On the Capacity Region of ALOHA Protocol for the Internet of Things
  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. 
Moslem Noori and Samira Rahimian and Masoud Ardakani
cs.NI cs.IT math.IT