Method to model vehicular communication networks as random geometric graphs

A method for generating a mathematical model including analysis results of a vehicular communications network using a computer including a non-transitory computer readable storage medium encoded with a computer program embodied therein, comprising:

• defining a vehicular communications network including a plurality of vehicles using the computer program;
• defining a plurality of communication nodes communicating with the plurality of vehicles;
• defining features of the vehicular communications network, including:
• geographic locations;
• mobility features;
• and communication features;
• generating a geographical model, a mobility model, and a communication model of the vehicular communications network using the computer program;
• generating a spatial distribution of the plurality of vehicles defining locations in relation to time of the plurality of vehicles in the vehicular communications network;
• calculating a probable radius of location for each of the plurality of communications nodes;
• defining a radius parameter for each of the plurality of vehicles such that each of the plurality of vehicles communicates within the radius parameter;
• calculating a probability that two edges of the probable radiuses intersect using the spatial distribution, such that a distance between the communication nodes is smaller than the radius parameter;
• generating a mathematical model of the vehicular communications network;
• generating a random geometric graph with a plurality of parameters;
• and
• displaying the random geometric graph on a display.

A computer program product comprising a non-transitory computer readable medium having recorded thereon a computer program, a computer system including a processor for executing the steps of the computer program for generating a mathematical model, the program steps comprising:

• defining features of a vehicular network, the features including:
• a
• graph of a street map within a geographic area;
• a number of vehicles within the geographic area;
• specified conditions for vehicles to communicate;
• and a driving distribution pattern of the vehicles;
• generating a random graph with a plurality of parameters;
• defining a plurality of communications protocols on the vehicular network;
• redefining a communication protocol over the random graph;
• analyzing a communication protocol's basic properties and associated features on the random graph;
• generating results of the analysis;
• translating the results of the analysis based on the random graph's parameters into results based on the vehicular network features;
• and
• displaying the random graph with the parameters, the parameters including:
• a number of graph nodes, a probability that any two nodes are communicably connected being expressed as a function of the vehicular network features.