Connectivity analysis of one-dimensional ad-hoc networks

Application and communication protocols in dynamic ad-hoc networks are exposed to physical limitations imposed by the connectivity relations that result from mobility. Motivated by vehicular freeway scenarios, this paper analyzes a number of important connectivity metrics for instantaneous snapshots of stochastic geographic movement patterns: (1) The single-hop connectivity number, corresponding to the number of single-hop neighbors of a mobile node; (2) the multi-hop connectivity number, expressing the number of nodes reachable via multi-hop paths of arbitrary hop-count; (3) the connectivity distance, expressing the geographic distance that a message can be propagated in the network on multi-hop paths; (4) the connectivity hops, which corresponds to the number of hops that are necessary to reach all nodes in the connected network. The paper develops analytic expressions for the distributions and moments of these random variables for general stationary MAP processes on a one dimensional space. The numerical results compare bursty vehicular traffic with independent movement scenarios described by a Poisson process, illustrate in examples the impact of a random communication range, and demonstrate the usefulness of MAP processes via comparison with vehicular simulation traces.