  In machine-type communication (MTC), a group of devices or sensors may need
to send their data packets with certain access delay limits for delay-sensitive
applications or real-time Internet-of-Things (IoT) applications. In this case,
2-step random access approaches would be preferable to 4-step random access
approaches that are employed for most MTC standards in cellular systems. While
2-step approaches are efficient in terms of access delay, their access delay is
still dependent on retransmission strategies. Thus, for a low access delay,
fast retrial that allows immediate re-transmissions can be employed as a
re-transmission strategy. In this paper, we study 2-step random access
approaches with fast retrial as a buffered multichannel ALOHA with fast
retrial, and derive an analytical way to obtain the quality-of-service (QoS)
exponent for the distribution of queue length so that key parameters can be
decided to meet QoS requirements in terms of access delay. Simulation results
confirm that the derived analytical approach can provide a good approximation
of QoS exponent.
