Connectivity Analysis of Mobile Linear Networks with Delay Constraint

The connectivity properties of a mobile linear network with high speed mobile nodes, dynamic node population, and a strict delay constraint are investigated. A new mobility model is developed to represent the steady state node distributions in terms of random node location and random node population. The model 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 new 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 by placing a bound on the maximum transmission distance. 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. Results presented in this paper provide insight on the design and operations of mobile linear networks, such as a vehicular ad hoc network (VANET) that has rapidly changing network topology and node density.