Connectivity of mobile linear networks with dynamic node population and delay constraint

The connectivity properties of a mobile linear network with high speed mobile nodes and strict delay constraint are investigated. A new mobility model is developed to represent the steady state node distribution, and it accurately captures the statistical properties of random node arrival, time-varying node speed, and the distinct behaviors of nodes following different traffic patterns.With the mobility model, the statistical properties of network connectivity are studied and identified. Unlike most previous works that do not consider the impacts of transmission latency, which is critical for real time applications, this paper identifies the quantitative relationship between network connectivity and delay constraint. The results are applicable to both delay constrained networks and delay tolerant networks. The connectivity analysis is performed with a novel geometry-assisted analytical method. Exact connectivity probability expressions are developed by using the volumes of a hypercube intersected by a hyperplane, and a hyperpyramid. The geometry-assisted analytical method significantly simplifies the connectivity analysis.