A Non-contagious Random Spread of Marketing Messages

In this paper we attempt to find a solution to the problem in the field of marketing communications of how to insure that a certain area will be sufficiently covered by the launching of items containing communication materials, when an immediate effect is required. It was found that it is possible to determine the necessary number of items for a given density of area coverage. The method comes from the theory of stochastic geometry and random tessellations. We give a mathematical formula based on two parameters; the first is the maximal distance between the resulting location of any launched item and any point on the area, and the second is the confidence probability. The model can be used in circumstances for which there exists an interest in communicating rapidly with a population segment located in a certain area in order to trigger immediate action.