Random Access Delay Distribution of Multichannel Slotted ALOHA With Its Applications for Machine Type Communications

An innovative iterative process is proposed to acquire the dynamic process of multichannel slotted ALOHA (S-ALOHA). It reveals the direct relation between the number of contending devices that perform their jth random access (RA) attempt at the ith RA slot and the newly arrived devices before the ith RA slot. These results allow engineers to analytically derive the probability density function of RA delay of multichannel S-ALOHA, as well as its cumulative density function and average value. Under stable RA attempts assumption, simplified form of the above analysis is given, with which we prove the number of preamble transmissions follows truncated geometric distribution. Taking the two traffic models proposed for machine type communications as examples, numerical results are presented to verify the effectiveness of the proposed iterative process and the accuracy of its simplified form, and illustrate the delay characteristics of simplified long term evolution RA channel.