Evaluation of hop-distance relationship for quasi-UDG model in wireless sensor networks

This paper presents an analytical method to evaluate the hop-distance relationship for quasi-UDG (Unit Disk Graph) model in wireless sensor network, where sensor nodes are randomly and independently deployed in a circular region by a Poisson process. Different from the UDG model, quasi-UDG model has the non-uniformity property for connectivity. We derive an approximate recursive expression of the probability of the hop count by a given geographic distance. The border effects and dependence problem are also taken into consideration. Furthermore, we give the expressions about the distribution of distance by a known hop count for inner nodes and those suffered from the border effects. The simulation results show that the analytical expressions can closely agree with the statistical data and the border effects cannot be ignored.