Analysis of the number of hops in wired-wireless heterogeneous networks

As more and more wireless communication scenarios, such as Internet of Things and 4G wireless networks, rely on the deployment of wireline networks, the analysis of the heterogeneous wired-wireless networks becomes critical. In this paper, the probability mass function (PMF) of the number of hops in heterogeneous wired and wireless networks is analyzed. The nodes are assumed to be spatially distributed following Poisson point process (PPP). The wireless links are formed by considering the spatial distances, and the wired links are randomly deployed. To derive the PMF of the number of hops, we first approximate the number of hops between any two nodes in the wireless-link-only network as a function of the Euclidean distance. Then one wired link is added and the PMF of the number of hops is derived. Finally, the analysis is generalized to the heterogeneous network with multiple wired links. Simulation results confirm the accuracy of our proposed approach.