Connectivity in Mobile Device-to-Device Networks in Urban Environments

Chase–escape in dynamic device-to-device networks

“…Controlling the long-range dependencies, we prove results on survival and extinction of malware in certain parameter regimes, and in particular again feature a phenomenon of in-and-out of survival with respect to the speed parameter. In the second set of results we complement these findings and present similar results in hybrid models in which the infection and patching processes are defined as an independent process on top of the (static) percolation model from [11].…”

“…On the other hand, let us mention Cox-percolation results [24,25,29], where the underlying point cloud is a Poisson point process with a random intensity measure that can, for example, be used to model urban environments such as street systems. Going further in this direction, in [11] sub-and supercritical regimes of percolation are established in a static spatial random graph model where the edge-drawing mechanism is designed to reflect realistic features of a connectivity network of moving devices in an urban environment. In brief, any pair of devices given by a Cox point process in which the environment is a planar random segment process is connected by an edge if and only if, on their path through the environment, they spend enough time on the same segment in sufficiently close proximity.…”

“…We present two sets of results for chase-escape dynamics on supercritical percolation models in the continuum. In the first set of results we use the construction of [11], as mentioned above, and consider a system of moving particles in an environment of line segments in R 2 . However, we now go substantially beyond the setup in [11] and not only consider the resulting connectivity graph but introduce a chase-escape dynamics that respects the mobility and connectivity behavior of the network components; see Section 1.1 for further discussions.…”

“…In the first set of results we use the construction of [11], as mentioned above, and consider a system of moving particles in an environment of line segments in R 2 . However, we now go substantially beyond the setup in [11] and not only consider the resulting connectivity graph but introduce a chase-escape dynamics that respects the mobility and connectivity behavior of the network components; see Section 1.1 for further discussions. Controlling the long-range dependencies, we prove results on survival and extinction of malware in certain parameter regimes, and in particular again feature a phenomenon of in-and-out of survival with respect to the speed parameter.…”

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We feature results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in Cali et al (2022), we consider an urban environment, represented by line segments in the plane, in which agents move according to a random waypoint model based on a Poisson point process. Whenever two agents are at sufficiently close proximity for a sufficiently long time the infection can be transmitted and then propagates into the system according to the same rule starting from a typical device.

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