On scaling limit of a cost in adhoc network model

Abstract

We are interested in giving a mathematical formula of a cost in adhoc network model. In our model, the cost is formulated as an application of first-passage percolation and the motion of devices is random, and an asymptotic density of devices is formulated by hydrodynamic limit. Under some technical assumptions, we give asymptotics of a cost in adhoc network model. In order to formulate this model, we extend the results of first-passage percolation given by Howard Newman [3] to that in inhomogeneous environments.