  Most existing works on random access for machine-type communication (MTC)
assume independent device activities. However, in several Internet-of-Things
(IoT) applications, device activities are driven by events and hence may be
correlated. This paper investigates the joint optimization of preamble
selection and access barring for correlated device activities. We adopt a
random access scheme with general random preamble selection parameterized by
the preamble selection distributions of all devices and an access barring
scheme parameterized by the access barring factor, to maximally exploit
correlated device activities for improving the average throughput. First, we
formulate the average throughput maximization problem with respect to the
preamble selection distributions and the access barring factor. It is a
challenging nonconvex problem. We characterize an optimality property of the
problem. Then, we develop two iterative algorithms to obtain a stationary point
and a low-complexity solution respectively by using the block coordinate
descend (BCD) method. Numerical results show that the two proposed solutions
achieve significant gains over existing schemes, demonstrating the significance
of exploiting correlation of device activities in improving the average
throughput. Numerical results also show that compared to the stationary point,
the low-complexity solution achieves a similar average throughput with much
lower computational complexity, demonstrating the effectiveness of the
low-complexity solution.
