable, an innovative iterative process with its simplified form is proposed to acquire the dynamic process of multichannel S-ALOHA. It reveals the direct relation between the number of contending devices that transmit the j-th preamble at the i-th RA slot and the newly arrived devices before i-th RA slot. It also presents an analytical way to compute the probability density function, cumulative density function and mean of access delay. Numerical results by the use of MTC traffic models proposed by 3GPP are conducted to validate the effectiveness of the proposed iterative process and its simplified form. These works provide engineers insights to design enhanced overload control mechanism for MTC applications.
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