Modeling of Time and Frequency Random Access Network and Throughput Capacity Analysis

In this paper, we model the random multi-user multi-channel access network by using the occupancy problem from probability theory, and we combine this with a network interference model in order to derive the achievable throughput capacity of such networks. Furthermore, we compare the randommulti-channel access with a cognitive radio systemin which the users are able to minimize the channels occupancy. Besides, we show that the sampling rate can be reduced under the Nyquist rate if the use of the spectrum resource is known at the gateway side. This scenario is referred as "cognitive radio" context. The mathematical developments and results are illustrated through various simulations results. The proposed model is particularly relevant in analyzing the performance of networks where the users are not synchronized neither in time nor in frequency as it is often the case in various Internet of Things (IoT) applications.