Spatial Point Process Modeling of Vehicles in Large and Small Cities

The uncertainty in the locations of vehicles on streets induced by vehicles passing and queueing make the spatial modeling of vehicles a difficult task. To analyze the performance of vehicle-to-vehicle (V2V) communication for vehicular ad hoc networks (VANETs), accurate spatial modeling is of great importance. In this paper, we concentrate on spatial point process modeling for random vehicle locations in large and small cities, performing empirical experiments with real location data of mobile taxi trajectories recorded by the global positioning system (GPS) in Beijing city of China and Porto city of Portugal. We find that the empirical probability mass functions (PMFs) of the number of taxis in test sets in different regions of Beijing or in Porto all follow a negative binomial (NB) distribution. Based on the above, we show that the Log Gaussian Cox Process (LGCP) model, whose empirical PMF nicely fits the NB distribution, accurately characterizes diverse spatial point patterns of random vehicle location in both large and small cities. This is verified by the minimum contrast method. The LGCP model can be applied to analyze performance metrics (i.e., connectivity, coverage, and capacity) and optimize the practical deployments of VANETs.