  Accommodating the needs of a large number of diverse users in the Internet of
Things (IoT), notably managing how the users access the common channel, has
posed unique challenges to the network designers. In this paper, we study a
heterogeneous IoT network consisting of multiple classes of users who may have
different service requirements. For this network, we consider the application
of irregular repetition slotted ALOHA (IRSA) that is shown to offer large
throughput for single-class networks. Then, we focus on finding the network
performance boundaries by studying the set of feasible throughput values for
each class, called the capacity region. To this end, we first introduce the
concept of dual network of a multi-class network meaning a homogeneous network
with the same number of users. We then prove that finding the capacity region
of the assumed multi-class network boils down to finding the maximum achievable
throughput of its dual network. Using this finding, we then discuss how any
given point of the capacity region can be achieved. Further, a delay
performance study is conducted to evaluate the average and maximum packet
transmission delay experienced by the users of each class.
