Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach

In this paper we analyze connectivity issues in one-dimensional ad hoc networks. Starting with a deterministic channel model, we show how an equivalent GI|D|(infinity) queueing model may be used to address network connectivity. In this way, we obtain exact results for the coverage probability, the node isolation probability and the connectivity distance for various node placement statistics. We then show how a GI|G|(infinity) model may be used to study broadcast percolation problems in ad hoc networks with general node placement in the presence of fading channels. In particular, we obtain explicit results for the case of nodes distributed according to a Poisson distribution operating in a fading/shadowing environment. In the latter case, heavy traffic theorems are applied to derive the critical transmission power for connectivity and broadcast percolation distance in highly dense networks. The impact of signal processing schemes able to exploit the diversity provided by small-scale fading by means of multiple antennas is considered. The analysis is then extended to the case of unreliable ad hoc networks, with an in-depth discussion of asymptotic results.