The dynamic nature of ad hoc wireless networks means that connections are continually made and broken due to user mobility. This mobility of devices, for example modelled by the random waypoint mobility (RWPM) model, can induce an inhomogeneous distribution of nodes, which in turn can cause nodes to become disconnected from the network. Motivated by Penrose’s result that the main obstacle for full connectivity in random geometric graphs (dim > 1) are isolated nodes, we first explore the cellular network setting where mobile users aim to connect to their closest base station. Within this context, regions of high node density can lead to isolated nodes due to increased levels of interference. By modelling users via a Poisson Point Process (PPP) with non-uniform intensity measure and analysing the connection probability of these mobile devices, we can identify under what conditions spatial densification of cellular networks can bring about increased network performance.

More generally, it remains an interesting problem to ask how these network inhomogeneities and boundaries affect the number of isolated nodes. By using a non-uniform PPP to model nodes within the network and employing a, more general, soft connection function (a link is realised between two nodes with a probability based on their Euclidean separation), we explore the connectivity of these temporal networks where the node density vanishes at the boundary.

This is joint work with Carl Dettmann and Woon Hau Chin. This work is supported by EPSRC grant EP/N002458/1 and Pete Pratt is partially supported by an EPSRC Doctoral Training Account. We would also like to thank the directors of the Toshiba Telecommunications Research Laboratory for their support.