| Summary: | Abstract The MAC (medium access control) of CSMA (carrier sense multiple access) is widely used in distributed wireless networks with random node locations. In CSMA MAC, two nodes that are within the range of one another cannot transmit packets simultaneously. Modeling the concurrently transmitting nodes is crucial for the performance analysis of the CSMA networks. In this paper, we study the density of concurrently transmitting nodes and propose another modification of classical hard core point process to accurately estimate the density of concurrently transmitting nodes, in the absence and in the presence of fading conditions. The MMHCP model we propose outperforms the popular Matérn type II model and the existing modified hard core point (MHCP) process model by avoiding the underestimation and alleviating the overestimation issues, respectively. We conduct extensive numerical analysis and simulations to evaluate the accuracy of our MMHCP model. Furthermore, we study the impact of the density of initial Poisson Point Process (PPP) and fading factor on the mean probability of successful reception and on the transmission capacity of networks from numerical analysis and simulations.
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